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(Theory) Tournament Hand Rankings v1
I'm tired of Slansky hand rankings for tournament poker, so I thought I would try and come up with my own...
(skip down to my results section if this is too boring) Theory: The key assumption behind the popular Slansky hand rankings is that your opponent knows your exact hand. Obviously this is unrealistic so I set about coming up with a ranking system where your opponent only knows what %range of hands you are on. My system is based on a simple push/call game. There are no blinds, however the caller needs >=50% equity to call (I'll call this the threshold%). So if Player1 pushes with an X% range, Player2 (the caller) knows the value of X and therefore comes up with an optimal call range, Y%. Player2 uses a range that attempts to counter Player1's calling range and both players must follow a strict hand ranking system. How accurately does this ranking system apply to tournament poker? This is largely effected by the choice of the threshold%. I made the arbitrary choice of 50% as a starting point, and in some situations this is a good approximation to real sit n' go play. More specifically, these hand rankings are most accurate when the effect of the bubble is exactly counteracted by the size of the blinds. More extreme bubble situations, or situations with small blinds are not well represented by my hand rankings. However, hand rankings for these situations could be determined simply by repeating my method for a new threshold%. Here is an example using PokerStars structure where my hand rankings are most accurate: Big Blind is t200 with t25 antes CO (t3844) Button (t3844) SB (t1968) BB (t3844) Co folds, Button folds, SB pushes... In this case BB needs 49.995% equity to call the push by SB, and my ranking system would represent near-optimal ranges. If someone could calculate the exact nash equilibrium in this case it would be interesting to compare the results to the ranges predicted by my hand rankings. The Results: Note: I did all this by hand using pokerstove and it is quite likely I made some small errors. 1. Calling Strength Hand Rankings If Player1 is pushing a range less than or equal to this X% then you have to fold the corresponding hand. This percentage gives you a rough idea of relative hand strength for calling. X%_____Hand 0.00%__AA 1.81%__KK 3.47%__QQ 5.13%__JJ 6.03%__TT 6.49%__AKs 6.49%__AKo 8.90%__99 9.80%__AQs 12.52%_88 13.42%_AQo* 14.33%_AJs 15.54%_77 17.04%_ATs 17.35%_AJo 17.65%_KQs 21.27%_ATo 22.17%_66 22.47%_A9s 26.40%_KJs 26.40%_A8s 26.40%_KQo 29.11%_A9o 30.62%_55 30.62%_A7s 31.52%_KTs 34.24%_A8o 34.24%_A6s 36.35%_A5s 38.16%_QJs 39.37%_KJo 39.37%_A7o 40.57%_44 40.87%_A4s 42.99%_A3s 43.29%_K9s 43.29%_KTo 43.29%_QTs 46.00%_A2s 46.30%_A6o 48.11%_A5o 49.92%_QJo 50.23%_K8s 50.23%_JTs 51.73%_K9o 52.64%_A4o 54.15%_Q9s 55.05%_K7s 56.26%_QTo 57.16%_A3o 59.58%_K6s 60.78%_K8o 61.69%_A2o 63.50%_J9s 64.40%_33 64.40%_K5s 66.21%_Q8s 66.52%_K7o 67.42%_JTo 68.63%_Q9o 70.44%_K4s 72.55%_K6o 72.55%_T9s 74.66%_Q7s 74.66%_K3s 77.38%_J8s 78.28%_Q8o 78.28%_Q6s 78.28%_K5o 79.19%_K2s 81.90%_J9o 83.71%_Q5s 84.62%_K4o 86.43%_T8s 87.33%_J7s 89.14%_Q4s 89.14%_Q7o 90.95%_K3o 91.86%_J8o 91.86%_T9o 93.67%_Q6o 93.67%_Q3s 95.48%_22 95.48%_98s 97.29%_J6s 97.29%_T7s 97.29%_K2o 99.10%_Q2s 99.10%_Q5o 100.0%_J5s 100.0%_T8o 100.0%_J7o 100.0%_Q4o 100.0%_97s 100.0%_J4s 100.0%_T6s 100.0%_J3s 100.0%_Q3o 100.0%_98o 100.0%_87s 100.0%_T7o 100.0%_J6o 100.0%_96s 100.0%_J2s 100.0%_Q2o 100.0%_T5s 100.0%_J5o 100.0%_T4s 100.0%_97o 100.0%_86s 100.0%_J4o 100.0%_T6o 100.0%_95s 100.0%_T3s 100.0%_76s 100.0%_J3o 100.0%_87o 100.0%_T2s 100.0%_85s 100.0%_96o 100.0%_J2o 100.0%_T5o 100.0%_94s 100.0%_75s 100.0%_T4o 100.0%_93s 100.0%_86o 100.0%_65s 100.0%_84s 100.0%_95o 100.0%_T3o 100.0%_92s 100.0%_76o 100.0%_74s 100.0%_T2o 100.0%_54s 100.0%_85o 100.0%_64s 100.0%_83s 100.0%_94o 100.0%_75o 100.0%_82s 100.0%_73s 100.0%_93o 100.0%_65o 100.0%_53s 100.0%_63s 100.0%_84o 100.0%_92o 100.0%_43s 100.0%_74o 100.0%_72s 100.0%_54o 100.0%_64o 100.0%_52s 100.0%_62s 100.0%_83o 100.0%_42s 100.0%_82o 100.0%_73o 100.0%_53o 100.0%_63o 100.0%_32s 100.0%_43o 100.0%_72o 100.0%_52o 100.0%_62o 100.0%_42o 100.0%_32o *AQo is slightly undervalued by this method, and is actually stronger than 88 for 12.22% < X < 12.97% 2. Pushing Strength Groupings This part of the results is best interpreted in groupings. 3.17% {QQ+,AJs+,AKo} 9.80% {44+,ATs+,KTs+,QTs+,JTs,AQo+} 14.93% {22+,A9s+,K9s+,Q9s+,J9s+,T9s,AJo+,KJo+} 29.71% {22+,A2s+,K4s+,Q6s+,J7s+,T7s+,96s+,86s+,75s+,65s,5 4s,A8o+,KTo+,QTo+,JTo} 49.92% {22+,A2s+,K2s+,Q2s+,J4s+,T6s+,95s+,85s+,74s+,64s+, 53s+,43s,A2o+,K7o+,Q9o+,J9o+,T8o+,97o+,87o,76o} 70.14% {22+,A2s+,K2s+,Q2s+,J2s+,T2s+,92s+,83s+,73s+,62s+, 52s+,42s+,A2o+,K2o+,Q5o+,J7o+,T7o+,96o+,86o+,75o+, 65o,54o} 90.05% {22+,A2s+,K2s+,Q2s+,J2s+,T2s+,92s+,82s+,72s+,62s+, 52s+,42s+,32s,A2o+,K2o+,Q2o+,J2o+,T3o+,95o+,84o+,7 4o+,63o+,52o+,43o} (copy/paste into pokerstove to view these better) |
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