Figuring the Odds of 3 Cards
Date: 08/07/97 at 01:00:37 From: Larry Ponder Subject: Figuring the odds of 3 suited cards In the card game Super Seven, how do you figure the odds against you of receiving three sevens? 6 deck shoe = 24 sevens 288 non-sevens. 24 / 288 = 12 12 to 1 for the first seven. Right? Now the shoe has only 5 of the same suit sevens, 323 of non-samesuit. How do you figure the odds of getting the second suited seven and then how do you figure the odds of getting the third suited seven? Thank you, Larry Ponder
Date: 08/07/97 at 18:42:23 From: Doctor Tom Subject: Re: Figuring the odds of 3 suited cards Hi Larry, You're on the right track. It's easier to work with probabilities, however. For example, instead of saying "12 to 1", it's easier to think "1 chance in 13". It's equivalent - it means out of 13 tries, you get 1 win and 12 losses, which is what "12 to 1" means. The advantage of probabilities is that there are nice rules about when they can be added or multiplied to give other probabilities. So let's calculate the probability of winning. If you only had to pick 1 seven to win, the probability of winning would be 1/13. Then, as you pointed out, after you've picked the first 7, there are only 5 cards that will help you out of the 287 remaining, so given that you made it past the first draw, you will make it past the second draw only 5 times out of every 287, or 5/287 of the time. For the third, with similar reasoning, you'll win 4/286 of the time. To win, you have to get past the first, second, and third draw successfully, and to get the probability of that, simply multiply the three probabilities: probability of win = (1/13)(5/287)(4/286) = 10/533533 = .000018742. Or another way to look at it is that out of every 533533 times you play the game, you'll win 10 times and lose 533523 times. -Doctor Tom, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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