#1
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Heads up problem vs blind man....
The statistics regarding the values of hands heads up vs two random cards got me thinking.
Many here will know the old one about a NL heads up game with no blinds and one player goes all-in blind every hand, what are his opponents chances of winning, and what is his best strategy. Answer, wait for aces, 84.9% (since a tied pot puts you back where you were) But what about a more real scenario, Ive kept the numbers limited to make it easier to discuss. Blinds 1/1, Stack 50/50 One player goes all in blind every hand, what is best strategy for opponent. Some hands that you might want to play with chances of winning: AA 84.9 KK 82.1 QQ 79.6 JJ 77.2 TT 74.7 99 71.7 AKs 66.2 The full table can be foundhere Remember, each time you fold, you effectively have 1% less chance of winning, so the best result will come from the %age of hands you are willing to play crossed with the %chance of winning the pot, and I can't quite figure it out. What I am pretty sure of is that the result will be a little scary for those who insist that morons should never win. Lori |
#2
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Re: Heads up problem vs blind man....
Lorinda, I think I have the answer. I have put my guess at the optimal strategy into the table below. Column 1 is the number of chips in front of the opponent. Column 2 is the weakest hand the opponent should play with that number of chips. Column 3 is the number of hands that are equal to or better than the weakest hand. Column 4 is the probability that the opponent will win with that number of chips using this strategy. There were two surprises in this table for me. First, I did not expect the opponent to play lots of hands when he held most of the chips. I guess the opponent just wants to put the small stack allin, even with inferior cards, just hoping to end the game. Second, I was surprised that the expert player beats the wild player only 61% of the time when they both start with 50. Irchan's Guess at the Optimal Strategy <pre><font class="small">code:</font><hr> Chips WHnd #hnd ProbWin 1 32o 169 0.015 2 32o 169 0.031 3 52o 166 0.047 4 52s 155 0.062 5 83s 139 0.078 6 T3o 129 0.093 7 96o 119 0.108 8 T3s 113 0.123 9 T5s 106 0.139 10 87s 101 0.154 11 Q4o 95 0.168 12 T8o 91 0.182 13 T7s 85 0.196 14 Q6o 82 0.21 15 22 80 0.223 16 Q4s 77 0.237 17 K4o 75 0.251 18 Q5s 72 0.265 19 K2s 71 0.278 20 K3s 66 0.291 21 T9s 63 0.303 22 A2o 60 0.316 23 A2o 60 0.328 24 K5s 56 0.339 25 Q9o 55 0.350 26 A3o 54 0.362 27 K8o 52 0.373 28 K8o 52 0.385 29 K8o 52 0.396 30 A4o 50 0.408 31 A4o 50 0.42 32 A4o 50 0.432 33 A2s 48 0.444 34 A2s 48 0.455 35 A5o 47 0.466 36 QTo 45 0.477 37 44 40 0.488 38 K9o 39 0.498 39 QJo 37 0.508 40 A4s 36 0.518 41 A4s 36 0.528 42 A4s 36 0.538 43 A7o 35 0.548 44 A5s 34 0.557 45 A5s 34 0.567 46 QTs 33 0.576 47 A6s 32 0.585 48 A6s 32 0.593 49 88 28 0.602 50 88 28 0.61 51 A6s 32 0.619 52 A5s 34 0.628 53 A5s 34 0.638 54 A4s 36 0.647 55 A4s 36 0.657 56 K9o 39 0.667 57 K9o 39 0.677 58 JTs 43 0.687 59 QTo 45 0.697 60 A5o 47 0.707 61 A5o 47 0.716 62 A5o 47 0.726 63 A5o 47 0.735 64 A2s 48 0.744 65 A2s 48 0.753 66 A4o 50 0.762 67 A4o 50 0.771 68 A4o 50 0.78 69 A4o 50 0.788 70 A4o 50 0.796 71 K8o 52 0.804 72 K8o 52 0.812 73 A3o 54 0.820 74 Q9o 55 0.827 75 Q9o 55 0.834 76 K5s 56 0.841 77 K7o 58 0.848 78 A2o 60 0.856 79 K6o 65 0.863 80 Q6s 68 0.871 81 K2s 71 0.878 82 Q5s 72 0.886 83 K4o 75 0.893 84 Q4s 77 0.9 85 22 80 0.908 86 Q3s 83 0.914 87 T7s 85 0.921 88 K2o 87 0.927 89 T8o 91 0.933 90 Q4o 95 0.939 91 T5s 106 0.946 92 T3s 113 0.952 93 J2o 121 0.959 94 75s 125 0.964 95 85o 136 0.97 96 52s 155 0.976 97 62o 167 0.982 98 32o 169 0.988 99 32o 169 0.994 </pre><hr> (For example, if the opponent had 71 chips in front of him before the game and the wild player raises allin, then the opponent should call with the best 52 hands = AA KK QQ JJ TT 99 AKs 77 AQs AKo AJs ATs AQo 66 AJo KQs ATo A9s KJs KTs A8s KQo 55 A7s A9o KJo QJs 88 K9s KTo A8o A6s QTs A5s A7o A4s QJo K8s K9o 44 A3s Q9s JTs A6o QTo K7s A5o A2s K6s A4o Q8s and K8o. If the opponent uses the strategy above, he will win 80.4% of the time with 71 chips.) Comments ? Cheers, irchans ( Cross posted on 2+2, rec.gambling.poker, and pokermonster ) |
#3
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What old one ?
Many here will know the old one about a NL heads up game with no blinds and one player goes all-in blind every hand, what are his opponents chances of winning, and what is his best strategy.
Call w/ every hand that has a pot equity of 50 % (or better) - that is J5s (or better). If there are blinds - you should call even more. |
#4
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Re: What old one ?
If there are no blinds, then calling with J5s+ or better has the highest expectation per hand.
If there are no blinds and each player has a finite stack size, then the strategy of calling with AA only maximizes the probability that you take all of the other guy's money. This is true in spite of the fact that you have less expectation per hand. |
#5
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Re: What old one ?
Thanks Irchans, great reply and great work, I will now be able to look for some kind of "counter" to this, and hopefully won't find one [img]/forums/images/icons/laugh.gif[/img]
61% is around what I had guessed (65%) and shows that the all-in strategy is a pretty strong one. Just out of interest, was it a computer sim, or did you use some formula to devise how to do it? If there are no blinds and each player has a finite stack size, then the strategy of calling with AA only maximizes the probability that you take all of the other guy's money. This is true in spite of the fact that you have less expectation per hand. Hence the reason that tourney players and ring players are very different animals. Lori |
#6
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Re: What old one ?
Hence the phrase "Never give a sucker an even break"
Lori |
#7
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and in tourneys with huge blinds...?
so how can this be practically applied to nl toyrneys with very high blinds at the end to determine the correct mathematical strategy for moving all in with hand x against one (or more) opponents with y times the amount of total blinds in their stack? Is this a good way to approach the question?
See my post in general theory 'the math of moving all in' as theres more specific questions there. fly me to vegas, jack |
#8
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Re: Heads up problem vs blind man....
infinitgames@yahoo.com (Irchans) wrote in message
> Lorinda: (edited) > >Blinds 1/1, Stack 50/50 > >One player goes all in blind every hand, what is best strategy for opponent. > > > >The full table can be found here > http://gocee.com/poker/he_ev_wins.html > > I think I have the answer. I have put my guess at the optimal strategy into > the table below. Column 1 is the number of chips in front of the opponent. > Column 2 is the weakest hand the opponent should play with that number of > chips. Column 3 is the number of hands that are equal to or better than > the weakest hand. Column 4 is the probability that the opponent will win > with that number of chips using this strategy. > > Irchan's Guess at the Optimal Strategy > [wrong table deleted] Oops. Barbara Yoon found a mistake in the original post. Here is the corrected table: <pre><font class="small">code:</font><hr> Chips WHnd #hnd ProbWin 1 32o 169 0.016 2 32o 169 0.031 3 62o 167 0.047 4 52s 155 0.062 5 75o 140 0.078 6 65s 128 0.094 7 T2s 118 0.109 8 T6o 112 0.124 9 J5o 107 0.139 10 87s 101 0.154 11 T6s 96 0.169 12 J5s 90 0.183 13 J6s 85 0.196 14 K3o 80 0.210 15 K3o 80 0.224 16 Q7o 77 0.237 17 K4o 75 0.251 18 Q5s 72 0.265 19 K2s 71 0.278 20 33 66 0.291 21 K3s 63 0.303 22 A2o 60 0.316 23 A2o 60 0.328 24 Q9o 56 0.339 25 J9s 55 0.350 26 K5s 54 0.362 27 K8o 52 0.373 28 K8o 52 0.385 29 K8o 52 0.396 30 K6s 50 0.408 31 K6s 50 0.420 32 K6s 50 0.432 33 44 48 0.444 34 44 48 0.455 35 QTo 47 0.467 36 K7s 45 0.478 37 K9o 40 0.488 38 QJo 39 0.498 39 K8s 37 0.508 40 A7o 36 0.519 41 A7o 36 0.528 42 A7o 36 0.538 43 A4s 35 0.548 44 QTs 34 0.558 45 QTs 34 0.567 46 KTo 33 0.576 47 A5s 32 0.585 48 A5s 32 0.593 49 QJs 28 0.602 50 QJs 28 0.611 51 A5s 32 0.619 52 QTs 34 0.628 53 QTs 34 0.638 54 A7o 36 0.648 55 A7o 36 0.657 56 QJo 39 0.667 57 QJo 39 0.677 58 A5o 43 0.687 59 K7s 45 0.697 60 QTo 47 0.707 61 QTo 47 0.717 62 QTo 47 0.726 63 QTo 47 0.735 64 44 48 0.744 65 44 48 0.753 66 K6s 50 0.762 67 K6s 50 0.771 68 K6s 50 0.780 69 K6s 50 0.788 70 K6s 50 0.796 71 K8o 52 0.804 72 K8o 52 0.812 73 K5s 54 0.820 74 J9s 55 0.827 75 J9s 55 0.834 76 J9s 55 0.841 77 K7o 58 0.848 78 A2o 60 0.856 79 J8s 65 0.863 80 Q6s 68 0.871 81 K2s 71 0.878 82 Q5s 72 0.886 83 K4o 75 0.893 84 Q7o 77 0.900 85 K3o 80 0.908 86 98s 83 0.914 87 K2o 86 0.921 88 Q2s 88 0.927 89 J7o 92 0.933 90 T6s 96 0.940 91 J5o 107 0.946 92 95s 114 0.952 93 85s 120 0.959 94 93s 126 0.965 95 85o 137 0.970 96 62s 156 0.976 97 42o 168 0.982 98 32o 169 0.988 99 32o 169 0.994 </pre><hr> (For example, if the opponent had 71 chips in front of him before the game and the wild player raises allin, then the opponent should call with the best 52 hands. The best 52 hands are all the hands better than or equal to K8o. If the opponent uses the strategy above, he will win 80.4% of the time with 71 chips.) The best hands in order are : AA KK QQ JJ TT 99 88 AKs 77 AQs AJs AKo ATs AQo AJo KQs 66 A9s ATo KJs A8s KTs KQo A7s A9o KJo 55 QJs K9s A8o A6s A5s KTo QTs A4s A7o K8s A3s QJo K9o Q9s A6o A5o JTs K7s A2s QTo 44 A4o K6s Q8s K8o A3o K5s J9s Q9o JTo K7o K4s A2o Q7s K6o K3s T9s J8s 33 Q8o Q6s J9o K5o K2s Q5s J7s T8s K4o Q4s Q7o T9o J8o K3o Q6o Q3s 98s T7s J6s K2o 22 Q2s Q5o J5s T8o J7o 97s J4s Q4o T6s J3s Q3o 98o T7o 87s J6o J2s 96s Q2o T5s J5o T4s 97o J4o 86s T6o T3s 95s 76s J3o 87o T2s 96o 85s J2o T5o 94s 75s T4o 93s 86o 65s 84s 95o T3o 92s 76o 74s T2o 54s 85o 64s 94o 75o 82s 83s 93o 73s 65o 53s 63s 84o 92o 43s 74o 72s 54o 64o 52s 62s 83o 82o 42s 73o 53o 63o 32s 43o 72o 52o 62o 42o 32o Thanks again to Barbara. Cheers, Irchans |
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