Yet More CP2-7 Hands

[Sweet]

[ 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!