An Amazing Hand Of Poker

arvanasays...

eric3579 asked me how I got those odds, so here it is -- skip if you don't like math!

There are 5 hands. The first card dealt can be anything, but the second through fifth cards all have to be different from the previous cards dealt.

Card 2 would have odds of 48:51 since there are 51 cards left in the deck and three of them can't be dealt to Player 2, as they would have the same face value as Player 1's card.

Cards 3, 4 and 5 would similarly have odds of 44:50, 40:49 and 36:48 respectively.

When Player 1 gets dealt a second card, there are 47 cards left in the deck, and 3 that would match his first card, so his odds of getting a pair are 3:47.

Likewise, Players 2–5 have odds of 3:46, 3:45, 3:44 and 3:43.

Now, multiply all of those odds together to get the odds of 5 different pocket pairs:

<u>48</u> . <u>44</u> . <u>40</u> . <u>36</u> . <u>&nbsp;3</u> . <u>&nbsp;3</u> . <u>&nbsp;3</u> . <u>&nbsp;3</u> . <u>&nbsp;3</u>&nbsp; <sub>=</sub> <u>&nbsp;&nbsp;&nbsp;1&nbsp;&nbsp;&nbsp;</u>
51&nbsp;&nbsp; 50&nbsp;&nbsp; 49&nbsp;&nbsp; 48&nbsp;&nbsp; 47&nbsp;&nbsp; 46&nbsp;&nbsp; 45&nbsp;&nbsp; 44&nbsp;&nbsp; 43&nbsp;&nbsp;&nbsp; 1493840

jwraysays...

The number of ways for all 5 players to get different pocket pairs is (13 P 5)*((4 C 2)^5). The number of possible hands is (52 C 2)*(50 C 2)*(48 C 2)*(46 C 2)*(44 C 2). Divide the first one by the second one. The probability is 6.69*10^-7, which matches Arvana's answer.

joedirtsays...

yeah "he played good poker".. this drives me nuts. Wow the guy called with pocket Aces. That is so far from "good poker". It's like holding with A-10 in blackjack.

Anyways, your worst matchup in poker like 2-7 and A-A still means you lose 20% of the time. I fold Aces a lot more than I fold J-10 suited.

T-mansays...

I've folded aces preflop a few times but only in satellites where the top X moves on, it was close to the "money" and I was safe to move forward, and a big stack had made a significant raise before me. In that situation there is no reason to risk my stack on someone not sucking out. Aces aren't a sure thing.

messengersays...

Arvana, your odds are accurate for a table with 5 players. But there were 6 players, and thus, 6 different ways to make 5 pairs -- only 5 of the 6 cards had to hit the second time around. I think you divide your number by 6 to get the right odds, but I wouldn't hang my name on that.

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