An Equity Play in Razz - Adam Stemple

There is a common situation that comes up in razz that a lot of people play badly. On fifth street, you have caught a pair, and your opponent has made what appears to be a rough low. He bets, since there is absolutely no way for you to have him beat at this moment. What is your play?

Let's look at the math-

For our example, we'll give you an extreme case of having A2344. You have the four lowest cards in the deck and a useless pair. Your opponent is showing T98 on board. With two down cards and two cards to come, you know he will need to use at least one of the cards showing in his final hand, making his best possible hand a smooth 8 (8432A). That is assuming he has two down cards 4 or under and catches perfect/perfect. This is unlikely as you hold many of the cards he needs. His most likely final hand will be a rough nine, or the supposed ten high he is representing at the moment. It doesn't matter anyway, because if you hit he will be stone dead. Now, what are the odds of that happening?

For him to win the hand, you must miss twice. All the cards between 7 and 5 for a guaranteed win, and 3 8's for at least a tie. We'll count 2 of the 8's as a win, because if you hit one, he needs to catch some very specific cards to tie. Since if you hit, your opponent is drawing dead, it is easiest to calculate how often you will miss on both 6th and 7th street.

On sixth street, you have 14 outs out of a possible 44 cards. Meaning 14 are good and 30 are bad. Your odds of missing 30 to 14 then or roughly 2-1. So 66% of the time you will miss on 6th street. On 7th street, you can take away one card bad card (you missed so one bad card is gone, your opponent's card is unknown so still counts in the deck) and get odds of 29-14. Still roughly 66%. So of the 66% of the times you miss on 6th street, you are going to miss again, 66% or the time. Well, 66% of 66% is 44%. And if you miss only 44% of the time, that means you hit the other 56%. Woops, you're a favorite! You are going to hit your unbeatable hand 56% of the time. And that is only if your opponent also hits perfect perfect and actually has what he is currently representing. When you factor in the fact that a 9 will win even if your opponent improves--and he may not even improve on the ten he is showing--you're a prohibitive favorite at this point in the hand. Raise and reraise here, and you will get good odds as a 2-1 dog on 6th street if you miss. Don't bluff the river if he checks to you--you will get called. Raise if you hit an 8 or under, and consider a bluff raise if he bets out--there is no hand that he could hit that would warrant anything more than a check/call.