Re: unique showdown probabilities for two preflop hand matchups
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There are 1326 possible preflop hands. There are roughly 1326^2 total preflop matchups (some of which are invalid because they share a card).
There are then roughly 1.7M entries in a full win/lose/tie matchup matrix.
Clearly some of these are equivalent. For example, AhTs vs. KhTs has exactly the same w/l/t breakdown as AcTh vs. KcTh, because both the rank and suit relationships are the same.
Q1: How many unique showdown probabilities are there for every possible two-hand matchup?
eastbay
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Is this what you're looking for. Here it is only for when both sides are suited
There are 78 different ABs hands you can make.
If Player A has ABs, Player B can only make 55 different suited hands of the same suit.
78*78 (ABs v CDs where suits are different) + 78*55 (ABs v CDs where suits are same). = 10374 different probabilities for suited v suited.
Obviously there are many 50%'s (KTs v KTs, KJs v KJs, etc) bt they are really different probabilities. I assume you want them seperate.
Suited v Unsuited+Unpaired
78(#suited)*78(#off and not of suited's suit) + 78*66(#off where Card A is of suited's suit) + 78*66 (#off where Card B is off suited's suit) = 16380. It's highly possible there a divide or multiply by 2 error in there, although I suspect I possibly got it right by accident.
Suited v Pairs
78*13(#pairs with none of suited's suit)+78*11 (#pairs with one of suited's suit) = 1872
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