9players
8*4 = 32 cards dealt to a full table and you get 4 of them
so theres a 28/45 chance the of Ah is out - since you know its not in your hand or the flop (52 - 4 - 3)
I think you have subtracted 4 twice? I.e. if 9 players are dealt in, there are 8 players each with 4 unknown cards, so there are 32 unknown cards not 28.
Anyway, don't use actual numbers at this stage... far better maths to assume an
n-handed game.
3 cards in the hand with the Ah (if its out)
7 hearts left in 44 remaining cards
P(one or more heart in 3 random cards) -
7/44*37/43*36/42*3 + 7/44*6/43*36/42*3 + 7/44*6/43*5/42
ITYM 7/44*37/43*36/42*3 + 7/44*6/43*37/42*3 + 7/44*6/43*5/42
multiply that by 28/45 and you get
0.256 (not 0.329) *************************
The correct calculation here is 1-((1-
h)^
n), where
n = the number of opponents, and
h = P(any given opponent holds the Ace-high flush) = 4/45*P(at least one of three cards is a heart).
You are very sloppy for a mathematician. Your homework is to calculate the corresponding probability for an
n-handed game of
m-card Omaha in which I hold the King of hearts and
k other hearts.
Well you are charming !
Yes I did this in a bit of a rush (my apologies) a 9 handed game does indeed have 9*4 cards dealt out. IMO your 'correct calculation' is likely to be of no help to anyone who can't already work out the answer, I'm actually a statistician (although you wouldn't think it from all the mistakes I managed to make, more haste less speed I guess!) and we are allowed to be sloppy because we are cleverer than mathematicians.
My methodology was just a simple a conditioning argument using,
P(nut flush out) = P(Ah dealt out)*P(nut flush out|Ah dealt out)
In order to make the calculation relatively simple. (and hopefully understandable although my rather rushed layout doesn't help with that much obviously)
If I wished to be a smartar*e I could have used up half an hour of my life working out the probability of the nut flush being out in an N-handed game of M-card Omaha but that wouldn't have been answering the question asked.
Stephen...very impressed by your first three posts Sir..welcome.
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