Calculating Draw Odds

[Idolatrous]

I want to calculate odds in Draw; odds you will be dealt a specific hand before the draw, odds you will hit a specific hand after the draw, odds you will hit a specific hand or better after the draw, etc.

I was looking at a full house, say I have AA478 in my hand, and I want to know the odds of drawing to a full house when I discard 478. Now I know that my odds of hitting an ace next hand are 1 - (45/47), and then the next card wouldn't necessarily matter, unless of course it was a 478, then the odds on the 3rd card would be decreased from 1- (42/45) to 1 - (43/45). And then there is all the possibilities of drawing an ace on the 2nd and 3rd card instead of the 1st, or not drawing it at all, and then not drawing it at all and drawing the 3 remaining 4's, 7's, or 8's.

Anyway, there has to be an easier way to do this, and I was wondering how it would be done quickest and easiest?

Idolatrous
http://5ivecarddraw.com

[MarkGritter]

[ QUOTE ]
I want to calculate odds in Draw; odds you will be dealt a specific hand before the draw, odds you will hit a specific hand after the draw, odds you will hit a specific hand or better after the draw, etc.

I was looking at a full house, say I have AA478 in my hand, and I want to know the odds of drawing to a full house when I discard 478. Now I know that my odds of hitting an ace next hand are 1 - (45/47), and then the next card wouldn't necessarily matter, unless of course it was a 478, then the odds on the 3rd card would be decreased from 1- (42/45) to 1 - (43/45). And then there is all the possibilities of drawing an ace on the 2nd and 3rd card instead of the 1st, or not drawing it at all, and then not drawing it at all and drawing the 3 remaining 4's, 7's, or 8's.

Anyway, there has to be an easier way to do this, and I was wondering how it would be done quickest and easiest?


[/ QUOTE ]

If you are doing it by hand, I find it easiest to work with combinations rather than trying to calculate it out card by card.

The following combinations will give you a full house:
AKK (2 aces * 4C2 kings = 12 combinations)
AQQ (12)
AJJ (12)
ATT (12)
A99 (12)
A88 (2 aces * 3C2 = 6 combinations)
A77 (6)
A66 (12)
A55 (12)
A44 (6)
A33 (12)
A22 (12)
KKK (4C3 = 4 combinations)
QQQ (4)
JJJ (4)
TTT (4)
999 (4)
888 (3C3 = 1 combination)
777 (1)
666 (4)
555 (4)
444 (1)
333 (4)
222 (4)

So, that's 12 * 9 + 6 * 3 + 4 * 9 + 1 * 3 = 165 combinations out of 47C3 = 16215. 165/16215 = 1.02% to draw to exactly a full house. (Note that I didn't count any quads.)

Which is, fortunately enough, exactly the numbers you will find here: http://www.poker1.com/mcu/tables/Table16.asp

[Idolatrous]

This works great, thank you so much. I knew it involved combinations some how, I just couldn't remember how Combinations worked, I was never that great at math. One final question on this, how would you convert it to Odds Against making the hand (97.3 to 1)?

[MarkGritter]

165 combinations out of 16215 total =
(16215 - 165) to 165 odds =
16050 to 165 =
97.2727272727... to 1

[mindflayer]

Wecome aboard!

[Big Limpin]

*dont forget about quads!
only 76.2 to 1 against to make FH or better