# Odds of getting 3 consectutive aces?

**URL:** <https://boards.straightdope.com/t/odds-of-getting-3-consectutive-aces/134883>\
**Category:** Factual Questions\
**Created:** [November 1, 2002, 7:14pm UTC](https://boards.straightdope.com/t/odds-of-getting-3-consectutive-aces/134883 "2002-11-01T19:14:44Z")\
**Posts on this page:** 2\
**Page:** 2

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**Author:** ![don\_t\_ask](https://avatars.discourse-cdn.com/v4/letter/d/e68b1a/32.png) [@don\_t\_ask](https://boards.straightdope.com/u/don_t_ask)\
**Post date:** [November 5, 2002, 4:23am UTC](https://boards.straightdope.com/t/odds-of-getting-3-consectutive-aces/134883/21 "2002-11-05T04:23:28Z")

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The odds quoted in the OP are obviously the odds of being dealt **any** three of a kind first 3 cards.

You will never work out the odds of three of a kind being your best hand with simple permutations. You have to eliminate every combination that includes a pair because you now have a full house. Similarly any hand where the other 4 cards contibuted to a straight, flush or straight flush has to be eliminated.

Of the 133,784,560 possible 7 card hands 6,461,620 have at best 3 of a kind and 1/13 of these would be aces.

A good table of probabilities is [here](http://www.poker.net/ps_probtables.php).

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**Author:** ![aahala](https://avatars.discourse-cdn.com/v4/letter/a/a88e4f/32.png) [@aahala](https://boards.straightdope.com/u/aahala)\
**Post date:** [November 5, 2002, 4:43am UTC](https://boards.straightdope.com/t/odds-of-getting-3-consectutive-aces/134883/22 "2002-11-05T04:43:01Z")

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"The odds quoted in the OP are obviously the odds of being dealt any three of a kind first 3 cards. "

Duh, now I get it.

52/52 times 3/51 times 2/50= 1/425

Thanks \<b\>don’t ask\</b\>

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