#11
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Re: Yet More CP2-7 Hands
[ QUOTE ]
I was surprised to see the *boats* at 64% instead of 74%, is that right? [/ QUOTE ] Err, sorry. Completely missed what you where getting at. The right number is really 64%. Sixes full would normally only be 70th percentile in back, but when we take the dead cards (from our hand) into account our opponent will have a better hand 36% of the time: <font class="small">Code:</font><hr /><pre> full house Fives full , 2077 , 0.642789 full house Nines full , 7666 , 0.703015 full house Jacks full , 9208 , 0.775356 full house Queens full , 9333 , 0.848679 full house Kings full , 9034 , 0.919653 full house Aces full , 2869 , 0.942193 quad Deuces , 1073 , 0.950623 quad Threes , 1059 , 0.958943 quad Nines , 998 , 0.966783 quad Jacks , 981 , 0.974491 quad Queens , 1012 , 0.982441 quad Kings , 975 , 0.990101 straight flush Six-high , 217 , 0.991806 straight flush Jack-high , 198 , 0.993361 straight flush Queen-high , 174 , 0.994728 straight flush King-high , 399 , 0.997863 straight flush Ace-high , 272 , 1.000000 </pre><hr /> |
#12
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Re: Yet More CP2-7 Hands
[ QUOTE ]
[ QUOTE ] I was surprised to see the *boats* at 64% instead of 74%, is that right? [/ QUOTE ] Err, sorry. Completely missed what you where getting at. The right number is really 64%. Sixes full would normally only be 70th percentile in back, but when we take the dead cards (from our hand) into account our opponent will have a better hand 36% of the time: <font class="small">Code:</font><hr /><pre> full house Fives full , 2077 , 0.642789 full house Nines full , 7666 , 0.703015 full house Jacks full , 9208 , 0.775356 full house Queens full , 9333 , 0.848679 full house Kings full , 9034 , 0.919653 full house Aces full , 2869 , 0.942193 quad Deuces , 1073 , 0.950623 quad Threes , 1059 , 0.958943 quad Nines , 998 , 0.966783 quad Jacks , 981 , 0.974491 quad Queens , 1012 , 0.982441 quad Kings , 975 , 0.990101 straight flush Six-high , 217 , 0.991806 straight flush Jack-high , 198 , 0.993361 straight flush Queen-high , 174 , 0.994728 straight flush King-high , 399 , 0.997863 straight flush Ace-high , 272 , 1.000000 </pre><hr /> [/ QUOTE ] I find this short table very philosophically significant. I am shocked to see 9s full at 70% as opposed to its usual 80%. It sort of quantifies how drastically the hand values change based on the cards you have in your hand. If realizing there is a shift in values is step 1, then certainly quantifying it is step 2. I would love to see more little tables like this one, where we can see the skew in one (or more) of the expected distributions of the opponents three hands based on the cards we hold. Any more interesting examples? Extreme examples? Examples with almost no skew? I always feel like have a long flush or a short suit makes it more likely for my opponent to have a flush in back... how right or wrong am I? How much does the front skew when we have no aces? Thanks! |
#13
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Re: Yet More CP2-7 Hands
Gritter for president.
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#14
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Re: Yet More CP2-7 Hands
Is there a hand that I can have that shifts the percentile of some possible front, middle, or back hand of my opponent by more than 20%? More than 15%?
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#15
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Re: Yet More CP2-7 Hands
Yes. Here are a couple examples:
Distribution of original 10M-hand middles: 0.050031, pair of Deuces KQT kickers 0.100094, A9876 0.150148, KT765 0.200120, QT976 0.250363, JT984 0.300508, J9852 0.351011, J6542 0.400702, T9642 0.451190, T7654 0.503044, 98753 0.550943, 98542 0.603604, 97542 0.655556, 95432 0.706090, 87632 0.757198, 87432 0.813030, 86532 0.857918, 85432 0.916812, 76532 0.951128, 76432 Distribution of middles after removing 2c2s2h3c3s3h4c4s4h5c5s5h7d: 0.050008, pair of Tens J76 kickers 0.100024, pair of Sevens 965 kickers 0.150118, AKT75 0.200172, AJ987 0.250353, KQT98 0.300345, KJ987 0.350071, K9765 0.400141, QJ954 0.450219, QT873 0.500447, Q8654 0.550603, JT872 0.600439, J9863 0.650188, J7654 0.700188, T9764 0.750282, T8754 0.805085, 98763 0.852758, 98642 0.900799, 96532 0.952053, 87542 This is a more than 20% shift in 87542. (Incidentally, the best setting for those cards is 55544 22247 333, which loses 0.87 points on average. 34455 23457 223 loses 1.63 points instead.) Second example, original front distribution: 0.051687, QJT 0.106333, KQJ 0.151715, AQ3 0.200677, AK8 0.252720, AKQ 0.300212, pair of Eights Six kicker 0.350101, pair of Tens Four kicker 0.400430, pair of Jacks Seven kicker 0.452320, pair of Queens Three kicker 0.509109, pair of Queens King kicker 0.552476, pair of Kings Five kicker 0.601870, pair of Kings Jack kicker 0.676056, pair of Kings Ace kicker 0.706992, pair of Aces Six kicker 0.772863, pair of Aces Jack kicker 0.808908, pair of Aces Queen kicker 0.870549, pair of Aces King kicker 0.912963, trip Fours 0.951167, trip Sevens Distribution after removing AAAKKKQQJJTT9 0.051001, T82 0.100480, J98 0.151278, Q92 0.200873, QJ6 0.251219, KJ4 0.300369, A65 0.351558, AQ6 0.400184, pair of Deuces Five kicker 0.451209, pair of Fives Queen kicker 0.502008, pair of Sevens Nine kicker 0.555665, pair of Eights Queen kicker 0.601940, pair of Nines Queen kicker 0.651645, pair of Jacks Five kicker 0.701717, pair of Queens Five kicker 0.793120, trip Deuces 0.835685, trip Threes 0.875156, trip Fours 0.909324, trip Fives 0.966090, trip Sevens QQ6 moves from < 50th percentile to 70. |
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