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SwissPoker
05-14-2005, 09:18 PM
1. I was wondering how Mike Caro arrives at 2592 combinations to Aces-up in 5draw (no joker) when drawing 3 to 2 aces?

I tried to figure it like this:

pair combinations (3 ranks with 3 cards): 3 * C(3,2) * 45 = 3 * 3 * 45 = 405
pair combinations (9 ranks with 4 cards): 9 * C(4,2)* 45 = 9 * 6 * 45 = 2430

for a total of 2835 two pair combinations

What am I doing wrong?

2. I tried to figure how Mike Caro arrives at 1854 combinations to 3-Aces in 5draw (no joker) when drawing 3 to 2 aces?

I tried to figure it like this:

no pair combinations (3 ranks with 3 cards): 3 * C(3,2) = 3 * 3 = 9
no pair combinations (9 ranks with 4 cards): 4 * C(9,2) = 4 * 36 = 144

What am I doing wrong? And how do I arrive at the exact combinations?

Thanks for any help.

gaming_mouse
05-14-2005, 09:57 PM
[ QUOTE ]
1. I was wondering how Mike Caro arrives at 2592 combinations to Aces-up in 5draw (no joker) when drawing 3 to 2 aces?

I tried to figure it like this:

pair combinations (3 ranks with 3 cards): 3 * C(3,2) * 45 = 3 * 3 * 45 = 405
pair combinations (9 ranks with 4 cards): 9 * C(4,2)* 45 = 9 * 6 * 45 = 2430

for a total of 2835 two pair combinations

What am I doing wrong?

[/ QUOTE ]

I don't follow what you are doing. But I get:

12 non-ace ranks, each with 6 (4 choose 2) possible pairs. Each of those pairs can have any of 44 possible kickers. Thus:

12*6*44 = 3186

which does not agree with either answer. Am I misunderstanding the question? I am counting the number of 3-card draws you can pull which, along with the aces you already hold, will give you 2 pair.

[ QUOTE ]
2. I tried to figure how Mike Caro arrives at 1854 combinations to 3-Aces in 5draw (no joker) when drawing 3 to 2 aces?

[/ QUOTE ]

2*( (48 choose 2) - 12*6) = 2112

Siegmund
05-15-2005, 01:15 AM
Three cards, each presumably of a different rank, have hit the muck.

gaming_mouse has ignored these 3 cards entirely, and given the odds for being dealt 2 pair if your first two cards are aces. The OP took these 3 cards into account only for pairing and not for kickers.

For a rank you discarded, there are 3 possible pairs and *42* possible kickers (the kicker can't make a full house and it can't be one of the other two cards you've already mucked.)

For the other nine ranks, there are 6 possible pairs and *41* kickers.

3*3*42 + 9*6*41 = 378+2214=2592.

To draw 3 aces: there are 2 aces and 45 non-aces left in the deck...

2*45C2 = 2*990 = 1980

...but of those 45C2 odd cards, 3*3+9*6 of them would make a full house. 2* (990-63) = 2 * 927 = 1854.

SwissPoker
05-15-2005, 02:11 PM