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12 replies to this topic

### #11 statman

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Posted 28 March 2008 - 08:14 PM

You have missed an assumption, one that is always made, and is usually wrong. For these probabilities to work that way that you intend, you must be the ONLY player. Otherwise, you must have the number of other players as well, as they will also get cards. This will change the combinatorics.
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### #12 Seventh Sage

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Posted 28 March 2008 - 08:25 PM

Dackombe has the denominator. Welcome to the Den!

The numerators are the challenge, for the reasons he mentioned.

Hint: you can discuss the probabilities one at a time, as if it were
eight puzzles. You might be surprised which one is the most
complicated to describe and calculate. Have fun with this.

To me, the interesting part is that it's fairly easy to look at five
cards and not confuse 4 of a kind with 2 pairs for example.
But if I'm a little bit sloppy with my math, I might count it that way.
Or even worse, count 4 of a kind simply as a pair.

What's needed is to describe what all 5 cards must or must not be.

Spoiler for most complicated?

Edited by Seventh Sage, 28 March 2008 - 08:25 PM.

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### #13 bonanova

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Posted 29 March 2008 - 05:29 AM

Great job, all ... !

Hands calculated so far:

By Dackombe:
Total hands - 2 598 960
Straight Flush - 40
Four of a Kind - 624
Full House - 3 744

By andreay:
Three of a Kind - 54 912
Two Pair - 123 552
Pair - 1 098 240
High Card - 1 317 888 <- very close, but slightly off.

Seventh Sage is correct about the most difficult one to calculate.
High Card.

Three numbers left to find.
Flush - fairly easy
Straight - easier
High Card - hardest

What we know is that these three must total
2598960 - [40+624+3744+54912+123552+1098240] = 1 417 848.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

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