Pot Odds from "The Theory of Poker"

[Wooderson]

I posted this in the beginners section and then noticed that this may be a better all-around place.

I've just recently decided to take my casual poker hobby a notch up so last week I bought the Theory of Poker and sat down to read. I've been stuck for the most part on the Pot Odds section. I'm going to use the examples Sklansky gives in the book pgs.35 - 41.

I understand how to calculate odds based on the scenarios presented on pgs 36-38. I am stuck on the first example Sklansky gives on pg. 39 and the resulting odds to improve:

In 5 card stud/razz you're dealt two 5's in the hole and your fist up card is an Ace. You have seen 7 other cards.


.....Number of 5's & A's................Chances for Aces Up
seen other than your own:.............or Three of a Kind:
................0................................. ......41.0%
................1................................. ......34.1%
................2................................. ......26.5%
................3................................. ......18.3%
................4................................. ......10.5%

I can't figure out how this is calculated at all. Let me take you through my thought processes on the first one - no other 5's or Aces seen. There are 52 cards minus the 3 I hold, so there are 49 cards that can help me. Of those 49 I've seen 7, so that leaves 42 cards. Of those 42 cards remaining, 5 (2 5's and 3 Aces) can help me improve to Aces Up or Three of a Kind. Calculated out, that appears to be 37:5 or 13.51%. Is this thought process wrong, because I'm sure not getting the 41.0% Sklansky shows.

So I tried something else: that 13.51% must mean the chance that the 4th card (not sure if it's 4th Street since we're in 7-stud/razz?) helps me improve to one of my two outs, and in reality I have four more chances to hit. So I tried this:

................Odds/Percent
4th Card.....37:5/13.51%
5th Card.....36:4/11.11%
6th Card.....35:3/ 8.57%
7th Card.....34:2/ 5.88%

That doesn't work either because it adds to 39.07%. Also the logic is flawed since if the 4th Card didn't help me there are still 5 cards out there that can meaning the odds on the 5th card to improve become 36:5 rather than 36:4 as I put above. So then I tried this:

................Odds/Percent
4th Card.....37:5/13.51%
5th Card.....36:5/13.89%
6th Card.....35:5/14.29%
7th Card.....34:5/14.70%

The cumulative percentage is 56.39%. Obviously that isn't the ticket either!

So those are all the ideas I had to figure out how Sklansky got 41.0% chance to improve to Aces Up or Three of a Kind with no 5's or Aces seen, and I still can't figure it out! That doesn't even take in to account trying to figure out my pot odds if I've seen 1, 2, 3 or 4 of the possible outs.

Please help me understand this because Sklansky doesn't go in to detail and it's driving me nuts!

Thanks a bunch - Wooderson

[doormat]

Wooderson,
You need to calculate your chance of missing the hand and then subtract that from 1 to arrive at the chance of making it. With none of your cards out, you have a 37/42 chance of missing on your first draw, then 36/41 chance of missing on your next, etc. You multiply these chances together: (37/42)*(36/41)*35/40)*34/39) = .5901
That is your chance of missing the hand, so your chance of making it is 41 percent.

doormat

[punkass]

you are also confusing odds with ratios. 37:5 is not the same as 5/37. 5/37 = 13.5%. 5:37 = 5/42 = 11.9%