Quote:
Originally Posted by Buddha  I was wondering what the odds are for someone getting the exact same 2 cards in back to back hands. I was dealing the other day at a game, and a guy had two black nines in back to back hands from the same deck. I know the odds have got to be pretty bad for that to happen, and not sure of the math to figure it out. Anyone able to help? |
The odds are approximately 1 in a million
.
Actually, they're much better than that-- a little less than 1/1000. By my calculations (which may be inaccurate, since it's a weekend
), that will happen about 7 in every 10,000 hands. Here's my math:
The first hand doesn't matter since you're not trying to get two specific cards on the first hand-- just to duplicate it on the second hand. After the first hand, you now have determined what you need to duplicate (in this case, the two black 9's). The probability of getting one of the two cards you need dealt to you is 2/52. If that is accomplished, you only need one more card, and so the probability of getting it is 1/51. Multiply those probabilities together, and you get 2/52*1/51= 0.000754, or 7.54/10,000ths.
You can also arrive at this via the mathematics of combinations: 52!/2!(50!) yields the same result.
Of course, if you wanted to be dealt the same two cards in sequence, say the 9 of spades then the 9 of clubs (again, provided you don't care what the first two cards are, just that you are re-dealt the same two in sequence), then your probabilities drop to 0.000377.
Want two specific cards two times in a row? That's where you're about 1 in 2 million. Want two specific cards dealt in the same sequence two times in a row? You're about 1 in 10 million.
I hope this was helpful. Class dismissed.
bjjensen
