By Tony Guerrera
This series of articles about independent chip modeling was by no means an exhaustive treatment of tournament endgame theory. Many different tournament situations exist, and I’ve only scratched the surface. Hopefully you’ve learned how to perform ICM analysis on your own so that you can perform it on unique situations that you conceive or encounter. I used custom software to do all the analysis in these articles, and I hope to make it available to the public at some point (as if I need another project to work on). For now, you’ll have to Google around to see what you can find. There are some free ICM packages out there, and also some very good ones that you can pay for.
ICM is extremely powerful; however, like any mathematical model, it has its limitations. This article will talk about tournament theory beyond ICM, and it should give you lots of things to tuck in the back of your mind next time you’re in a tournament.
Analysis Across Multiple Hands
ICM assumes that all players implement the same strategy meaning that, effectively, you don’t need to account for analysis across multiple hands. However, to optimize your monetary EV (mEV), you really need to account for different playing strategies, the position of the blinds, and other such factors. Ultimate end game analysis should account for all players’ pushing and calling distributions and should then optimize your decisions as a function of those distributions, accounting for blinds and the play of future hands.
Writing software to do such analysis is really complicated, nevermind doing it on the fly in a tournament. In the absence of completely solving the tournament endgame (which I think is possible), the next best thing we can do is to study lots of specific examples to look for trends such as “it’s usually best to pick on short stacks instead of large stacks.” By keeping those concepts in the back of your mind while you’re playing, your decisions should be more educated, thereby improving your mEV.
Where’s Your Edge?
Not everyone plays an optimal end game, and part of your edge in tournaments will be exploiting those holes through detailed study you’ve put in away from the table. However, in general, skill will not be much of a factor in the end game of most tournaments since the blinds are so huge with respect to the blinds and because its more likely that the average skill of your opponents who’ve lasted until the end will be higher than the average skill of your opponents in the beginning.
Therefore, it’s imperative that you look for opportunities to accumulate chips early, when you have a chance to apply your superior skills across four betting rounds instead of just one, and when weak players still have chips. It’s the players who take the chips from the weak players early on that have the best mEV going into the end game.
To accumulate chips, you need to open your game up beyond the traditional tight-aggressive approach taken by most players. You’ll also need to abandon the notion that your skill edge is big enough such that you should avoid gambles early on. Professional players who say things such as “I’ll fold AA to a preflop all-in on the first hand of WSOP” are way overestimating the impact that their skill has on their tournament results. You shouldn’t be taking 50/50 coin flips; however, any time you’re better than 55%, you should be willing to risk your entire stack.
Taking calculated risks early on doesn’t mean that you’re pissing away your chips on unwarranted adventures. It does mean that you should be in there slugging whenever you think you have an edge.
Current –mEV Can Mean +mEV Overall
Sometimes, a play that’s obviously –mEV according to the ICM can actually by +mEV overall. As an example, suppose blinds are 50-100, and the stacks are as follows:
Button (You): 4,000
Small Blind: 3,000
Big Blind: 1,000
Under The Gun: 2,000
Action folds to you and you raise to 300 with JTs. The small blind folds and the big blind pushes all-in to 1,000 with a distribution that you assume to be something along the lines of [AA,88]||[AK,AJ]. Against this distribution, P(win) = .3434, P(tie) = .0076, and P(lose) = .6491. ICM analysis suggests that calling has an mEV of $227.30 and that folding has an mEV $228.81.
Folding has $1.51 more mEV according to ICM analysis; however, calling here has a huge benefit not considered by ICM. Conventional players don’t want to risk all their chips on a gamble. By showing that you’re willing to call an over the top raise with JTs, you’re showing that anyone who goes all-in over the top of you will be putting their tournament life on the line. As a result, many conventional players will go into a shell, meaning that you’ll be able to raise and steal blinds with reckless abandon. In fact, even if the reraise all-in was to something like 1,500, I would seriously entertain making this call provided that your opponent is on the distribution described. If you lose and end up having 2,500 chips at the end of this hand, you’re still in great shape compared to the other stacks.
Games Within Games Within Games
This JTs call, along with other plays you make consider are sometimes referred to as metagame plays. Metagame considerations are those that go into the game within the overall big picture. Anytime you seemingly sacrifice mEV when you are, in fact, creating game conditions that are overall +mEV, you are using metagame considerations. Metagame considerations are vital to success at the highest levels of tournament poker. Do be warned that some players take this idea too far as a way of justifying bad play.
It can be a fine line to walk, so just make sure you’re always honest with yourself. Keep all of this in mind when using ICM, and when thinking beyond ICM, and your mEV should go throught the roof!
Tony Guerrera is the author of Killer Poker By The Numbers and co-author of Killer Poker Shorthanded (with John Vorhaus)
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