Odds of Drawing a Given Card Problem

[trader56]

In the book, Winning Low Limit Hold 'Em by Lee Jones, the author states that computing the odds of making a draw on the next card involves comparing the number of cards that don't make your draw to the number that do.
For example, if you have a pair of jacks, and the flop comes down with a queen, a three, and a nine, what are the chances of getting 2 pair?
Well, 9 cards out of the 47 unseen will help you - 3 threes, 3 nines, and 3 queens - and the 38 other cards left will not.
So, the odds are 38:9, or about 4 to 1 against making the two pair.

In comparing this to some figures in a chart published by the United States Playing Card Company, they state that the odds of making the pair are about 5:1 against, so this is close. But, in using the same hand, they state that the odds of getting trips on the draw are 8:1 against.

For the life of me I can't get the numbers to work out to 8:1 using the Jones method. Can someone plese tell me where I'm going wrong, and show me the right calculation?

I'd much rather use a formula than simply memorize a chart, if I can.

Thanks for any help!

[Songwind]

I agree, I get 22:1 against for trips on the turn.

Maybe you're mis-applying the chart?

[D.H.]

[ QUOTE ]
For the life of me I can't get the numbers to work out to 8:1 using the Jones method. Can someone plese tell me where I'm going wrong, and show me the right calculation?

[/ QUOTE ]

The odds of making a set on the flop when holding a pocket pair is close to 8:1. Maybe that's what you are reading from the chart.

[trader56]

Thanks for your replies! I posted this question on the Poker Theory section of the forum, and I think Pokeryogi has solved the problem. He writes:

"You have 2 cards to come:
2/47 plus 2/46 = 0.086031 which converts to 10.6 to 1.
I could be wrong.
Still learning,
PY"

This seems to be in line with what the chart I looked at said. If anyone can add to this, please feel free to do so!
Thanks again for the help!

[uuDevil]

[ QUOTE ]
In comparing this to some figures in a chart published by the United States Playing Card Company, they state that the odds of making the pair are about 5:1 against, so this is close. But, in using the same hand, they state that the odds of getting trips on the draw are 8:1 against.

[/ QUOTE ]

Are you sure these aren't odds for 5-card draw poker instead of holdem? See this site:
Draw Poker Odds (http://www.winneronline.com/strategies/drawpoker.htm)

This is a part of one of their tables:

<font class="small">Code:</font><hr /><pre>
Chances of making:
Any improvement Two Pair Three of a Kind Full House Four of a Kind
Drawing three cards to a Pair 1 in 2.5 1 in 5 1 in 8 1 in 97 1 in 360
</pre><hr />

Sorry about the crappy formatting.

Note, however, that "1 in 5" is odds of 4:1 against, and "1 in 8" is 7:1. I'm guessing you might be confused about this. If not, nevermind.... /images/graemlins/blush.gif

[trader56]

Hi uuDevil,

Thanks for the info - you might be right about looking at Draw tables vs Hold 'Em.

Do you know where there might be similar charts for the various other games, including Hold 'Em?

Thanks for your help and patience with a rookie LOL!

[uuDevil]

[ QUOTE ]
Do you know where there might be similar charts for the various other games, including Hold 'Em?


[/ QUOTE ]

They are all over. Here is one for Holdem, from the RGP FAQ:

http://www.rgpfaq.com/odds-holdem.html

There are really only a handful of numbers that matter. And though it isn't really necessary, I recommend learning how to calculate odds yourself. If you're going to gamble, some familiarity with probability can only help. Do a search here for posts with examples and other resources. BruceZ and Bozeman are a couple of posters to look for.

Good luck.