#1
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ranking hands against \"push hands\" preflop
Most people are familiar with the following way of ranking hands:
http://www.jazbo.com/poker/huholdem.html which is win percentage against a random hand. Problem is, most people don't play random hands. They play select hands. If instead of computing these numbers against a random hand, we compute them against typical "push" hands: say any pair, or any ace, how does the list change? What hands have positive expectation against a random hand that is any pair or any ace? I did a calculation, and came up with these numbers: Gah! I can't get netscape to paste these damn numbers in. I'll post tomorrow. Anyone want to hazard a guess at what hands have +EV against any pair or any ace? Also, I want to double-check how I did the calculation. I tried to take into account the probability that your opponent holds hand X given your hole cards Y, since some possibilities are "blocked" by your holdinds. Details to come. eastbay |
#2
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Re: ranking hands against \"push hands\" preflop
From the top of my head:
I would guess that the win% of the top hands in jazbo's list will improve dramatically, while the bottom hands will lose much value. Pairs lower than 77 will lose some value, Aces with 7 kicker and below will lose value dramatically, while medium and med-high connectors will somewhat improve. For example: in their list, 55 is little better than QJs. I would say that in your list, QJs will stand better. Is this even close? |
#3
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Results are in
Ok, here's the results I'm getting when comparing against the "any pair, any ace" set of hands. These are win fractions.
AAo: 0.868701 KKo: 0.717437 QQo: 0.694589 JJo: 0.671537 TTo: 0.648316 AKs: 0.633812 99o: 0.618106 AKo: 0.615742 AQs: 0.602706 88o: 0.594209 AQo: 0.582691 AJs: 0.570817 77o: 0.568266 AJo: 0.548738 66o: 0.543522 ATs: 0.539245 55o: 0.518897 ATo: 0.515079 A9s: 0.498569 44o: 0.489243 A9o: 0.471471 A8s: 0.468405 33o: 0.45922 A8o: 0.439287 A7s: 0.439104 JTs: 0.435095 QJs: 0.432201 KQs: 0.429669 QTs: 0.428981 22o: 0.428917 KJs: 0.426322 KTs: 0.423085 T9s: 0.421997 J9s: 0.41557 A6s: 0.412231 98s: 0.410088 Q9s: 0.409378 A7o: 0.407937 T8s: 0.407644 A5s: 0.406675 JTo: 0.403909 K9s: 0.40339 87s: 0.401158 J8s: 0.401144 QJo: 0.400481 KQo: 0.397427 QTo: 0.39714 97s: 0.395388 Q8s: 0.394819 KJo: 0.393954 T7s: 0.392131 A4s: 0.391515 76s: 0.390746 KTo: 0.390595 T9o: 0.390155 K8s: 0.38856 86s: 0.386708 K7s: 0.385625 J7s: 0.385609 J9o: 0.383063 A3s: 0.381557 96s: 0.380882 K6s: 0.380852 Q7s: 0.379169 A6o: 0.379119 65s: 0.377947 98o: 0.377458 T6s: 0.377398 Q6s: 0.377175 Q9o: 0.376213 T8o: 0.374833 A5o: 0.373404 K5s: 0.372262 75s: 0.372141 A2s: 0.371275 J6s: 0.37076 K9o: 0.369575 Q5s: 0.368592 87o: 0.368155 85s: 0.36804 J8o: 0.367665 54s: 0.365187 J5s: 0.364974 K4s: 0.364348 95s: 0.362213 97o: 0.361791 Q8o: 0.360678 Q4s: 0.360674 64s: 0.359884 T5s: 0.35859 T7o: 0.358288 76o: 0.357173 A4o: 0.357137 J4s: 0.357052 K3s: 0.356324 74s: 0.353963 K8o: 0.35376 T4s: 0.353475 86o: 0.352724 Q3s: 0.352646 J7o: 0.351098 K7o: 0.350695 84s: 0.349813 J3s: 0.34902 K2s: 0.348201 53s: 0.346731 A3o: 0.346479 96o: 0.346298 K6o: 0.345598 T3s: 0.345439 Q2s: 0.344518 Q7o: 0.343993 94s: 0.34389 65o: 0.343729 T6o: 0.34255 Q6o: 0.3419 63s: 0.341299 J2s: 0.340887 93s: 0.33867 43s: 0.33766 75o: 0.337437 T2s: 0.337301 K5o: 0.336543 73s: 0.335466 A2o: 0.335453 J6o: 0.335241 85o: 0.33291 Q5o: 0.332851 83s: 0.331219 92s: 0.330518 54o: 0.330241 J5o: 0.329216 K4o: 0.328023 52s: 0.327759 95o: 0.326483 82s: 0.325903 64o: 0.324395 Q4o: 0.324329 T5o: 0.322591 62s: 0.322283 J4o: 0.320689 K3o: 0.319379 42s: 0.318872 74o: 0.31797 T4o: 0.317097 72s: 0.316582 Q3o: 0.315681 84o: 0.313391 J3o: 0.312037 K2o: 0.310618 53o: 0.310492 32s: 0.309713 T3o: 0.308441 Q2o: 0.306915 94o: 0.306866 63o: 0.304498 J2o: 0.303267 93o: 0.301252 43o: 0.3009 T2o: 0.299667 73o: 0.298163 83o: 0.293484 92o: 0.292463 52o: 0.290183 82o: 0.287756 62o: 0.284141 42o: 0.280797 72o: 0.277943 32o: 0.271115 Some notes: * good pairs and aces increase in rank vs. other pairs and aces, due to the "domination" effect. * There aren't many hands which have a win pct > 50% against a random pair or ace! The only "winners" are: AAo, KKo, QQo, JJo, TTo, AKs, 99o, AKo, AQs, 88o, AQo, AJs, 77o, AJo, 66o, ATs, 55o, ATo * If you want an edge of 70% or better, you have to wait for KK or AA. * The best hand other than an ace or pair is JTs! Maybe that old idea about JT being the "best hand" wasn't _so_ crazy. * Note the abysmal rank of A2o, which some guy at the aviation club came over the top all-in with last night on WPT... to lose. * Fossilman's semi-famous T9s play isn't far from as good as you can do if you don't have an ace or pair in front of you. Higher suited connectors are better, but not by much. * T8s ranks better than A5s! Beware dominated aces! Here's a side-by-side on the top 15 hands in each case: vs. As, pairs vs. random hand -------------|---------------| AAo: 0.868701 AAo: 0.852037 KKo: 0.717437 KKo: 0.823957 QQo: 0.694589 QQo: 0.799252 JJo: 0.671537 JJo: 0.774695 TTo: 0.648316 TTo: 0.750118 AKs: 0.633812 99o: 0.720573 99o: 0.618106 88o: 0.69163 AKo: 0.615742 AKs: 0.670446 AQs: 0.602706 77o: 0.66236 88o: 0.594209 AQs: 0.662089 AQo: 0.582691 AJs: 0.653927 AJs: 0.570817 AKo: 0.65318 77o: 0.568266 ATs: 0.646024 AJo: 0.548738 AQo: 0.644298 66o: 0.543522 AJo: 0.635612 Note how much AKo jumps up. Also note that AJs goes down in rank, but AJo goes up! Comments welcome! eastbay |
#4
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Re: ranking hands against \"push hands\" preflop
[ QUOTE ]
From the top of my head: I would guess that the win% of the top hands in jazbo's list will improve dramatically, while the bottom hands will lose much value. Pairs lower than 77 will lose some value, Aces with 7 kicker and below will lose value dramatically, while medium and med-high connectors will somewhat improve. For example: in their list, 55 is little better than QJs. I would say that in your list, QJs will stand better. Is this even close? [/ QUOTE ] Draw your own conclusions from the results I just posted. I'd say you hit some ideas correctly and missed a little with others. eastbay |
#5
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Re: Results are in
Interesting. I think the biggest surprise to me was how high JTs ranked, at least relative to KQs, QJs, KJs.
Keep in mind that as the table gets down to 2 or 3 players people will push with hands other than pairs and aces, which will change these odds around a fair bit. |
#6
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Re: Results are in
Very interesting
I think these rankings paint a far more accurate picture of what hands are good calling hands. How hard would it be for you to rank vs a random chance of a slightly more refined list of possible opposition hands I'd actually like to take some hands like A2o-A6o off the list and add some hands like KQ, KJ, and suited broadway cards Also, does this list take into account the greater likelihood that your opponent is holding AK than a pair, etc... [ QUOTE ] * There aren't many hands which have a win pct > 50% against a random pair or ace! The only "winners" are: AAo, KKo, QQo, JJo, TTo, AKs, 99o, AKo, AQs, 88o, AQo, AJs, 77o, AJo, 66o, ATs, 55o, ATo [/ QUOTE ] This is a very powerful point. I think that this point almost comes close to a suggested calling requirement against shortstacks pushing on the bubble Good Post Brad S |
#7
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Re: Results are in
[ QUOTE ]
Very interesting I think these rankings paint a far more accurate picture of what hands are good calling hands. How hard would it be for you to rank vs a random chance of a slightly more refined list of possible opposition hands I'd actually like to take some hands like A2o-A6o off the list and add some hands like KQ, KJ, and suited broadway cards [/ QUOTE ] Dirt simple. Give me any list, I'll give you the rankings. [ QUOTE ] Also, does this list take into account the greater likelihood that your opponent is holding AK than a pair, etc... [/ QUOTE ] Yes it does. This was slightly tricky to get right and there's still one point which seems "wrong" to me but it's the only way I can the probabilities to sum to unity (which is of course a necessary condition for it to be correct) Here's the case I'm confused by: when you hold an offsuit non-pair hand and your opponent holds a suited hand that matches both of your cards in rank, how many different hands can he be holding? [ QUOTE ] [ QUOTE ] * There aren't many hands which have a win pct > 50% against a random pair or ace! The only "winners" are: AAo, KKo, QQo, JJo, TTo, AKs, 99o, AKo, AQs, 88o, AQo, AJs, 77o, AJo, 66o, ATs, 55o, ATo [/ QUOTE ] This is a very powerful point. I think that this point almost comes close to a suggested calling requirement against shortstacks pushing on the bubble Good Post Brad S [/ QUOTE ] Thanks. Glad you got something out of it. eastbay |
#8
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Re: Results are in
Here's the results for:
column 1: random hand column 2: any ace, any pair column 3: aces except A6o-A20, all pairs, KQs, KJs, KTs, QJs AAo: 0.852037 AAo: 0.868701 AAo: 0.852403 KKo: 0.823957 KKo: 0.717437 KKo: 0.725878 QQo: 0.799252 QQo: 0.694589 QQo: 0.690498 JJo: 0.774695 JJo: 0.671537 JJo: 0.657249 TTo: 0.750118 TTo: 0.648316 TTo: 0.624291 99o: 0.720573 AKs: 0.633812 AKs: 0.609668 88o: 0.69163 99o: 0.618106 AKo: 0.590376 AKs: 0.670446 AKo: 0.615742 99o: 0.587292 77o: 0.66236 AQs: 0.602706 AQs: 0.57245 AQs: 0.662089 88o: 0.594209 88o: 0.557937 AJs: 0.653927 AQo: 0.582691 AQo: 0.550575 AKo: 0.65318 AJs: 0.570817 AJs: 0.536638 ATs: 0.646024 77o: 0.568266 77o: 0.526918 AQo: 0.644298 AJo: 0.548738 AJo: 0.512433 AJo: 0.635612 66o: 0.543522 66o: 0.503295 KQs: 0.634004 ATs: 0.539245 ATs: 0.500597 66o: 0.632847 55o: 0.518897 55o: 0.480924 A9s: 0.627812 ATo: 0.515079 ATo: 0.473856 ATo: 0.627196 A9s: 0.498569 A9s: 0.456724 KJs: 0.625673 44o: 0.489243 44o: 0.45548 A8s: 0.619438 A9o: 0.471471 KQs: 0.435427 KTs: 0.617886 A8s: 0.468405 33o: 0.430012 KQo: 0.614538 33o: 0.45922 A8s: 0.427111 A7s: 0.60984 A8o: 0.439287 A9o: 0.426667 A9o: 0.607708 A7s: 0.439104 KJs: 0.424205 KJo: 0.605667 JTs: 0.435095 QJs: 0.417834 55o: 0.603249 QJs: 0.432201 JTs: 0.413598 QJs: 0.602592 KQs: 0.429669 KTs: 0.412861 K9s: 0.599885 QTs: 0.428981 QTs: 0.409806 A5s: 0.599229 22o: 0.428917 22o: 0.40465 A6s: 0.599058 KJs: 0.426322 KQo: 0.404582 A8o: 0.598706 KTs: 0.423085 A7s: 0.400662 KTo: 0.597369 T9s: 0.421997 T9s: 0.40004 QTs: 0.594676 J9s: 0.41557 A8o: 0.395024 A4s: 0.590336 A6s: 0.412231 J9s: 0.394774 A7o: 0.588392 98s: 0.410088 KJo: 0.39268 K8s: 0.583123 Q9s: 0.409378 Q9s: 0.390815 A3s: 0.582203 A7o: 0.407937 K9s: 0.389992 QJo: 0.581327 T8s: 0.407644 A5s: 0.388996 K9o: 0.578099 A5s: 0.406675 98s: 0.387872 A5o: 0.576945 JTo: 0.403909 QJo: 0.386162 A6o: 0.576804 K9s: 0.40339 T8s: 0.385036 Q9s: 0.576643 87s: 0.401158 A6s: 0.384929 K7s: 0.575377 J8s: 0.401144 JTo: 0.382016 JTs: 0.575279 QJo: 0.400481 KTo: 0.380491 A2s: 0.573789 KQo: 0.397427 J8s: 0.379669 QTo: 0.572887 QTo: 0.39714 A4s: 0.379591 44o: 0.570228 97s: 0.395388 QTo: 0.377687 A4o: 0.567276 Q8s: 0.394819 87s: 0.37745 K6s: 0.566407 KJo: 0.393954 Q8s: 0.375597 K8o: 0.560181 T7s: 0.392131 K8s: 0.374595 Q8s: 0.560177 A4s: 0.391515 97s: 0.372826 A3o: 0.558426 76s: 0.390746 K6s: 0.372184 K5s: 0.557929 KTo: 0.390595 76s: 0.372178 J9s: 0.556625 T9o: 0.390155 A3s: 0.371324 Q9o: 0.553584 K8s: 0.38856 K7s: 0.370786 JTo: 0.552457 86s: 0.386708 T7s: 0.368944 K7o: 0.551853 K7s: 0.385625 86s: 0.368841 A2o: 0.549265 J7s: 0.385609 T9o: 0.36802 K4s: 0.548846 J9o: 0.383063 A7o: 0.366712 Q7s: 0.543023 A3s: 0.381557 65s: 0.366508 K6o: 0.542212 96s: 0.380882 K5s: 0.365975 K3s: 0.54055 K6s: 0.380852 96s: 0.364085 T9s: 0.540275 Q7s: 0.379169 Q6s: 0.363528 J8s: 0.540156 A6o: 0.379119 J7s: 0.363448 33o: 0.536931 65s: 0.377947 A2s: 0.362706 Q6s: 0.536126 98o: 0.377458 J9o: 0.362007 Q8o: 0.535978 T6s: 0.377398 T6s: 0.360074 K5o: 0.533119 Q6s: 0.377175 Q7s: 0.359384 J9o: 0.532492 Q9o: 0.376213 K4s: 0.358869 K2s: 0.532117 T8o: 0.374833 Q9o: 0.357511 Q5s: 0.527694 A5o: 0.373404 Q5s: 0.357398 T8s: 0.523344 K5s: 0.372262 54s: 0.356239 K4o: 0.523254 75s: 0.372141 75s: 0.356145 J7s: 0.523248 A2s: 0.371275 K9o: 0.356027 Q4s: 0.518553 J6s: 0.37076 98o: 0.355184 Q7o: 0.517636 K9o: 0.369575 J6s: 0.354933 T9o: 0.515296 Q5s: 0.368592 A5o: 0.354299 J8o: 0.514881 87o: 0.368155 85s: 0.352519 K3o: 0.514236 85s: 0.36804 T8o: 0.352024 Q6o: 0.51022 J8o: 0.367665 K3s: 0.351458 Q3s: 0.510192 54s: 0.365187 J5s: 0.351416 98s: 0.508008 J5s: 0.364974 Q4s: 0.350273 T7s: 0.50639 K4s: 0.364348 A6o: 0.349771 J6s: 0.506059 95s: 0.362213 64s: 0.34944 K2o: 0.505067 97o: 0.361791 95s: 0.347766 22o: 0.50334 Q8o: 0.360678 J8o: 0.3459 Q2s: 0.50169 Q4s: 0.360674 J4s: 0.344284 Q5o: 0.50118 64s: 0.359884 87o: 0.344273 J5s: 0.499868 T5s: 0.35859 A4o: 0.344211 T8o: 0.497192 T7o: 0.358288 K2s: 0.343822 J7o: 0.496799 76o: 0.357173 T5s: 0.343757 Q4o: 0.491256 A4o: 0.357137 Q3s: 0.342832 97s: 0.491177 J4s: 0.357052 Q8o: 0.34129 J4s: 0.490705 K3s: 0.356324 K8o: 0.339623 T6s: 0.489407 74s: 0.353963 T4s: 0.339354 J3s: 0.482316 K8o: 0.35376 97o: 0.33917 Q3o: 0.482174 T4s: 0.353475 53s: 0.338841 98o: 0.48095 86o: 0.352724 74s: 0.338648 87s: 0.479363 Q3s: 0.352646 76o: 0.338626 T7o: 0.479061 J7o: 0.351098 K6o: 0.336951 J6o: 0.478422 K7o: 0.350695 J3s: 0.336835 96s: 0.474283 84s: 0.349813 K7o: 0.335606 J2s: 0.473782 J3s: 0.34902 A3o: 0.335351 Q2o: 0.472934 K2s: 0.348201 Q2s: 0.335165 T5s: 0.472163 53s: 0.346731 84s: 0.335088 J5o: 0.471789 A3o: 0.346479 86o: 0.334934 T4s: 0.465305 96o: 0.346298 T7o: 0.334884 97o: 0.462958 K6o: 0.345598 65o: 0.332685 86s: 0.462433 T3s: 0.345439 T3s: 0.331932 J4o: 0.461843 Q2s: 0.344518 63s: 0.331813 T6o: 0.4609 Q7o: 0.343993 43s: 0.330534 95s: 0.457219 94s: 0.34389 K5o: 0.330441 T3s: 0.456925 65o: 0.343729 94s: 0.330436 76s: 0.453718 T6o: 0.34255 96o: 0.329697 J3o: 0.452735 Q6o: 0.3419 J2s: 0.329159 87o: 0.450488 63s: 0.341299 J7o: 0.328611 T2s: 0.448395 J2s: 0.340887 Q6o: 0.328314 85s: 0.44545 93s: 0.33867 A2o: 0.326099 96o: 0.444893 43s: 0.33766 93s: 0.325807 J2o: 0.443464 75o: 0.337437 T6o: 0.325271 T5o: 0.442489 T2s: 0.337301 T2s: 0.324283 94s: 0.43862 K5o: 0.336543 Q7o: 0.32402 75s: 0.436755 73s: 0.335466 K4o: 0.322831 T4o: 0.435021 A2o: 0.335453 54o: 0.321911 93s: 0.432643 J6o: 0.335241 Q5o: 0.321886 86o: 0.432389 85o: 0.33291 75o: 0.321674 65s: 0.431334 Q5o: 0.332851 52s: 0.320948 84s: 0.427016 83s: 0.331219 73s: 0.320877 95o: 0.426671 92s: 0.330518 J6o: 0.319385 T3o: 0.425925 54o: 0.330241 92s: 0.318174 92s: 0.424152 J5o: 0.329216 85o: 0.317667 76o: 0.423207 K4o: 0.328023 83s: 0.317427 74s: 0.418493 52s: 0.327759 J5o: 0.315777 T2o: 0.416663 95o: 0.326483 K3o: 0.314888 54s: 0.414534 82s: 0.325903 64o: 0.314505 85o: 0.414255 64o: 0.324395 Q4o: 0.314258 64s: 0.413333 Q4o: 0.324329 62s: 0.313897 83s: 0.408735 T5o: 0.322591 42s: 0.312957 94o: 0.40669 62s: 0.322283 82s: 0.312573 75o: 0.405099 J4o: 0.320689 95o: 0.31243 82s: 0.402716 K3o: 0.319379 J4o: 0.308142 73s: 0.400359 42s: 0.318872 T5o: 0.307999 93o: 0.400175 74o: 0.31797 K2o: 0.306695 65o: 0.399423 T4o: 0.317097 Q3o: 0.306286 53s: 0.39693 72s: 0.316582 32s: 0.304503 63s: 0.395336 Q3o: 0.315681 53o: 0.303372 84o: 0.394448 84o: 0.313391 T4o: 0.303309 92o: 0.390959 J3o: 0.312037 74o: 0.303023 43s: 0.386419 K2o: 0.310618 72s: 0.302883 74o: 0.385478 53o: 0.310492 J3o: 0.300162 72s: 0.381559 32s: 0.309713 84o: 0.299082 54o: 0.381532 T3o: 0.308441 Q2o: 0.298062 64o: 0.380084 Q2o: 0.306915 63o: 0.295713 52s: 0.378493 94o: 0.306866 T3o: 0.295358 62s: 0.37669 63o: 0.304498 43o: 0.294601 83o: 0.374818 J2o: 0.303267 94o: 0.29395 42s: 0.36829 93o: 0.301252 J2o: 0.291929 82o: 0.368256 43o: 0.3009 93o: 0.289012 73o: 0.366002 T2o: 0.299667 T2o: 0.287156 53o: 0.362627 73o: 0.298163 52o: 0.284284 63o: 0.360756 83o: 0.293484 73o: 0.284069 32s: 0.359844 92o: 0.292463 92o: 0.280829 43o: 0.351438 52o: 0.290183 83o: 0.280242 72o: 0.345816 82o: 0.287756 62o: 0.2766 52o: 0.342826 62o: 0.284141 42o: 0.275857 62o: 0.340731 42o: 0.280797 82o: 0.275057 42o: 0.331977 72o: 0.277943 32o: 0.266933 32o: 0.323012 32o: 0.271115 72o: 0.264864 eastbay |
#9
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Re: Results are in
great info. printed off and tucked into my poker binder already
Thanks Brad S |
#10
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NIcely formatted chart of the same numbers
http://rwa.homelinux.net/poker/hand-rankings.html
Notice our friend at the bottom of the rankings for the "refined set" of push hands, set C. [img]/images/graemlins/wink.gif[/img] eastbay |
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