Why does (13;1)(4;2)(48;1)(44;1)(40;1) fail in calculating a pair in Poker?

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The discussion centers on the failure of the calculation method (13;1)(4;2)(48;1)(44;1)(40;1) in determining a pair in Poker. The correct calculation involves using combinations rather than permutations, as the original approach mistakenly treats different arrangements of the same hand as unique. The correct formula for calculating two pairs is (13;2)(4;2)(4;2)(48;1), but this also fails due to similar miscalculations related to Full Houses. Understanding the distinction between combinations and permutations is crucial for accurate Poker hand evaluations.

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The correct way is [tex]\left(\begin{array}{cc}13\\1\end{array}\right \left(\begin{array}{cc}4\\2\end{array}\right[/tex](12;3)(4;1)(4;1)(4;1)

But why does (13;1)(4;2)(48;1)(44;1)(40;1) fail? I would have thought that after you get the two that match there are 48 left to choose from that don't macht, and 44 that don't macht, and so on.
 
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Your approach treats QQJT9 and QQ9TJ as two different hands.

That's fine if you're counting permutations instead of combinations... but if you meant to count permutations, then you didn't count hands like JT9QQ... so you're wrong either way.
 
Hurkyl said:
Your approach treats QQJT9 and QQ9TJ as two different hands.

That's fine if you're counting permutations instead of combinations... but if you meant to count permutations, then you didn't count hands like JT9QQ... so you're wrong either way.

And so then calculating two pair I did (13;2)(4;2)(4;2)(48;1) and subtracted Full Houses. I suppose this failed for the same reason?
 

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