general calculations questions

[tomcain]

Hello

Some general questions to see if my rusty math understandings are correct


Pre-flop 10 handed

1. Someone has an ace - 10*(4/52) = 77%

2. Someone has an ace, if I don't - 9*(4/50) = 72%

3. 2 People have an ace - 10*(4/52) * 9*(3/51) = .77*.52 = 40%

4. 2 people have an ace, if I don't - 9*(4/50) * 8*(3/49) = .72*.49 = 35%

TIA, Tom

[chapstick]

[ QUOTE ]
Hello
Some general questions to see if my rusty math understandings are correct

Pre-flop 10 handed

1. Someone has an ace - 10*(4/52) = 77%
[\quote]

You have to be very careful. Imagine you had 13 handed table. Only 26 cards are dealt on the deal. But according to your calculation, the probability of someone having an ace would be 13*(4/52) = 100%! Clearly there is something wrong.

I get that the probability for only one person to have a single Ace at a 10 handed table is %36.6. Here's how:

There are 52 cards in the deck. 10 players, means that 20 cards are dealt. You only want one of those cards to be an ace.

The total possible ways to chose 20 of 52 is C(52,20). Of the 52 cards, 4 are aces and 48 are non-aces. The total number of combinations that have 1 ace and 19 non aces is
C(48,19)*C(4,1). So, the probabaility is

C(48,19)*C(4,1)/C(52,20) = 36.6%.

Related to this, I get that the probability of at least one ace being dealt to a 10 handed table is 86.7%.

The odds of exactly two aces being dealt out (not necessarily a pocket pair for anyone) is 34.8%, and the probabaility of three aces being dealt out is 13.47%. The probability of all four aces being dealt out is 1.8%.

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2. Someone has an ace, if I don't - 9*(4/50) = 72%
[\quote]

If you don't have an ace, then there are 50 cards left in the deck. The 9 players will get 18 cards. You want only one of them to be an Ace. There are C(50,18) ways to make the possible combinations. There are 4 ways to chose an ace (from C(4,1)). You need to choose 17 non-aces from the remaining 46 cards. So, the chances are

C(4,1)*C(46,17)/C(50,18) = 38.8%

The remaining two require more explanation. If nobody else answers them, ask them in a separate thread I'll try to get to them later.

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3. 2 People have an ace - 10*(4/52) * 9*(3/51) = .77*.52 = 40%

4. 2 people have an ace, if I don't - 9*(4/50) * 8*(3/49) = .72*.49 = 35%

TIA, Tom

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[tomcain]

Thanks for the info. I'll have to think about this more. I guess that is why my degree is in computer science instead of statistics. /images/graemlins/smile.gif