probability theory question

[unclemyles]

Hello,

Ken Warren states that in a 10 player game where all 10 players play each hand you have a 1/10 probability to win the 1st hand, 1/100 chance to win both hands and a 1/1000 chance of winning 3 hands in a row.

The argument. In my mind.

If you win 1 hand your probability resets to 1/10 that you will win the next hand, not 1/100 because the cards are randomly shuffled and your position in time is reset. The 1/100 chance of winning the second hand was from a different place in time. Is this correct? Does your probability reset?

So I have 2 ways to look at probabilty.

If 2 Aces fall on the flop then the probability that 2 aces will appear on the flop again in the next hand are greatly decreased because the random pattern is less likely to repeat. Or since the deck is shuffled the randomness gets reset to zero and 2 Aces have the same chance of falling on the flop a 2nd time.

I am no math major so your responses are greatly appreciated in helping me put probability into a working context with these examples.

David

[gaming_mouse]

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Hello,

Ken Warren states that in a 10 player game where all 10 players play each hand you have a 1/10 probability to win the 1st hand, 1/100 chance to win both hands and a 1/1000 chance of winning 3 hands in a row.

The argument. In my mind.

If you win 1 hand your probability resets to 1/10 that you will win the next hand, not 1/100 because the cards are randomly shuffled and your position in time is reset. The 1/100 chance of winning the second hand was from a different place in time. Is this correct? Does your probability reset?

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Yes, it does. Starting now, the chance that you win the next 2 hands is 1/100. After you have already won the first hand, the chance that you win the second is 1/10. This of course assumes all players are evenly matched.

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So I have 2 ways to look at probabilty.

If 2 Aces fall on the flop then the probability that 2 aces will appear on the flop again in the next hand are greatly decreased because the random pattern is less likely to repeat.

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This is a ridiculous, but very common, viewpoint.

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Or since the deck is shuffled the randomness gets reset to zero and 2 Aces have the same chance of falling on the flop a 2nd time.

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This is correct.

[MagicFlea]

Ken Warren was looking from a fixed point of view. With the example of aces, you would say "my chances of getting pocket aces is .5%" and "my chances of getting pocket aces for the next two hands is .5% x .5% or .0025% (didn't count the zeros...)

what you were thinking of is called conditional probability, where you have some information, in other words, "what are my chances of getting pocket aces twice in a row when I know I got them the first time". In this case since individual poker hands are independent events, you take the probability of the whole event (.0025% from before) and divide by the probability of what you know (.5%) to get .5%.

[Snoogins47]

It's very unlikely that Red will come up 12 times in a row, but that doesn't give you any incentive to bet on Black after the first 11.

[BruceZ]

Would you feel safer taking your own bomb on a plane because the odds against there being 2 bombs are astronomical?

[LetYouDown]

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Would you feel safer taking your own bomb on a plane because the odds against there being 2 bombs are astronomical?

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LOL. I have no idea why, but that made me almost fall out of my chair. Well done.

[henrikrh]

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Would you feel safer taking your own bomb on a plane because the odds against there being 2 bombs are astronomical?

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Lol, that's a nice way of looking at it.