Become a Casino Math Wiz - Calculating Probabilities on the Fly

I just saw the Wizard's new blog post on wizardofodds.com regarding a texas hold'em calculator. While this is an excellent tool, you can actually perform this calculation in your head at the poker table (or table game such as Let It Ride).

I first read about this calculation in Phil Gordon's "Poker: The Real Deal" I believe he called it the Rules of Two and Four. Anyway, here's how it goes:

1) Count the number of outs you have to make your hand. (An out is a card that will make you complete your hand.) For example, if you have 10H, JH and the flop comes Qh, Kh, 2c, then you have a total of 15 outs to make a straight or better (which you'll probably need to win the hand)--2 to make a straight flush, 7 to make a non-straight flush, and 6 to make a regular straight.

2) Multiply by the number of cards left to see. In the above example, the multiplier would be 2 for the turn and river combined, and your current number is 30.

3) Multiply by 2. This final number is your percent chance of getting one of your outs, which would be 60% in the example.

Note that this number is inherently off by approximately 1-2%, but always on the low side, so feel free to add 1 or 2 to your final number.

Now how do you use this number? Using the above example, let's say you're heads-up against an opponent who bet the size of the pot. You know that he doesn't have 3 of a kind, so you can ignore the probability that he will get a full house and beat your potential straight or flush. Let's say that you know he has either AK or AQ. Since the odds of winning are 60% and calling would make you're investment 33%, since your probability of winning is greater than the percent of the money you're putting in the pot, it is profitable to call.

You can also apply this principle to table games such as Let It Ride. Let's say you have 5c6d7s and the first dealer card comes to be 8d. Your only way to win the hand would be to get a straight. That means you have 8 outs. According the Phil's Rules, you have a slightly better than 16% chance of winning (close to 17%). Paytable 1 gives 5 to 1 on getting a straight. Therefore, you're putting in 1 unit to win a 6 unit "pot," which amounts to you putting in 16.67%. Since your winning probability is approximately the same (or slightly higher) than your pot odds, then you should let your bet ride (ie not call back bet #2).

Hope this helps everyone become a math wiz.

Heh, not to pee in your Cheerios, but this is one of the first tools I learned in poker!

I do know it only works for probabilities up to around 1/3. Above that, it gets sketchy. For example, 9 outs (flush draw) percentage is less than 9 * 4 = 36%, about 1/3 if IIRC.

But yeah, as a matter of common practice and most situations, it's a good rule-of-thumb.

When I was first learning poker, I made up (I think I did, anyway I haven't heard it anywhere else) something called "The 7 P's of Poker" to help me evaluate decisions:

1. Position.
2. Pot.
3. Player. (my opponent(s) history and type of play)
4. Piles. (my stack and opponent's stack)
5. Probability
6. Pips. (cards in play)
7. Pollyanna. (do you feel lucky)

I think later I thought of an 8th "P" but I can't think of it now.

Quote: ItsCalledSoccer

Heh, not to pee in your Cheerios, but this is one of the first tools I learned in poker!

I do know it only works for probabilities up to around 1/3. Above that, it gets sketchy. For example, 9 outs (flush draw) percentage is less than 9 * 4 = 36%, about 1/3 if IIRC.

But yeah, as a matter of common practice and most situations, it's a good rule-of-thumb.

I know that posting that seems so basic is like preaching to the choir on this site, but my reason was twofold. For those people that haven't heard of this shortcut before, it's a good easy rule to learn. Also, it just proves that easy math can be about as accurate as the combinatorial analysis and Monte Carlo Simulations that the Wizard does, as this rule of thumb is not usually off by more than a percent or two.

This rule does work above 1/3, as it is especially useful for Omaha which frequently has up to 17 to 20 outs after the flop alone (giving a 68-80% chance to hit your hand). However, when playing poker against an opponent you often have to be worried that your opponent could be drawing to a better straight or flush.

Again this is an easy rule to apply to Let It Ride, as there are a number of rules to memorize for each decision point, which all depend on the paytable. So instead of memorizing the whole list, it's easier to just apply this rule as you're playing (if you're good with doing fast math in your head).

Quote: svirgile

I just saw the Wizard's new blog post on wizardofodds.com regarding a texas hold'em calculator. While this is an excellent tool, you can actually perform this calculation in your head at the poker table (or table game such as Let It Ride).

No you can't.

Your method will only produce a very crude estimate. It's useful only when you do not know any other information.


The Wiz' calculator provides EXACT odds based upon ALL the cards dealt.

The calculation is supposed to be an estimate, as you can't memorize all possible permutations or use a computer when you're sitting at the tables. And the calculation is only different by about 3% at most. The point of the calculation is to show that with a little bit of math, you can make your own calculations (or estimates) and still be very close to the real answer.