The Tsunami

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Game Theory: Rochambeau to Poker (Part 2)

Even an expert can pick up a new trick or two. For the KillerEV faithful who’ve been wondering what I’ve been up to for the past two weeks, I was recently in Florida visiting HerschelW from PokerPwnage.com. The focus of the trip was to put together some videos about short-stacked play in multitable tournaments (MTTs) to toss up on PokerPwnage.com. The videos we made cover the following topics:


  • Equity and All-in Calls
  • Reshipping
  • Exploitative Play vs. Non-Exploitable Play
  • Non-Exploitable Shoves
  • Equilibrium Calling Ranges


Many top MTTers don’t currently understand all the material in these videos. But even though I’ve been ahead of the curve as a theoretician, translating cutting-edge theory into results can still be difficult. Besides making videos for PokerPwnage, HerschelW and I spent some time talking about some recent tournament hand histories of ours. From those two discussions, I’ve reached the following conclusion:


I need to be better about knowing when I can go from lines of play that are tough for my opponents to exploit to lines of play that do a better job of exploiting holes in my opponents’ games. Additionally, on a related note, I need to play still fewer tables than I have been recently so that I can fully take advantage of my ability to perform quality on-the-fly analysis (I’m dropping my absolute maximum number of tables from 15 to 12).


Thanks to my time in Florida, I’ve reached a new breakthrough in implementing the theory that I dedicate so much of my time to. After dropping the number of tables I’m playing and avoiding non-exploitable autopilot in situations where I can clearly gain more chips from opponents in other ways, I’ve been crushing my opposition! I guess online poker is yet another case where quality trumps quantity. Don’t get me wrong, being tough to exploit is still a cornerstone of my poker philosophy and how I play; however, if being tough to exploit is all you’re concerned with, you are not winning as much as you could be assuming that your game selection is good (where good game selection means that you’re playing in games against competition that makes clearly exploitable mistakes).


Recall from Game Theory: Rochambeau to Poker (Part 1) that when choosing to play non-exploitably in Rock-Paper-Scissors, you’re ensuring that you and your opponent will win the same number of games in the long run no matter what strategy your opponent chooses. However, poker is different in that if you play perfectly, mistakes from opponents will result in you gaining chips. (Notice that I’m referring specifically to situations where we’re concerned solely with chip EV. This is because if you play perfectly in situations where maximizing chip EV doesn’t necessarily maximum monetary EV, opponents’ mistakes can potentially cost you money as well). Let’s investigate a few situations to see how changes in strategy affect your expected stack. For all these situations, you’re at a 9-handed table, blinds are T100-T200, antes are T25, you’re in the small blind, and action folds to you.


Case 1:


You jam approximate non-exploitable jamming range with respect to chip EV: {22+, Ax, Kx, Qx, J2s+, J3o+, T2s+, T6o+, 92s+, 96o+, 84s+, 86o+, 73s+, 75o+, 63s+, 65o, 53s+, 43s} (75.3% of hands)


Big blind calls with equilibrium range: {22+, Ax, Kx, Qx, J2s+, J6o+, T5s+, T7o+, 96s+, 98o, 86s+} (59.6% of hands)


Your expected stack is about (.247)(T1900) + (.753)(.404)(T2425) + (.753)(.596)(.471)(T4225) = T2100


(The first term in this EV calculation is from when you fold, the second term is from when you jam and the big blind folds, and the third term is from when you jam and the big blind calls)


Case 2:


You jam approximate non-exploitable jamming range with respect to chip EV: {22+, Ax, Kx, Qx, J2s+, J3o+, T2s+, T6o+, 92s+, 96o+, 84s+, 86o+, 73s+, 75o+, 63s+, 65o+, 53s+, 43s} (75.3% of hands)


Big blind calls about 78.7% of equilibrium range: {22+, Ax, K2s+, K4o+, Q4s+, Q8o+, J5s+, J8o+, T7s+, T8o+, 97s+, 98o+, 87s} (46.9% of hands)


Your expected stack is about (.247)(T1900) + (.753)(.531)(T2425) + (.753)(.469)(.448)(T4225) = T2107


Case 3:


You jam approximate non-exploitable jamming range with respect to chip EV: {22+, Ax, Kx, Qx, J2s+, J3o+, T2s+, T6o+, 92s+, 96o+, 84s+, 86o+, 73s+, 75o+, 63s+, 65o+, 53s+, 43s} (75.3% of hands)


Big blind calls about 48.3% of equilibrium range: {22+, A2s+, A4o+, K6s+, K9o+, Q8s+, QTo+, J9s+, JTo+} (28.8% of hands)


Your expected stack is about (.247)(T1900) + (.753)(.712)(T2425) + (.753)(.288)(.407)(T4225) = T2142


Case 4:


You jam any two (100% of hands)


Big blind calls about 48.3% of equilibrium range: {22+, A2s+, A4o+, K6s+, K9o+, Q8s+, QTo+, J9s+, JTo+} (28.8% of hands)


Your expected stack is about (.712)(T2425) + (.288)(.382)(T4225) = T2191


(The first term in this EV calculation is from when you jam and big blind folds; the second term is from when you jam and big blind calls)


Case 5:


You jam approximate non-exploitable jamming range with respect to chip EV: {22+, Ax, Kx, Qx, J2s+, J3o+, T2s+, T6o+, 92s+, 96o+, 84s+, 86o+, 73s+, 75o+, 63s+, 65o+, 53s+, 43s} (75.3% of hands)


Big blind calls slightly wider than equilibrium range: {22+, Ax, Kx, Qx, J2s+, J5o+, T2s+, T6o+, 96s+, 97o+, 85s+, 87o, 75s+, 64s+, 54s} (65.9% of hands)


Your expected stack is about (.247)(T1900) + (.753)(.341)(T2425) + (.753)(.659)(.483)(T4225) = T2105


Case 6:


You jam any two (100% of hands)


Big blind calls slightly wider than equilibrium range: {22+, Ax, Kx, Qx, J2s+, J5o+, T2s+, T6o+, 96s+, 97o+, 85s+, 87o, 75s+, 64s+, 54s} (65.9% of hands)


Your expected stack is about (.341)(2425) + (.659)(.446)(4225) = T2069


Case 7:


You jam 88.7% of non-exploitable jamming hands {22+, Ax, Kx, Q2s+, Q3o+, J2s+, J5o+, T2s+, T6o+, 93s+, 96o+, 85s+, 87o, 75s+, 64s+, 54s} (66.8% of hands)


Big blind calls slightly wider than equilibrium range: {22+, Ax, Kx, Qx, J2s+, J5o+, T2s+, T6o+, 96s+, 97o+, 85s+, 87o, 75s+, 64s+, 54s} (65.9% of hands)


Your expected stack is about (.332)(T1900) + (.668)(.341)(T2425) + (.668)(.659)(.498)(T4225) = T2109


Some Conclusions that We Can Draw from these Results


When you and your opponent are playing the equilibrium strategy, your expected stack is 75 chips more than the 2025 chips you had before the hand started. When your opponent calls too tightly or too loosely in response to you jamming the equilibrium range, you don’t realize big gains with respect to your stack. However, the gains are non-negligible with respect to your 75 chip equilibrium gain. For example, in case 2, where the big blind calls with 78.7% of the equilibrium range, you gain 82 chips instead of 75 ((7/75)(100%) = 9.33%). The further your opponent deviates from equilibrium, the more you gain. Furthermore, as your opponent goes further from equilibrium, you can realize even further gains by making proper exploitative adjustments.


The Botton Line


If you don’t have evidence that your opponents are deviating from equilibrium, you should play equilibrium ranges. Furthermore, if your opponents are off by only a little bit (such that you probably can’t realistically tell that your opponents are deviating from equilibrium play), then you’re also probably best off sticking with equilibrium ranges. However, as soon as you see you opponents making noticeable deviations from equilibrium, you should be ready to pounce by making an appropriate exploitative adjustment. It may seem ridiculous that players call with only half the hands that they should in some circumstances. However, if you open jam 10bb from the SB with antes in play, how often are you getting called by hands like JTo, Q8s, or K6s?


May Your EV Always Be Positive!


Tony Guerrera (The Tsunami)



  



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