Sunday, December 20, 2009

Part 3

Going Deep in an Online PLO8 Tournament, Part 3 – Catastrophe Play, Shorthanded Play, and Why Play plo8 at all?

By Dan “FNJ” Wolcott

For part 3, I had originally planned to take you hand for hand through a series of short-handed and low M battles. However, I realized as soon as I put together a draft, that this made the article almost as exciting as the 1040 short form for tax filing.

So instead, I’ll switch things up. I’ll talk about PLO8 MTTs in general, look at a catastrophe hand, offer some general principles for low M play at a full table, and then walk through some Low M decisions.

Why PLO8 MTTs?

As grown up with a mortgage and a day job, I do not have as many opportunities to play MTTs as the average 20 year-old, but I certainly enjoy dedicating an evening to duking it out with the good players, the naked aggression players, and the blessed fools who make these PLO8 MTTs profitable. I have a strong feeling that 10% of the field is actually drunk and playing completely for entertainment purposes in any given tournament, and that 40% of the field makes very poor post-flop decisions.

At the risk of eliminating the suspense, I will confess that I ultimately win this tournament. But winning a single PLO8 MTT is meaningless. I have seen any number of holy fools take down tournaments through naked aggression in combination with being rewarded for making awful decisions. I assert that of all the current popular variants of poker, PLO8 is the one that provides more opportunities for the unskilled to ‘luckbox’ their way out of tight situations, and find scoops when 90% of the possible outcomes lead them to a chop or a loss.

So why bother with this variant at all, since it is clearly a field full of land mines and a guaranteed tilt factory? Precisely because these MTTs are currently populated with a tremendous amount of players who make awful decisions. If you are able to get all your chips in the middle with a favorable chance of scooping against these unskilled players, you can work your chipstack into something that will take you to the final table. Granted, the holy fools have you outnumbered in most tournaments, but you only need to put your money in good a handful of times to amass a stack that could take you to the final table. Better still, if you survive to the final table, your skill advantage will give you a much better chance to cash out higher than those who habitually push QQT4 rainbow from under the gun at a full table.

For the Hold’em tournament players, let me contrast this with your game of choice. In an NLHE tournament, you will occasionally get your chips in the middle with your opponent drawing dead, but more often you will get your chips in the middle in situations where you are the 70/30 favorite, but if your opponent hits, you will lose the contents of the pot, conceivably your entire chipstack. In a PLO8 tournament, you can often get your chips in the middle when you have a lock on ½ of the pot, and you have a decent number of scoop or ¾ outs for a freeroll. When playing against the unskilled, wouldn’t you prefer to lock down half the pot?


Meanwhile, back at the Tournament

We are back from the 2nd break, and we are still waiting for the bubble. As you will see from the hand play to come, this will be a good time to discuss play in Harrington’s ‘Red-Zone’, and how the split-pot aspect of this game affects the zone concepts. I do not have statistical or mathematical proof of my assertions on zone play, and I hope that this starting point generates some productive debate on the two plus two discussion forum.

Hand Play

Level 9 – Hand 120 – Blinds go up to 150/300. There are 29 players remaining, and payouts begin with 12th place.

Level 10 (Hand 130) Blinds go to 200/400, and I was quiet for the whole 9th level, except for an abortive steal attempt that I abandoned at the flop. My M is less than 8. I should steal when I can, and not be too afraid of coin-flips.

Hand 130 – I steal from the button w/J♣4♠5♣6♦ and the SB and BB fold.

In a tournament, you should always be on the lookout for good stealing opportunities. In a split pot game, you should always be happy to walk away with the blinds, even when you have a very strong hand, because even the mighty A23K double-suited is only a 60/40 favorite against the top 70% hand range.

In this particular case, I had a read that SB and BB would have a tight defending range and that fold equity would make this a profitable play. If either of them play back at me, this is a reasonably coordinated hand with some strength in each direction.
• If there is a defense with AWhh, this hand is a 58/43 dog, but J456 is actually the favorite to make a low if villain only has two low cards, thanks to counterfeiting.
• If either villain has an AAxx hand, it is a virtual coin flip, unless the X is a 5 or better. AA3h is only a 61/39 favorite here.
• If either of the villains is inclined to defend too lightly, this hand is virtually a coin flip (53/47) against the top 70-80% of O8 hands and it is a favorite for the low.

Hand 142 – 4♦ A♦ Q♥ A♠ Small Blind (200/400) Chips 4768 (raise to 1200)

No limpers, and an obvious steal hand. Big Blind has 3,879 after posting, and calls the 800.
lop A♣ K♦ Q♣ (pot = 2400; bet 2400 and call a reraise for 679 more)

This is a good news/bad news flop. I am extremely likely to be ahead, since villain has a 7.5% chance of having a JT combination in any random hand, and if villain does turn over JT, I still have redraws to a full house. I cannot give a free card to any drawing hand, such as combinations of flush, straight and backdoor low draws, so I must take my chances that villain does not have JT.

Villain turns over Q♦ J♥ T♣ 4♠ and I am now a big underdog.

Turn/River 6♥7♠ and I now have less than one big blind left, 489 chips.

It is worth commenting on villain’s play here. Villain paid an additional 800 to see a flop, with implied odds of 3079 chips behind. As you can see, this gamble worked out very well for the villain. If either of us had less chips in play, this would not be a great move on villain’s part.

Now that I am in the Red Zone, this is a good time to talk about the concept of zones as discussed in the Harrington/Robertie NLHE tournament books.
Yellow Zone Guidelines

Arbitrarily, let us call 2M to 5M the yellow zone. The split pot element makes the distinction between green and yellow very fuzzy. In fact, I would go as far as to assert that the concept of zones barely even applies to the PLO8 game, except perhaps for the red zone, which is somewhere below 2M.

But here are some guidelines for suggested ‘book’ play in the speculative yellow zone.

• Continue generally tight from early position.
• Be ready to open raise from late position with any hand that is capable of making a low, or any hand with significant high-card strength.
• Get involved in multi-way raised pots with A2Wx
• Defend your Big Blind with a wider range when facing a raiser for heads-up, especially late position raisers.
• Do not defend your Big Blind with junk when there is a raise with one or more callers.
• If you have a read that SB and BB are tight, open-steal with any garbage hand that is not hopeless in either direction. (See hand 130 above.)

You should (sensibly) gamble more in the yellow zone than you do in the green zone. If nothing else, it will make your tablemates hesitant to steal your big blind.

Red Zone Guidelines

Arbitrarily, let us call anything below 2M the Red Zone.

Just as cockroaches can be tough to kill, short stacks can be tough to eliminate. Here are some ‘roaching’ tips.

• If there is an early position raise and you think the blinds are likely to fold, often call with random junk that can make a low, especially with two wheel cards and a third ‘emergency low’ card. With 2M or less, chopping the blinds with an aggressive player pushing AAxx, A2xx or worse is a very good proposition.
• Open raise from early or middle position with WWLX or better
• Open-raise from late position with a very wide range of hands that can make a low
• Virtually never fold your Big Blind pre-flop in a heads-up situation, even when you cannot make a low
• Push any random junk from the Small Blind to open.

Probability states that we will get a hand that contains either AAxx or AWxx about 20% of the time. This means that there is a 75% chance that we will find an AWxx combination to push, if we have six hands before the blinds. If we find nothing playable in those six hands, we are mostly obligated to play a ‘flippament’ in the big blind and begin the selection process over again if we are lucky enough to survive.

Low M Play in Practice

My stack is 489, and blinds are 200/400. It may seem as if I am the walking dead here, but I try not despair, but pick my spots and give myself the best chance to recover. On the bright side here, I have eight hands to choose from before I must put in my chips involuntarily. Also, the tournament is pre-bubble, so the table may be more cautious in general.

Hand 143 – Fold 5♠ 6♥ T♣ 8♠ on the button after a raise and a caller. This is a hand I would be willing to put in heads-up against AAxx or A2xx with the hope of chopping the blinds, but with two players in, my chances at the low are presumably negligible, and my high possibilities with this hand are also negligible.

Blinds have gone up to 300/600, which means I am now below 1M.

Hand 144 – Open call 9♠ 6♦ 7♠ T♦ from the cutoff. This hand has a plausible but poor low, but it is very coordinated for the high, despite the lack of broadway cards.
There are three callers, the final board is 4♣ 3♣ 8♦ 3♦ 2♦ and the weak backdoor flush is good for half of the four way pot. My chipstack is now 978, or 1.5M

Hand 145 - fold T♣ 7♣ K♣ 6♠ after an early raiser with four players yet to act behind me. While this hand has some play heads-up, it will be a huge underdog if any of the four remaining players get involved.

Hands 146-149
Open-fold 6♦ 5♦ 8♣ 9♠ with five players to act.
Open-fold 8♦ 2♦ T♦ 5♦ - with six players to act.
Open-fold 8♣ A♦ T♠ 9♣ - with six players to act.
Open fold 2♣ 9♥ K♥ 4♥ - with seven players to act.

Note that any of these hands would have been playable for a heads up confrontation, but from early position they become folds for the same reason as hands 143 and 145.


Hand 150 – Call a raise for heads-up from BB with 5♠ J♠ 7♥ A♦. I am very fortunate to find an ace-wheel combination. Of course, with 978 chips, the only hands I could have folded here involve trips. I make a broadway straight for a double up against 6♣ 9♦ 6♦ A♠.

My chipstack is now 2256, or 2M. This gives me enough to be picky for at least the next six hands, and in some circumstances, I may even choose to fold my next big blind.

Hand 151 – Open raise from the Small Blind with 9♣ A♥ A♠ 9♦

A no-brainer push results in a chop with T♦ 4♥ 9♠ 3♠. No change to stack (2256).

Hands 152-154
Fold J♣ 6♣ 3♥ T♣ after one limper
Open-fold T♥ 8♦ 6♥ 7♠

This hand has a similar shape to hand 144, but since I have more than 2M, I am playing ‘yellow zone’ which makes this a fold.

Fold 8♠ 2♦ K♠ 9♦ after one raise.
Open-fold K♠6♣6♦3♦

Hand 155 – Open Push A♦9♠2♣5♥ with seven players behind, and there is one caller. This hand is acceptable for heads up or multi-way play from any position with a very low M, since it has a reasonable chance of making top pair heads up, and it has a very decent chance to make the best low in a multi-way pot.

Happily, my one caller holds 2♣3♣4♣6♥ and my Ace-high is good enough for a scoop when neither of us make a pair or a low. I more than double up to 5412, or 4.5M.

Another player is eliminated to spare me the agony of surrendering a big blind, so I get to fold my small blind for 400, and fold hands 156 and 157.

Hand 158 I double up again with A♦A♥6♣9♠ and my stack is now 11,224, a little more than 9M and I am arguably in the green zone.

Summary

The moral of the story is that even with a walking-dead chipstack, you always have some chance of coming back in a split-pot game. If you pick your spots wisely and get a little cooperation from the deck, you may just find a double-up or two and work your way back into the hunt.

Tuesday, June 02, 2009

Article 2

Originally Published in twoplustwo.com on-line magazine. All rights revert to the author 3 months after publishing.

Going Deep in an Online PLO8 Tournament, Part 2 – Middle Stage Play

Abbreviations used in this article.

MP = Middle Pair (6-8);
HP = High Pair (9-K)
WW = Two distinct wheel cards, e.g. 2, 3, 4, 5
X, Y = any card distinct from the cards stipulated
L=6,7,8
H=9-K

Early Middle Stage Play

After the first break, the tournament begins to show more diversity in stack sizes. You need to be aware of situations where pot-odds dictate a call with marginal hands and marginal draws, and you will need to be careful that you are not stealing with weak hands in situations where small stacks will be pushing any reasonable hand. Beginning at the 100/200 level, the blinds are now becoming big enough to merit raising with marginal hands against the right opponents.

Raising/Stealing Ranges – Pre-Bubble

While blind steals are very much dependent upon stack size and opponent tendencies, I will classify some hand ranges and my opinion of them. I do not have hard data to support my assertions, and I expect that other successful PLO8 tournament players will disagree with at least some of what I say here.

Always Raise Hands:
[AAWX] You should always pot any two aces with a wheel card, and almost always repot with this hand shape if someone else has already opened the pot.

[AALX] To open, from any position, and to repot against any player you perceive to be a frequent raiser. About 1% of the time you may want to lay this hand down based on your perception of anyone who reraises you. If you fold this hand more than 1% of the time, that is too often, and those few folds should occur in multi-way pots when your side card is an 8 and you lack suitedness.

[AAA2 – AAA3] These are the only trip hands with any safety at all. You are largely raising on the diminished probability that anyone has an ace to defend with, and if you are faced with a maniac who comes over the top with garbage, you are largely still looking at chops and scoops when all the chips go in the middle.

Often Raise Hands

[A23H – A2LK – A2HP] To open, these hands are fine for stealing from any position, and these are often correct hands for raising any very active players especially with any suitedness. These are mostly fine hands for flat calling for heads up against a raiser.

[AWHX – AWMP] Table dependent, but often fine to open from middle to late position. These are generally not re-raising hands, although these can be flat call hands depending on suitedness and overall hand coordination.

[AWW6 – AWW8] Often fine to open from middle to late position, and occasionally early position. Often a fine flat call hand as well.

Late Raise to Steal Hands

[AAHH] Read dependent. If it goes in the middle you are often a slight underdog, unless villain turns over any AALX hand, when you become a bigger underdog. Personally, I will often fold this hand shape when there is already a significant pot-sized bet and one caller.

[AAAX] Late position to open. If blind defender will call with more than 60% of his hands, it is okay to fold this.

[WWWH] Late position to open

[WWHP] Late position to open

You can very creative with your button open-steal hands if you have a good read on the SB and BB, assuming you know enough about pot odds and overall equity well enough that you can make the mathematically correct play when reraised.

I plan to discuss the mathematics of pushing with junk hands in a later article.

Never Steal Hands

Personally, I never steal with quads or trips, and a villain must be very tight before I will raise with junk that cannot make better than an 8 low.

Hand Play

Level 5 – Blinds 75/150 – 52 players remain, payouts start at 12th

Hand 57 A[diamond]2[heart]5[diamond]9[diamond] Cutoff (75/150) Chips 3,220 (raise to 675 after 1 limper)

The table is eight-handed, and there are four folds, and one loose limper who is two from the button. While I do not have a powerhouse, I do have a reasonable degree of certainty that this raise will take this down, unless the button or blinds come up with an A2xx hand or better. It works, and I increase the stack by 425, or better than 10% without seeing a flop. If I had been called, the plan was to be aggressive with any low draw with a pair, or with a diamond draw, two pair or better, and otherwise not pump more money into the hand.

A flat call with this hand in this position is not an awful play. However, that allows two random hands to see the flop which means that I need to fit the flop very well to continue.


Hand 59 A[diamond]A[club]5[spade]K[heart] Middle Position (75/150) Chips 3,595 (raise to 525 to open)

Completely standard raise, even against a tight opponent I could not fold this to a re-raise. Note this is two pre-flop raises in short order since the break.

Hand 62 A[spade]3[spade]9[heart]K[spade] Big Blind (75/150) Chips 3,670 after posting (check after 4 limpers)

This hand is enough for blind stealing in an unopened pot. However, with four limpers, plus my two recent uncalled raises, a pre-flop raise will prematurely build a pot while I am specifically hoping to flop a deuce or spades, and giving up on a lot of flops multi-way.

Flop 6[diamond] 3[diamond]J[spade] (pot=750; check-fold to a 150 bet and two callers)

I have third pair, no low draw, and backdoor flush draw in a multi-way pot. Fold.

Hand 63 A[club]3[club]T[diamond]7[diamond] Small Blind (75/150) Chips 3,595 after posting (call)

A medium strength hand and an easy call after 1 under-the-gun caller for a 3 way pot. A UTG call often indicates an A2xx hand, so raising here with this stack and these blinds would be ill-advised

Flop A[diamond] T[heart] 9[heart] (pot = 450; Bet 450)

I have top two pair on a one-low board, with a weak backdoor low draw. Ideally, this bet will knock out any strong low draws that do not have hearts, or even take down the pot right now. Under-the-gun calls.

Turn 3[heart] (pot = 1,050; check)

I check and villain checks behind. If villain has the nut flush but not the nut low, he should bet this scary turn card, since his call on the flop represented a draw. My top two may still hold up.


River 7[club] (pot= 1,050; check)

I have four pair, any low on villain’s part is good, and there are many high hands that beat me. Villain checks behind with A[spade] 2[club] K[diamond] J[heart], demonstrating that he called a pot-sized bet on the flush-draw flop with an gutshot draw and no backdoor low. Incidentally, villains hand is strong enough for a steal from early position. . Do not play like this villain.

Hand 64 J[club]Q[heart]3[heart]J[diamond] Button (75/150) Chips 4,270 (fold after 1 limper)

Even on the button, I will not consider ‘set-mining’ without either significant high-card strength or a couple of wheel cards. The implied odds are no good unless I have some chance at the low, or strong high-side redraws. If the set should hit and get action, it is either a split pot or else there are redraws to hands bigger than a set.

Hand 65 2[heart]3[heart]4[club]8[diamond] cut-off (75/150) Chips 4,120 (call)

After four folders, this could be a steal hand, but since I have made two pre-flop raises in the last 10 hands, I choose not to put myself in a situation where I am behind if there is a re-raise. If someone raises my limp here, I will likely call. Button calls, SB completes, BB checks.

I had a peer review this article, and his comment for this hand was “Blech. Raise or fold.” That is a reasonable (and concise) critique of this play.

Flop 6[club]3[diamond]7[club] (pot = 600; check)

I have a gutshot and a plausible low draw. No reason to build a pot. Checked all around.

Turn K[spade] (pot=600; call 150 after a bet and a call)

The small bet seems to indicate a likely nut low attempting to build a multi-way pot. The biggest problem with marginal hands is that they often lead to marginal calls.

River 5[club] (pot = 1,050; call 300 after a bet and a call to close the action)

My gutshot hits, but I am behind clubs or a higher straight, and I hold 3rd nut low. This is a choice between calling and folding, and so I pay 300 for a reasonable chance to collect 1000. Small blind turns over a ten-high flush (along with a pair and a worse gutshot), and Big Blind turns over 2nd nut low. Marginal hands are tricky to play post-flop, as this one demonstrates.

Hand 65 K[heart]Q[heart]K[spade]3[club] middle position (75/150) Chips 3,670 (fold)

Same concept as hand 64. I see a lot of players treat this as a raising hand from any position with any chipstack. There will occasionally be times when this hand dictates a raise, but almost always in short-handed, high-blind situations.

Hand 74 A[club]2[club]6[club]6[heart] middle position (75/150) Chips 3,595 (raise 525)

I have been quiet for a rotation, and this is a hand where I would prefer to be heads-up, or to take it down preflop. Raise and no callers.

Level 6 – Blinds are 100/200 and stack is 12M. Not desperate, but I must be willing to steal and take a few coin flips with this lower-than-average stack. There are 41 players remaining.

Hand 75 A[club]2[club]8[club]Q[spade] early position (100/200) Chips 3,820 (raise 700)

Big Blind calls, with 1148 behind, meaning that there are very few flops where I can fold.

Flop T[spade]5[diamond]3[heart] (pot = 1,500; call 1,148)

Nut low draw plus a gutshot. Easy call. Villain turns over A[spade]8[spade]J[heart]T[club]

Turn/River 6[heart] 9[diamond]

A chop, for a net gain of 50. If I am unwilling to flip, the chip stack can only get worse.

Hand 77 2[club]9[diamond]T[diamond]3[spade] Big Blind (100/200) Chips 3,670 after posting (call 500)

This is an awful hand, where the only redeeming feature is the 23 low draw. However, the raiser is the same short-stacked (5M) villain from hand 75, so I do not expect a true powerhouse. I call with intention of calling on the flop with any low draw, any pair (any pair means that I have a two-pair draw), any gutshot draw, and folding anything worse than that. This is risky, but I want to build a table image that will discourage stealing from my BB in later rounds.


Flop 2[heart]3[club]K[heart] (pot = 1,500; bet 1,000 to put villain all-in)

Bottom two pair is certainly good enough. I want villain to fold any weak low draw, so I bet out. Villain calls with A[spade]3[spade]A[diamond]6[heart], which is stronger than I expected. Villain is a 60% favorite in the hand, with a 3 in 8 chance of scooping, and a 5 in 8 chance of taking the low.

Turn/River Q[club]T[heart]

This is winning ugly at its best! I have increased the stack to a playable 18M, and I have shown the table my willingness to defend with unpredictable trash, assuming that my tablemates are paying attention.

Hand 84 A[club]2[spade]6[club]7[diamond] Big Blind (100/200) 5,368 after posting (check after 1 early limper and SB folds)

This is now a six handed table. This hand is worth a steal to open, but it is unlikely to be ahead of the early limper who has a bigger stack than mine. Flat call is the best choice.

Flop 9[spade]2[diamond]5[heart] (pot = 500; bet 400)

If the limper came in with A2xx, this flop provides no succor. I bet with the intention of often giving up if called (A3xx should usually call here.) Villain folds. My play here shows the trouble with open-limping with A2xx when the blinds are worth stealing.

Hand 85 2[club]3[club]4[spade]5[heart] Small Blind (100/200) Chips 5,768 after posting (call after 1 limper)

Although it has very limited high potential, I consider this an okay open-steal hand, and it certainly merits completing from the small blind, and often merits limping after other limpers. It can be argued that this hand is not strong in enough in either direction to get involved after one limper, since that typically means that one ace is already accounted for, and we are very much looking for an ace on the flop. .This is very similar to hand 65 as a starting hand.

Flop A[heart]3[spade]5[heart] (pot=600; check-raise to 800 after a bet of 200 by Big Blind)

Any board that can make a wheel but not a flush could be described as binary. If you do not have the wheel, you should not get involved. Ideally, you should have the wheel with a redraw to hearts before leading out here. The big stack on my left made a correct play by betting small with nothing into two opponents to take down what is often an orphan pot. My reraise represented the wheel, and villain did not have the wheel.

Theoretically, I could reraise with nothing after the 3rd player folded and achieved the same result, but that is a very high risk play. Representing the wheel too often is much like representing the nuts in hold’em too often.

Hand 88 A[club]A[spade]6[spade]Q[spade] middle position (100/200) Chips 6,468 reraise to 2,100

Villain flat calls, indicating a very likely A2xx hand, as most AAWx hands would put it all in here. (Villain started with 5200 chips.)

Flop 7[heart]4[diamond]T[club] (pot = 4,500; call 3,140)

This hand plays itself. It’s clear villain has A2xy, and I hope the xy does not involve two pair or an open-ended straight draw. Villain turns over A[heart]2[heart]3[diamond]4[spade].

AAxx vs A2xx is the most common all-in preflop situation. Here are a few relevant statistics.

Preflop, this is a 60/40 situation. The A2 hand will scoop roughly 30% of the time, The AAxx hand will scoop roughly 45% of the time, and the other 25% of the time is a chop. Observe that the A2xx hand will come out fine 55% of the time, and the AAxx hand will come out fine 70% of the time. Who would you rather be?

Postflop, the low hand is now a 53% favorite, with a 5/8 chance of making the low, and a 5/16 chance to make the high. A234 has a two-pair draw and some backdoors, and a low draw that is almost exempt from counterfeiting

Turn/River A[diamond]J[spade] for a chop.

Hand 89 – A[diamond]2[diamond]5[club]9[diamond] 2nd position (100/200) Chips 6,418 (raise to 700 with 5 players yet to act)

The Big Blind so far has been tight-aggressive, and appears unwilling to defend with marginal hands. With a this hand shape, stealing is preferable to post-flop play. No resistance.

Hand 92 – A[club]2[club]5[spade]7[spade] under the gun (100/200) Chips 6,918 (call with 8 players yet to act.

This is a late position steal hand, and it also a good balancing hand for an early position call that can stand up to a raise. I do not like raising this early, as I might end up getting my chips in the middle pre-flop against an A2xy hand that has better side cards in both directions.

I routinely see novice players get very excited about double-suited A2xy hands, but my chip stack is deep enough that I prefer to play this hand post-flop, where I can use the leverage of a made low with counterfeit protection to push a marginal high hand out of the pot by the river.

There are two late position callers, small blind folds, big blind checks.

Flop 5[club]T[heart]2[heart] (pot 900; check-fold to a pot-sized bet.)

Despite flopping two pair, this is a dreadful situation. A3xx or A4xx with any heart draw should certainly bet the pot here, as should A3Tx, and a very brave 34xx hand could also bet. As I have no meaningful redraw, this is an easy fold.

Level 7 Blinds go to 125/250 my stack is still close to 15M. There are 36 players remaining, or exactly half of the starting field.

Hand 99 – A[spade]2[club]8[club]T[club] 3rd position (125/250) Chips 6,393 (fold as 3rd to act with six players left to act.

From a later position, this hand would be a steal hand. With a better emergency low or a suited ace, I could happily see a flop or even consider a steal from this position. However, I would hate to be reraised with this hand but I would be unable to fold, despite mostly being behind any raising hand here.

Level 8 starts at hand 112 Blinds go up to 150/300. I have been quiet since hand 92. My stack is close to 15M. There are 33 players remaining.

Hand 113 A[club]7[club]Q[spade]8[spade] Button (150/300) Chips 5,993 (Raise to 1,050 to open)

Compare this hand with hand 99. This has high card strength, an emergency low, and it merits a button steal. The small blind has a healthy stack and has shown a willingness to defend with many hands, although defending from the small blind often narrows the hand range to AWxy hands.

Flop K[diamond]T[heart]6[heart] (pot = 2,400; fold to a 2,400 bet)

Wrong colored flop. The small blind could have made this bet with a naked flush draw and a pair of threes, and I am still behind. This is an easy fold, and I have just lost 20% of my stack from a steal gone awry.

Hand 115 – A[club]5[heart]6[diamond]J[club] 5th position (150/300) Chips 4,943 (fold after one limper)

At 11M, I am not yet desperate. This is an open-steal hand from late position, but after one limper I prefer not to see a flop with this marginal hand , even with position.

Hand 125 – A[diamond]4[heart]8[spade]J[spade] 3rd position (150/300) Chips 4,493 (fold)

This is a button-steal hand, since it has AW, a face card and some suitedness. With a healthier stack, However, we are approaching the bubble and I am not on the button, so I let this go and wait for a better opportunity.


Hand 128 – A[club]2[spade]3[heart]K[diamond] Big Blind (150/300) Chips 4,193 after posting (raise to 2,250 after one limper and a min-raise to 600)

There are very few hands that are ahead of A2Kx, and with A23K, this is an automatic raising hand in the same way as AAWx. Villain flat calls my reraise with 3690 behind, which makes me assume villain will show down A2xx.

Flop 6[heart]8[diamond]Q[diamond] (pot = 4,950; bet 2243 all-in, villain calls)

There was virtually no flop I could have folded with this stack size and this hand, especially since I have to assume villain shares two cards with me. Villain calls with A[diamond]3[diamond]5[club]6[club], and I am sweating on the turn but squeak out a chop.

Turn/River 9[diamond] 7[diamond]

Second Break at the conclusion of hand 129.

Blinds will be going up to 200/400, and I will return to the table with about 8M. This is not a desperate stack, but it is far from commanding.

During levels 5-8, I got a much better distribution of random hands than in the first four levels. There was such a richness of hands, that I actually threw away a junk A2xy hand, and I was much less tempted to fool around with marginal hands, except to make steals. While I did manage to double my stack over four levels, my stack growth was not enough to bring me to a commanding stack. As mentioned in the text, I could have increased my aggressiveness with a few of these hands.

Saturday, April 04, 2009

Going Deep in an Online PLO8 Tournament, Part 1 – Early Stage Play

Originally published in 2p2 magazine, all rights go to the author.

Overall strategy for early levels

Situations to Seek:

Getting it all-in preflop with a 60% or better hand. Ideally, if I can get it all-in preflop against one or two opponents with some AAWx (Ace-Ace-Wheel plus any fourth card) combo, I will not hesitate.

Getting involved multiway with A23x, A24x, A25x, preferably with some flush draws. I would prefer not to get it all-in preflop, but I can mostly call a raise up to maybe 20% of my stack preflop for a multiway pot.

Getting maximum value out of secure hands. I would ideally like a lock on the high side with multiple players chasing the low. Other strong selections include having a nut low with redraw and a strong high side draw, or even flopping strong draws in both directions, such as the often heartbreaking favorite nut-flush-draw/nut-low-draw. (NFD/NLD)

Playing Marginal Hands only with position and large fields. By marginal hands, I mean hands that do not contain AAxy or A2xy. This includes all kinds of ‘Yahtzee!’ and ‘Bingo’ hands that can scoop a pot with an appropriate board. Four high cards with a suited Ace, any three wheel cards, suited ace hands are all candidate hands.

Situations to avoid:

One way chases on a two way board, especially awful in a heads up situation when the opponent is betting heavy. It’s usually not a good situation in multi-way pots either.

Clichéd nut lows in deep pots. If I make a low using A2, it’s much more likely that I am not the only such low than if I make it with 35 or 25. If I have nut low using A2, but I have no real high draws, and no counterfeit protection, it will occasionally be correct to fold it on the flop in the face of heavy multi-way action.

Going deep with Naked Aces. AAxy is typically a pre-flop favorite, but in the early levels, all kinds of hands are getting the correct odds to call a pre-flop raise. If the pot is going deep, and I have a pair of aces and no redraws, this is frequently not a good situation.

Hand Play

Level 1 - Starting 3,000 in chips, 10/20 blinds.

Hand 7 – 2[diamond]3[spade]4[heart]8[spade] Big Blind (10/20) Chips 2,845 (check)

I check this middling but not hopeless hand after two limpers and a small blind completion. I am mostly looking for an ace on the flop. If my opponents hold zero aces, there is a 30% chance to flop one or more aces. If they hold one ace, that drops to 24%. With two aces out, it’s 16%. I’m not getting fantastic implied odds, but there are plenty of chips behind if I hit a bingo.

Flop 3[club]5[club]J[diamond] (pot = 80; check-call 40)

Three checks and late position bets 40. I call with my open-ended straight draw, since the price is still low and I have no reason to assume my 24 low is beaten yet. The other two players call as well.

Turn A[spade]. (pot = 240; bet 180)

Bingo! I now have the nut low, and am only behind right now to anyone else with 24 and a club draw. SB checks, I bet 180, or ¾ of the pot, to prevent any weak draws from staying for free. Three callers, but I have no idea what they could hold, since it is early in the tournament, and these may be unskilled players. Any 24 with the club draw should have raised here, as should any 246x which is free-rolling for a better straight. Thus, I am very likely ahead at this point. I have 2,625 behind.

River Q[diamond] (pot = 960; bet 960)

I am now behind KTxy for the high (unlikely), tied with 24xx for the low, but still very likely ahead of all three callers. Because it is early in the tournament, I would like to get as much from the weaker players as possible, so I bet the pot when the SB checks, and AJ77 in late position (the lead bettor on the flop) is kind enough to pay off, and the other two fold.

Hand 8 –3[diamond]6[heart]9[club]7[spade] Small Blind (10/20) 4,535 chips (fold)

Despite being offered 7 to 1 odds to see a flop, I fold. With a hand like this, it is nearly impossible to make a hand that can scoop and also get paid. (The chances of somehow making quads and getting paid by AAxy are microscopically smaller than 7 to 1, especially since nobody raised pre-flop.)

Level 2 – Blinds are 15/30. No change in strategy.

Hand 23 – A[club]2[diamond]3[heart]9[diamond] Big Blind (15/30) 4,370 chips (raise to 120)

There are 3 limpers, two of whom have previously shown non-standard (dubious) preflop hand selections, so my low draw is probably miles ahead right now. I would like to build up a pot early to give the other players motivation to chase, so I raise to a non-threatening 4bb (120), and 2 of the players come along. The pot is 390, the two other players have 2,900 and 4,000, and the dream is to see them competing for the high side when I have a made low.

Flop Q[diamond]5[heart]8[spade] (pot = 390; check)

I have no high draw, and although I may be giving away my hand with this check, the option of lead betting and getting raised is not at all appealing. All three of us check

Turn 5[diamond] (pot = 390; check)

Betting is now plausible with a weak diamond draw and a good low draw, but given the check-calling passivity I have seen at this the table, I’d rather make a hand before putting more chips in. The action checks around.

River J[diamond] (pot = 390; call 180)

I have a weak flush, and the SB leads out for half the pot. There are three likely meanings here:
1) SB has nothing, but assumes that the other players were chasing lows and cannot call a bet.
2) SB has a diamonds flush, just as likely better than mine.
3) SB has a full house, which seems unlikely, since anyone with a 5 should have bet the turn to shut down any low draws.

After a moment of consideration, I decided that the 180 does not represent enough of my stack to preclude a curiosity call. I expect to lose, but I also wish to advertise that I cannot be easily bluffed.

I call, third player folds, and the bettor shows JJ37 for an unlikely riverboat. I filed this information on the SB on my right for later use.

Level 3 – Blinds 25/50, my stack is 4,100. Game plan largely unchanged.

Hand 32 – Q[spade]4[spade]8[diamond]5[club] SB (25/50) 4000 chips (call)

This is a very weak hand, and a fold is better play, but since only the button has limped, I take the pot odds of 5 to 1 on a trash hand. BB checks.

Flop A[club]2[spade]K[spade] (pot = 150; bet 100)

I have 3rd nut low draw, and 2nd nut flush draw. Since the button did not show strength pre-flop, I lead out for 2/3 of the pot, the BB calls and the button folds.

Turn J[diamond] (pot = 350; check)

I check and the BB checks. I am likely behind in one of the two directions, but not necessarily both, so I want to get to the river cheaply without a made hand

River 9[diamond] (pot = 350; check)

The low-draw/flush-draw combo has missed both ways, as it will around 40% of the time. I will not bluff without a pair, and BB is happy to check behind with K[diamond]2[diamond]3[club]3[spade], an unimproved two pair. Calling the flop with two pair and no low draw is potentially a negative EV play. I could have won a very big pot if a low hit on the turn and allowed me to safely build up the pot in case I hit a spade on the river. However, since the turn and river are bricks, BB wins a small pot.

I have a reasonable amount of information on the players to my immediate right and left, and have seen them make small mistakes that went unpunished, as often happens in PLO8 tournaments. Let’s hope the table doesn’t break up anytime soon!

Hand 33 –4[spade]7[spade]2[diamond]5[heart] on the button, (25/50) 3,900 chips (call)

While this is a marginal hand, three wheel cards occasionally gives big draws, so I call after one early limper. Given what I know of the limper, I am likely ahead for the low draw. The Small Blind folds and the Big Blind checks.

Flop 5[club]5[diamond]9[heart]. (pot = 175; bet 100)

Two checks and I lead out for half the pot and the SB calls.

Turn A[diamond] (pot = 375; call 100)

Small blind leads out for 100. I do not have the diamond draw, but I am not folding trips with a reasonable low draw, but I am not excited enough about my kicker to raise.

River 8[spade]. (pot = 575; call 150)

BB leads for 150, and I have a reasonable made low (but not nut), and trip fives with a poor side card. Raising is an option here, although there are some big blind hands that have us beat.
· 235 with any card higher than 7
· 245 with any card higher than 7.
· 2388, 2488, 2399, 2499

Otherwise I am likely ahead here, and may want to raise. However, will any hands weaker than mine pay me off?

23xx – These hands will pay me off, but I will not gain anything. They may even put me to the test with a reraise.
5 plus a card higher than 7. These hands are also chopping the pot with me. Ideally, I would like to see any combination of 5Txx, 5Jxx, 5Qxx, 5Kxx to fold to my reraise, but if the other two cards make any plausible low, it is unlikely that villain will fold to a repot.
24xx with no fives– I would get ¾ of the pot, so I want to build a pot as much as possible.

It is worth noting that with this hand at this level against an unknown opponent, hand reading is too tricky. I have not shown strength, and villain has also not shown strength, but we both have both shown an unwillingness to fold for small bets. I can likely rule out villain holding a true monster, such as 23 with a full house, but there are few other combinations that I can rule out with this betting sequence, especially when I am at a stage when many unskilled players still possess chips.

In the end, I go with caution and call. The BB turns over A[spade]T[spade]T[club]9[club], meaning that he was leading out with an overpair and no low draw. While failing to raise on the river was an error, it was probably a low-cost error, since BB should have folded to a repot. Still, it’s tough to win tournaments by leaving potential chips un-won.

Hand 34 – 2[diamond]3[spade]5[diamond]7[diamond] Cutoff position (25/50) 3,500 chips (call)

Given the playing habits of my tablemates so far, after two limpers I choose to see a flop cheaply with a very marginal hand that will often end up second best. It does not help to have three cards of one suit, since I am damaging my chances at a flush draw. If an ace does not fall on the flop, I am done with the hand, but if it does, I am optimally looking for a hand where two other players are competing for the high side, and I have a lock low. Any nut low I make here is a ‘non-cliché’ low, of course. This limp represents less than 2% of my stack. If it were much more than that, this hand is a clear fold.

Flop 3[heart]5[heart]7[heart]. (pot = 300; fold)

The UTG limper leads out for a pot-sized bet, and I fold. Even without the flush on the board, it is usually wise to fold with three low pairs, since I cannot make a meaningful low, and building a pot chasing the full house against a made low with any high draw (or a made high) is not good policy.

Incidentally, a hand like A[heart]2[club]xy without a flush should generally bet this flop in the hopes of getting weak flushes to fold. Any A2xy hand without the ace of hearts or a flush should generally not escalate the hand early, since there is a reasonable chance that an A2xx with hearts is in the mix.

Hand 35 – A[diamond]A[heart]2[heart]6[heart] mid-position (25/50) 4,300 chips. (raise 225)

After one limper UTG, I raise the maximum to 225 and the player on my immediate left (from hand 33) and the UTG limper both call. My opponents have 5,300 (left) and 1,800 (UTG).

Flop 6[diamond]6[club]8[club]. (pot = 750; bet 300)

I would love to build up a huge pot against any A2xy hand, or against any 6xyz hand without an 8. I lead out with a sucker continuation bet of 300, slightly less than half the pot. I also want to charge overpairs such as QQxy or JJxy to stay, lest they get a boat for free on the turn. I’d also like to see the small bet interpreted as weakness and be raised. The player on my immediate left calls, and we are heads-up.

Turn 9[diamond]. (pot = 1,350; bet 300 call a raise to 850)

I made an underbet of 300 (I believe I misclicked, but this is an awful bet size!) and villain raises to 850. After a moment, I flat call. I do not have a made low, and cannot rule out a garbage hand such as 88xx or 99xx for the villain, so there is no need to further inflate the pot right now.

River J[club] (pot = 3050; check)

I check, and villain checks behind with K[heart]K[spade]Q[club]9[club], and his clubs are good.

Playing this hand more aggressively from the flop might have won a small pot quickly, or it might have knocked me out of the tourney if villain had committed early with his overpair and a flush draw.

It is worth noting that nemesis called the two (undersized) bets with an overpair, a non-nut flush draw and no low draw, after calling a preflop raise with a marginal hand. One of the commonly accepted tenets of PLO8 is ‘never chase for half the pot’ which is exactly what nemesis did. It is even worse to chase a non-nut hand. In all fairness, my underbets did not show strength, and a big bet on the flop would have likely taken down the pot.

Level 4 – Blinds are now 50/100 and I have 2,900 in chips, or 20M. This is a playable stack and I am far from desperate.

Hand 53 – 2[diamond]3[club]5[club]6[club] UTG (50/100) 2,700 chips (call)

I limp with another marginal three-wheel hand. This is a limp out of boredom, since I haven’t seen a flop for 18 hands. This table has not been very aggressive, so I take a chance that I will not be raised by any hands weaker than AAxy, especially since it would be easy to interpret my UTG limp as a very strong hand, even though it actually is not. All players fold down to the BB, who has a stack larger than ours, and the BB checks. Much like hand 34, I am looking for an ace on the flop. However, since I am only against the BB, I have to assume that any low I make with 23 is very likely to hold up.

Flop K[diamond]9[spade]2[spade]. (pot =250; check)

The BB checks. I have bottom pair and a backdoor low draw, but would have to fold to a check-raise. Seeing the turn for free is better than inadvertently betting into two pair or a flush draw.

Turn 2[club], (pot=250; bet 250)

BB checks, and there is no reason to assume I can make more money by waiting till the river to bet, so I bet the pot, and BB goes away. Not a fantastic hand, but after 18 consecutive folds, it’s encouraging to see a flop and take down a small pot.

Hand 54 – A[spade]2[heart]8[club] 9[spade] BB (50/100) 2,800 chips (check).

There is one EP limper, and the SB completes.

Arguments for checking this hand include:
· backup low (8) is the worst possible emergency low.
· side card (9) has no high strength
· Because the blinds have increased in proportion to my stack, betting the pot could present a very difficult decision on the turn for all my chips with a weak holding
· There are less limpers than in the prior hand
· fold equity is minimal
· If my raise is called, I am out of position for the rest of the hand
· A check keeps the hand completely secret. Because my opponents are unlikely to give me credit for A2xy, I have a better chance of ending up in a big 3 way pot with nut low, and one of the opponents putting in chips on the assumption that his 2nd nut low hand will be good.

Arguments for raising with this hand include:
· There is only one early position limper, whose low is probably worse than A2
· It has an ‘emergency low’ to help with counterfeit protection heads-up
· It has a suited ace
· It has 89, which gives us some chance at a straight
· The Small Blind probably completed with a junk hand and would fold to a raise.
· Given that I have folded every hand for two rotations around, my table image is presumed tight.
· I could win 200 chips without a fight.
· I will be out of position for the remainder of the hand if I do not end it now.

I choose to check because I am looking for a big score at this time. I can either risk an extra 10% of my stack now for a likely 7% increase, or I can risk zero additional chips for a potentially bigger payoff.

Flop J[club]7[spade]2[diamond] (pot = 300; check)

I have bottom pair, backdoor flush draw, gutshot straight, and a very weak low draw. I check and it is checked around. I could make a half-pot bet, but if either villain raises me here, I would have to fold my draws. A3 and A4 are certainly not folding if I take a stab here.

Turn T[club] (pot=300; bet 300)

I have the temporary nuts. There are no possible river cards that preserve the nut hand status, so I would like to take the pot down right now. A pot-sized bet, and nemesis (hands #33 and #35) calls.

River J[heart] (pot =900; bet=700)

This is probably one of the least harmful cards in the deck. Given the action so far, it is very doubtful that villain holds a jack, since top pair plus a low draw, or two pair on the flop would have merited a bet, and the call on the turn strongly indicates a drawing hand. I bet 700, and nemesis folds.

Hand 56 – 2[heart]3[club]6[diamond]8[diamond] Button (50/100) 3,400 chips (call)

There are two limpers, and I elect to limp in with this speculative hand from the button. The SB completes and BB checks. This is a much more sensible limp than hand 53, although choosing to fold this preflop is also sensible.

Flop Q[heart]7[spade]8[spade] (pot=500; fold)

The 3rd player to act bets 300. I am mostly looking for an ace on the flop, and I didn’t get one. I fold 3rd nut low draw and middle pair.

Hand 56 concludes level 4.

Break

Stack is 3,200 at the conclusion of four levels. The bad news is that I failed to increase the chip stack while the weaker players are still splashing their chips like drunken sailors. The good news is that I have outlasted half of the field, as there are 36 players remaining out of a field of 72. The payouts begin at 12th place, so I will need to increase the stack to get to the prizes.

In terms of hand distribution so far, I have seen two A2xx hands, and one AA2x hand out of 56 hands, and not a lot of playable aces in general. Without going into the statistics, I’m quite certain that my starting hands have been below average expectation. This led to a lot of folding, and eventually took me to playing marginal hands out of position, which is an easy way to get into big trouble.

In the early stages of a PLO8 tournament, the player skill level is often low enough that hands cannot be read with any degree of certainty. I have to choose between risking my stack against an enigmatic holding and taking smaller risks for smaller rewards. My choices so far in this tournament have kept me alive, but not built up a big stack.

Tuesday, January 13, 2009

ICM PLO8 article

ICM Decisions in Split-Pot Tournaments

The Problem

Congratulations, we have just made it to the final table of a Pot-Limit Omaha Eight or Better Multi-Table Tournament! Now what?

There are 8 remaining at the final table. We are past the bubble and playing to maximize our value on a sliding pay scale. The Payouts, Chip Counts, and Current ICM Values (aka cEV) prior to posting our big blind are as follows:

Position Payout
1 $1,950
2 $1,475
3 $1,100
4 $840
5 $575
6 $450
7 $350
Total $6,740

Chips Current ICM Value
Player 1 21,000 $936
Player 2 7,000 $601
Player 3 38,000 $1,181
Player 4 6,000 $568
Hero 26,000 $1,020
Player 6 32,000 $1,107
Player 7 (BS) 53,000 $1,327
Total 183,000 $6,740


Player 7 has been working the big stack and raising the table more than her share. In the last 10 hands, she has been involved in 6 hands and her cards were exposed four times at showdown. Those hands were:

A578 – Three of one suit
A8JJ – Three of one suit
QQ89 - rainbow
AKJ9 - double-suited

The blinds are 1000/2000 and you are in the BB. As expected, the Bully raises to 5000, and the table folds around to you. If find you have a very strong hand, what is the best possible play? Let’s take a look our table observations and then take a look at the math.

• There are two stacks at less than 3M, in serious danger of elimination
• The difference between being eliminated now and outlasting the two small stacks $575 compared with $350, or a 60% improvement in pay.
• A double-up here makes us the chip leader, giving us a better shot at first prize, especially as cautious as this table has been.
• Based on prior behavior, if we reraise, we expect that the bully will reraise and put us all-in 100% of the time.
• Based on prior behavior, if we flat call, we expect villain to respond to our flop bet with an all-in move about 70% of the time and to fold the other 30%.

Now let’s look at the math. Here are our ICM values in the following scenarios.
• We fold preflop ($995)
• We flat call and fold on the flop ($948)
• We bet the flop and bully folds ($1079)
• We chop the pot and profit by T500 ($1031)
• We double up ($1329)
• We are eliminated ($350)
• We get ¼ of the pot ($803)
• We get ¾ of the pot ($1195)

Option 1 - Push or Fold Only

Here is the ICM value of AA23 double-suited, the strongest possible hand in PLO8. We will assume that villain repots and put us all-in, and we will use propokertools.com simulations of AA23ds versus a random hand to determine the remaining distribution.

Percent ICM Value Result
Losses 17.50% $350 $61.25
Chops 18.35% $1,031 $189.14
Scoops 61.41% $1,329 $816.18
3/4 1.71% $1,195 $20.40
1/4 1.04% $803 $8.32
100.00% ICM Value $1,095


Compared to folding AA23 double-suited preflop ($995), we confirm that raising with the best possible hand is a positive equity play and increases our cEV by about 10%. The ICM model needs to be very severe before we should contemplate folding a monster starting hand.

If we assumed that villain would fold pre-flop 30% of the time that we reraise, the numbers for AA23 would come out as follows.

Percent ICM Value Result
villain folds preflop 30.00% $1,079 $323.70
Losses 12.25% $350 $42.87
Chops 12.84% $1,031 $132.40
Scoops 42.99% $1,329 $571.32
3/4 1.19% $1,195 $14.28
1/4 0.73% $803 $5.82
100.00% ICM Value $1,090

Assuming that villain will always call our reraise, the weakest double-suited hands we can push with and still be marginally profitable include A2Q5 ($996), A35J ($994), A45J ($996), A5JJ ($996). Any AAxx hand that includes one low card will be profitable, but the strong high-side hand AAKK double-suited is only worth $970, somewhat worse than folding that hand preflop.

For the remainder of the article, we will focus on the hand A23K double-suited. Its pushing value is $1009. If the villain folds 30% of the time when we reraise with this hand, our value goes up to $1030. Our risk of ruin is 24% if villain always calls and 16.5% if villain folds 30% of the time that we repot.

Option 2 – See and evaluate a flop and push a wide range of draws and made hands

A second option is to see and evaluate a flop, and only push where we have a flop that meets any of the following conditions.

1) We have a made nut low
2) We have a nut-low draw with one card needed (treat this as a semi-bluff)
3) We have a made high side hand, such as trips or better.
4) We have a high side only semi-bluff hand (Flush draw, pair of aces, pair of kings, and we will classify two pair as a semi-bluff for outcome calculation purposes)

First we generate the number of flops that qualify, and determine the number of flops where we will plan to check fold. For A23K double-suited, we estimate 5840 combinations out of 17, 296 possible flops (34% chance) where we have a flopped nut low or a nut low draw. In addition to these low chance flops, these high-side flops exist outside of the low flop chances.

High Hand Flops Combinations Percentage
Trips or full house 552 3.19%
Quads 4 0.02%
Broadway Straights 64 0.37%
Flopped Flushes discounting 3 low card flushes and 2 low card flushes 140 0.81%
Flush draws with 2 high flush cards and any third card 592 3.42%
Flush draws with 1 high flush cards, one low flush card and one other high card 840 4.86%
Two Pair plus one high card 864 5.00%
(discount flush draw combinations) -272 -1.57%
A King plus one or two high cards (two pair draw) 1752 10.13%
(discount flush and flush draw combinations) -72 -0.42%
An Ace plus two high cards (two pair draw) 513 2.97%
(discount flush and flush draw combinations) -98 -0.57%
Total 4879 28.21%

We estimate that we can push on 62% of all possible flops. We will check-fold the 38% of flops that do not contain a low draw or at least a pair of kings. We simplify the model with the following assumptions.

• Villain will fold 30% of the time that we pot the flop
• For any made low flop we are mostly free-rolling for the high, and chopping 75%, scooping 25%.
• For any two-card low flop, we are struggling to survive when called, and we are losing 40%, chopping 50%, and scooping 10%.
• For any high-hand flop with a made hand, we are scooping 60%, chopping 30% and losing 10%.
• For any high hand flop with a draw or any two-pair and one-pair hands, we are losing 40%, chopping 30% and scooping 30%.

Our outcomes table appears as follows

Occurrence Combinations Percentage
Fold Flop 6577 38.03%
Made Low Chop (75%) 2122.5 12.27%
Made Low Scoop (25%) 707.5 4.09%
Low Draw Loss (40%) 1204 6.96%
Low Draw Chop (50%) 1505 8.70%
Low Draw Scoop (10%) 301 1.74%
Made High Scoop (60%) 456 2.64%
Made High Chop (30%) 228 1.32%
Made High Loss (10%) 76 0.44%
High Draw Loss (40%) 1647.6 9.53%
High Draw Chop (30%) 1235.7 7.14%
High Draw Scoop (30%) 1235.7 7.14%
Total 17296 1

We reorganize our outcomes as follows.

Occurrence Percentage ICM Gross Value ICM Calculated
Fold Flop 38.03% 948 $360
Villain Folds Flop to our bet (30%) 18.59% 1079 $201
Scoop 10.93% 1329 $145
Chop 20.60% 1031 $212
Loss 11.85% 350 $41
Total 1 $960


Our expected cEV from a stop and go where we push the best 62% of flops is actually worse than folding preflop. Our risk of ruin drops from 24% to 12% compared with pushing preflop.

Option 3 – See and evaluate a flop and push a narrow range made hands

What if we evaluate a flop and only continue on hands where we have a very strong flop? Let us revise our betting criteria as follows:

1. We have a made nut low
2. We have a made high hand, two pair or better.
3. We have a nut low draw (need one card to make low) plus any flush draw or open ended low straight draw.

Let us assume that villain will fold 30% of the time that we push on the flop. Let’s also assume that we are mostly either scooping or chopping when we push on the flop, and that we will include a small portion of losses rather than attempting to quantify the number of times that we will get quartered. This strategy offers the lowest risk of ruin (5%) for any option, and offers the best cEV for any of the post-flop options.

Occurrence Percentage ICM Gross Value ICM Calculated
Fold Flop 52.90% 948 $501.46
Villain Folds Flop to our bet (30%) 14.13% 1079 $152.47
Scoop 11.93% 1329 $158.50
Chop 16.14% 1031 $166.35
Loss 4.91% 350 $17.19
Total 1 4737 $996


In other words, compared to folding pre-flop, it is marginally profitable to call with A23K double-suited and only push on highly selective criteria where we have a virtually guaranteed chop and are free-rolling for the other half of the pot. Despite offering a lower overall value than pushing preflop, this may be the best option when playing against certain categories of villains, because it offers the lowest risk of ruin (5%) for any option, and offers the best cEV for any of the post-flop options.


Option 4 – Pure Stop and Go

It can be argued that the villain will tighten up if we put her to the test. If we treat this as a stop-and-go play where we always bet the flop, and villain folds to 65% of our all-in flop bets (an optimistic scenario, unless villains standards for continuing are much tighter than our own) and puts us all-in on the remaining 35% of flops.

Occurrence Percentage ICM Gross Value ICM Calculated
Fold Flop 0.00% 948 $0
Villain Folds Flop to our bet (65%) 65.00% 1079 $701
Scoop 5.46% 1329 $73
Chop 10.30% 1031 $106
Loss 19.23% 350 $67
Total 1 $948

The stop and go scenario above is close in value to the call-and-evaluate model in option 2. However, the number is ‘terribly optimistic.’ If we change our assumption so that villain would fold to our stop and go in the same proportion as we folded in option #2 (38 %), the outcome would degrade as follows.

Occurrence Percentage ICM Gross Value ICM Calculated
Fold Flop 0.00% 948 $0
Villain Folds Flop to our bet (38%) 38.00% 1079 $410
Scoop 9.68% 1329 $129
Chop 18.25% 1031 $188
Loss 34.07% 350 $119
Total 1 $846


It can be argued that if the villain is only folding 37% of the time, villain will be on a draw a significant portion of the time. When we arbitrarily increase the overall chops and scoops, the numbers look better, but this is still not a profitable play compared with pushing only on the strongest flops.

Occurrence Percentage ICM Gross Value ICM Calculated
Fold Flop 0.00% 948 $0
Villain Folds Flop to our bet (38%) 38.00% 1079 $410
Scoop 14.00% 1329 $186
Chop 26.00% 1031 $268
Loss 22.00% 350 $77
Total 100.00% $941




Concluding Thoughts

Much like any other MTT, there are certain times in the tournament when it is correct to push with virtually any hand, and there are times when we should only consider pushing our strongest hands. In this situation with two life-support stacks and a villain who does not perform hand valuations well, we must be highly selective on our pushing hands, since we have minimal fold equity and we stand to lose so much more value in elimination than we could gain in a double up.

By the same token, we should not necessarily cave in to a big stack bully with our strong but not monster hands: with the chips to see a flop without committing, we may prefer to see a flop with our stronger two-way hands, and push on flops where we are very likely to survive and preferably thrive, but give up on flops that do not give us much hope in either direction, without giving up too much tournament equity. Because it reduces volatility, this strategy is particularly recommended when you believe you have a significant skill edge over the villain.

Sunday, June 01, 2008

Month in progress - Full Tilt

June 1 - AM one PLO (high) HU SNG - won
(1, 0 )
Midafternoon one PLO8 HU sng - won
(2,0)

Friday, October 05, 2007

Stars Blog Tourney

I think I've paid my blogging dues. I wanna play.


Online Poker

I have registered to play in the PokerStars World Blogger Championship of Online Poker!

This Online Poker Tournament is a No Limit Texas Holdem event exclusive to Bloggers.

Registration code: 1880285

Sunday, December 17, 2006

Suspension of Blogging

Effective immediately, I am done with poker blogging, unless it's worth a free roll for an on-line tourney. Otherwise, I find it's no longer productive in terms of improving my game, or improving your game. Consider this my new year's resolution come early.

You can find me on the 2+2 boards, playing on-line, or playing live.

To the handful of people who've been reading my blog, thanks for stopping in and sharing your opinions.