Odds of at least one player holding 72 on an 8-man table.

[FoldALot.]

While watching the new HSP episode I was wondering how often you will see hands with one player (or more) holding 72. It is 8-handed, right?

So I made some amateurish calculations and came up with 16.18%.
Maybe a probability buff can confirm this? Thanks in advance.

[jay_shark]

The probability no individual player holds 7-2 is (1326-16)/1326 . Now take this number to the 8th power and take the complement . This is a good enough approximation .

9.255% .

[BruceZ]

[ QUOTE ]
While watching the new HSP episode I was wondering how often you will see hands with one player (or more) holding 72. It is 8-handed, right?

So I made some amateurish calculations and came up with 16.18%.
Maybe a probability buff can confirm this? Thanks in advance.

[/ QUOTE ]

The exact answer, by the inclusion-exclusion principle for 72o or 72s is:

8*16/C(52,2) -
C(8,2)*16*9/C(52,2)/C(50,2) +
C(8,3)*16*9*4/C(52,2)/C(50,2)/C(48,2) -
C(8,4)*16*9*4*1/C(52,2)/C(50,2)/C(48,2)/C(46,2)

=~ 9.407% or 9.6-to-1


A good and easy approximation is:

1 - (1310/1326)^8 =~ 9.255% or 9.8-to-1