Ask The Wizard #54
With two arguments f(x,y)= combin(13,x)*combin(13,y)*12/combin(52,5).
With three arguments f(x,y,z)= combin(13,x)*combin(13,y)*combin(13,z)*12/combin(52,5).
With four arguments f(w,x,y,z)=combin(13,w)*combin(13,x)*combin(13,y)*combin(13,z)*4/combin(52,5).
The probability of all four suits is COMBIN(13,1)3*COMBIN(13,2)*4/combin(52,5) = 26.37%.
The probability of three suits is COMBIN(13,3)*COMBIN(13,1)2*12 + COMBIN(13,1)*COMBIN(13,2)^2*12/combin(52,5) = 58.84%
The probability of two suits is COMBIN(13,3)*COMBIN(13,2)*12 + COMBIN(13,4)*COMBIN(13,1)*12/combin(52,5) = 14.59%
The probability of one suit (including straight and royal flushes ) is 4*combin(13,5)/combin(52,5) = 0.20%.
So three suits are the most frequent outcome.
If used in blackjack, the Match Play will usually only pay even money. This decreases the value of the Match Play itself by 2.3%, which is way too much. Of the true even money bets, the best game to use a match play on in the Player bet in baccarat. That has a probability of winning of 49.32% of bets resolved. For the don’t pass in craps, that probability is 49.30%.The value of a Match Play on the Player bet is 47.95% of face value, assuming you wouldn’t have bet otherwise.