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#1
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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) |
#2
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Re: (Theory) Tournament Hand Rankings v1
Here is the full list of Player1's "pushing strength" hand ranking system.
I include this for interest. These rankings should not be directly applied because this set of hand rankings is derived from a very specific and tailored counter-range which makes it less suitable for comparing relative hand strength. The X% on the left is the tightest range that includes the corresponding hand. X%_____Hand 0.45%__AA 0.90%__KK 1.21%__AJs 1.51%__AQs 1.81%__AKs 2.71%__AKo 3.17%__QQ 3.47%__KQs 3.92%__66 4.37%__55 4.83%__JJ 5.13%__QJs 5.58%__77 6.03%__TT 6.49%__99 7.39%__AQo 7.69%__ATs 7.99%__QTs 8.30%__KJs 8.60%__JTs 8.90%__KTs 9.35%__88 9.80%__44 10.71%_KQo 11.01%_J9s 11.92%_KJo 12.22%_T9s 12.52%_K9s 12.97%_33 13.42%_22 14.33%_AJo 14.63%_Q9s 14.93%_A9s 15.23%_T8s 15.54%_98s 15.84%_A5s 16.14%_K8s 16.44%_A8s 16.74%_K6s 17.04%_Q8s 17.35%_K5s 17.65%_A4s 17.95%_K7s 18.25%_J8s 18.55%_87s 19.46%_ATo 19.76%_A7s 20.06%_97s 20.97%_QJo 21.27%_76s 22.17%_JTo 22.47%_A3s 22.78%_86s 23.08%_T7s 23.38%_J7s 23.68%_65s 23.98%_A2s 24.28%_54s 24.59%_A6s 25.49%_A9o 26.40%_A8o 27.30%_QTo 27.60%_75s 27.90%_K4s 28.81%_KTo 29.11%_Q7s 29.41%_Q6s 29.71%_96s 30.62%_A7o 31.52%_A5o 32.43%_T9o 32.73%_T6s 33.03%_K3s 33.33%_Q5s 34.24%_J9o 35.14%_A4o 35.44%_64s 36.35%_A6o 37.25%_A3o 38.16%_A2o 39.06%_Q9o 39.37%_85s 40.27%_98o 40.57%_J6s 40.87%_K2s 41.18%_95s 42.08%_K9o 42.38%_Q4s 42.68%_J5s 42.99%_53s 43.29%_Q3s 44.19%_T8o 45.10%_87o 45.40%_Q2s 45.70%_74s 46.00%_J4s 46.30%_43s 47.21%_97o 48.11%_76o 49.02%_K8o 49.92%_K7o 50.23%_63s 51.13%_J8o 51.43%_J3s 51.73%_T5s 52.64%_Q8o 53.54%_K6o 53.85%_84s 54.15%_J2s 55.05%_86o 55.35%_52s 56.26%_K5o 57.16%_65o 57.47%_T4s 58.37%_K4o 59.28%_T7o 59.58%_T3s 59.88%_T2s 60.18%_73s 60.48%_94s 60.78%_93s 61.69%_75o 62.59%_54o 63.50%_K3o 64.40%_96o 65.31%_Q7o 66.21%_K2o 66.52%_42s 67.42%_Q6o 68.33%_J7o 68.63%_62s 69.53%_Q5o 69.83%_92s 70.14%_83s 70.44%_82s 70.74%_32s 71.64%_85o 72.55%_Q4o 73.45%_T6o 74.36%_64o 74.66%_72s 75.57%_J5o 76.47%_J6o 77.38%_Q3o 78.28%_74o 79.19%_53o 80.09%_95o 81.00%_Q2o 81.90%_J4o 82.81%_43o 83.71%_T5o 84.62%_63o 85.52%_J3o 86.43%_T4o 87.33%_84o 88.24%_J2o 89.14%_T3o 90.05%_52o 90.95%_94o 91.86%_T2o 92.76%_73o 93.67%_42o 94.57%_93o 95.48%_92o 96.38%_62o 97.29%_83o 98.19%_82o 99.10%_32o 100.0%_72o Notice the %'s on the left here also correspond to the % ranges in the first hand rankings chart so you can work out the (near) optimal push/call combinations for Player1 and Player2. |
#3
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Re: (Theory) Tournament Hand Rankings v1
I cross-posted this in the Poker Theory Forum, with just a little more info on the method I used:
http://forumserver.twoplustwo.com/showfl...c=#Post11320771 |
#4
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Re: (Theory) Tournament Hand Rankings v1
How is this applicable?
Ie, when are we playing without blinds? Also, when does cEV trump $EV? |
#5
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Re: (Theory) Tournament Hand Rankings v1
When I say there is no blinds I mean its like a cash game with no blinds, the caller needs at least 50% equity.
It's not based on cEV, It's based on EV according to ICM for specific bubble/blind size conditions: "when the effect of the bubble is exactly counteracted by the size of the blinds" making the push/call tournament game analogous to a push/call cash game with no blinds. Stack sizes, blind sizes and opponents ranges all change relative hand strength. Repeating this ranking method for different threshold% values can account for different blind/stack sizes. Opponents push range is also incorporated in the Calling Strength hand rankings, It's the % on the left. My Pushing Strength hand rankings however are not applicable and are simply theoretical, they assume your opponent calls optimally and that they know your range exactly. As groupings I think they can be used as rough guidelines. Edit: I also gave an example in my OP where BB should exactly follow my calling strength hand ranking system. |
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