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Poker/Odds Question

Skeptical Greg

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Skeptical Greg
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I'm too lazy to figure this out myself, but it goes like this.

When I'm logging into an on-line poker game -Texas Holdem- , they
throw little ' factoids ' onto the screen while it's loading.

One I see a lot is " The chance of being dealt pocket Aces is 220 to 1.. "

Correct number or not, wouldn't the odds of being dealt any pocket pair be the same?
 
Are you remembering it slightly off? Shouldn't it be 221 to 1?

(52 x 51) / (4 x 3)

And yes, it is the same for any specific pocket pair.
 
Peregrinus said:
When and why did these folks stop playing real poker? :confused:
Click to expand...


That would be 1997 - the year the "pocket cam" was invented. Before that, watching poker could be deadly boring. Once people were able to see the hole cards of each player, the game became far more interesting to watch. The poker variant which was the easiest to follow was Texas Hold 'Em. Once more people started to watch Hold 'Em, more people started to play it.

Also important in popularizing the game was "Celebrity Poker Showdown," a tv show where celebrities played Hold 'Em.
 
Molinaro said:
Are you remembering it slightly off? Shouldn't it be 221 to 1?

(52 x 51) / (4 x 3)

And yes, it is the same for any specific pocket pair.
Click to expand...
They are using sloppy language. The probability of being dealt with pocket aces (which is more exciting than being dealt pocket twos) is 1/221.

There are 6 ways that you can be dealt pocket aces and 1320 ways of NOT being dealt pocket aces (a total of 1326 ways of being dealt 2 cards). So the odds against being dealt pocket aces is 1320 to 6 or 220 to 1.

The odds against being dealt any pocket pair is 33 to 1.
 
psionl0 said:
The odds against being dealt any pocket pair is 33 to 1.
Click to expand...


The odds are 16:1. Did you forget to divide by 2 somewhere in your calculation?

Code: 
# probability of being dealt a pair
p <- 13 * choose(4,2) / choose(52,2)
# [1] 0.05882353

# odds against p
(1 - p) / p
# [1] 16
 
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Peregrinus said:
When and why did these folks stop playing real poker? :confused:
Click to expand...

I figure the "texas" part of the name was because it has a bigger table- more players from the deck of 52.

But somehing about the odds is different. I used to be pretty good at other games, not I'm worth a dam at Hold'em. I THINK it's because with those common cards, the hands are closer together? The odds of the hands are the same, but it's a closer race between finishers?
 
casebro said:
But somehing about the odds is different. I used to be pretty good at other games, not I'm worth a dam at Hold'em. I THINK it's because with those common cards, the hands are closer together? The odds of the hands are the same, but it's a closer race between finishers?
Click to expand...


Yeah, the odds do change somewhat, and you also get situations in which getting a better hand can screw you over, because the common cards give the other guy an even better hand.

Imagine you had J10 suited as hole cards, and the flop come JJA. You've got three of a kind. Then the turn is another A, giving you a full house. By most measures, you have a better hand. But what if the opponent's hole cards are AK? He now has a full house as well, and it beats yours. If you hadn't pulled the full house, your triple J would have beat his two pair, so getting a "stronger" hand screwed you over.
 
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