OverCard PreFlop Odds

The typical response to overcards versus a pocket pair is that it is a race. While sometimes this is true, often its closer to 60-40 with the pair ahead. However, I had always assumed that the more small pocket pairs in the hand, the better. There is a lot more money and you still have the same amount of outs while the pairs aren't gaining too much. Let's break it down.

Say you have $1,000 and you push all in with A-Q offsuit. Pocket tens calls you. The tens wins the hand 57% of the time. So if you play this hand 100 times, you lose $7,000. Not much of a race when you look at it that way.

Now let's add a second pocket pair to the mix. You only win now 35% of the time. However, because the pot is $3000 it's slightly better. If you play this hand 100 times, you win a total of $105,000 for a net gain of $5,000. That's better.

Let's go one step farther and add a third pocket pair. Do you think it get's better or worse for A-Q? Before I ran this exercise, I assumed it would be even better. Was I right? We'll add pocket jacks to the mix and see. Now A-Q wins a pot of $4,000 29% of the time. Now there is a gain of $16,000 over 100 hands. This is the situation I was in when I got knocked out of Bodog's Sunday Guarantee. A-Q vs Jacks vs Tens vs 4s. The 4s made a full house to take down the huge pot but I really couldn't ask for a better situation.

Or could I? What about if there are 4 or 5 or 6 pocket pairs? Does it just keep getting better for A-Q or is there a peak somewhere along the line? If you add a fourth pair, pocket sixes, you drop down to +$15,000 over 100 hands. If you add a fifth or sixth, it drops to +$8000 and then -$2000. Granted these are all unlikely scenarios but it's interesting to know just in case.

One final question, how big of a difference does having a suited A-Q make? Against three pocket pairs it makes $20,000 over 100 hands. That's $4,000 more just for having suited cards. (And people say being suited is overrated!). If there is a fourth, it drops marginally but stays around the $20,000 mark. The same can be said if there are five pocket pairs.

Concluding point: If you are going to race with overcards, its better to be suited, but no matter what the best that you can hope for is three smaller pocket pairs calling your all in. Not more and not less.

*All values presented are approximates and will change slightly depending on the exact nature of the hands that you might be up against.*