Texas Hold'em Math 04

Calculating Runner-Runner Odds

Let's say you get dealt pocket tens:

Your opponent is dealt pocket nines:

You make a pre-flop raise and he calls you. The flop comes out:

You have trips. You make a bet and your opponent goes over the top of you and goes all-in. You call. Everyone's cards are turned over.

Calculating odds here isn't important, since your "control" over the hand is over. But for the sake of example, let's look at your opponent's chances of winning the hand by catching something runner-runner.

We approach this problem by first deciding HOW your opponent can win. He can get two consecutive nines, which would give him quads. He could also catch a seven and an eight, which would give him the straight. Those are the only hands that can save him.

OK, so to get quad nines he needs a nine on the turn AND a nine on the river.

To figure out the math, we use our handy percentage charts. He has two outs on the turn, which equals a 4.26% chance. Assuming he makes that, he has one out left for the river (the other nine). The odds of making one out for the river is 2.17%.

The way to calculate the OVERALL percentage is by MULTIPLYING these two percentages, since they both must occur. This gives your opponent a .0924% chance of winning. That's basically a 1 in 1000 chance.

Now what about the straight draw? The straight is more likely to happen, since there are more cards to hit. There are four sevens and four eights in the deck. That means there are eight outs on the turn card (either the seven or eight). If your opponent makes THAT card, he'll have four outs on the river.

For example, if he hits the seven on the turn, there are four eights left to make on the river.

Using the percentage charts, you can see there's a 17.02% chance of making one of the outs on the turn, and an 8.70% chance of making one of the outs on the river. See below:

Once again, we multiply these numbers to figure the chance that BOTH scenarios will happen. The answer is a 1.481% chance that your opponent will catch a runner-runner straight. You can add this to the .0924% chance of a four-of-a-kind. This equals a runner-runner "miracle" chance of 1.573%.

So you're in pretty good shape of winning the hand.

In general, I do NOT make runner-runner calculations at the poker table. It's just not practical, since the number is so small and because it requires so much math.

As a general "rule", you can treat the odds of a runner-runner as about 1%. That seems to be the "average" for many situations. You can decide for yourself whether or not to factor this 1% in your decisions. I don't use it.

OK, so now you know how to calculate outs, how to use the percentage charts, and how to calculate runner-runner situations. Let's look at how to calculate POT SIZE. After this you'll be equipped for real "pot odds" situations.