Deuce To Seven Triple Draw: Breaking On The Turn

In Deuce to Seven Triple Draw Lowball (27TD) some of our most difficult turn decisions revolve around whether or not to break a pat hand to aggression. Breaking the best pat hand costs us a lot in expectation, thus we must be careful to do it only when the time is right.

Suppose we open-raise from the cutoff with 2-3-4-7-K and receive a call from the small blind. The small blind draws two and we take one. We improve to an 8-7-4-3-2 low, and the small blind check-calls our flop bet and draws one. After standing pat we get check-raised on the turn and are thus faced with a difficult decision; one that is highly player dependent.

Against a straight-forward player our only real option is to call and draw after our opponent presumably pats. Our opponent almost always has a seven or a better eight, thus we should break and take a shot at making either no. 1 (7-5-4-3-2) or no. 2 (7-6-4-3-2).

Things are a little more difficult when we are up against someone with some creativity in their game. For example, it’s possible they have a smooth nine such as 9-5-4-3-2 that unblocks an ‘8-7’ holding such as the one we hold that may break to aggression. Or perhaps they have seen all of the other sevens, and are making a play.

Since breaking the best hand costs us a ton of equity, we have to examine the math to see how often we are allowed to make a “bad break” and still come out ahead in the long term.

After calling the turn check-raise there are 7.5 big bets in the pot. Let’s assume X is the probability that Hero’s hand is good, and (1-X%) is the probability that we got outdrawn. If we choose to pat our equity is X%, which is simply the probability that our holding is best.

If we opt to break our equity would be X% * (Probability we outdraw our opponent’s worse pat range including 9-5-4-3-2) + (1-X%) * (Probability we outdraw a range of superior pat hands).

As a simplified example, let’s assume that villain has either 9-5-4-3-2 X% of the time or 8-5-4-3-2 with a frequency of (1-X%). When we break and draw, we have 29% equity against the nine and 16% equity against the smooth eight. When staying pat our equity is X%, which is simply the probability of having the best hand. We can then set the following equations equal to each other in order to solve for the breakeven X%:

Equity When Standing Pat = Equity When Breaking
X% = X%(.29) + (1-X%).16
X = 18.3%

Thus, in this particular example, Hero has more equity patting when villain has an inferior low more than 18.3% of the time. However, this should only be used as a guide as raw equity is not the final decider. Since the hand doesn’t end on the turn, we must consider the total expectation of bets won or lost.

Suppose we have perfect clarity that our opponent has the 9-5-4-3-2 low 30% of the time and 8-5-4-3-2 the other 70%. Under this assumption, patting would “preserve” 2.25 big bets (30%*7.5).

If we break, our equity against that assumed range would be 20% calculated as follows: (30%)(.29)+(70%)(.16) = 20%. And when taking this line we would only expect to net out 1.5 big bets (.20*7.5).

When compared to patting, breaking causes us to take a 10% equity hit and lose approximately .75 big bets from what is in the middle on the turn. Clearly this means we should pat our holding, right? Not necessarily, as that ignores the impact of river betting.

On the river, had we broken and improved to a seven we will often collect one bet from the nine and two from the smooth eight. But when we pat and face a river bet we are getting 8.5:1 on a call, a price usually too good to pass up for most players.

It’s important to realize that we lose money on the river even when these calls are theoretically correct.

For example, if our opponent bets the nine low a third of the time he has one, we must call as the odds are 7:1 we hold the best hand and are getting 8.5:1. However, even though we are getting the right price we are losing .6 big bets on the river betting round:

Villain Hand Probability Bets Win/Loss
8-5-4-3-2 70% 1 -1 -0.7
9-8-5-3-2 10% 1 1 0.1
9-8-5-3-2 20% 0 0 0
-0.6

This .6 big bet loss on the river erodes much of the .75 big bet gained from patting on the turn, and this fact is often overlooked.

With the implied odds inherent with a draw to 2-3-4-7 we are instead making money on the river and this generally would make breaking the slightly better play; even with a relatively high 30% chance that you are breaking the best hand.

However, in reality your hand simply isn’t good 30% of the time in this situation. Most players would simply be content to call and draw to 2-3-4-5. And if they have an inferior ‘8-7’ holding they are typically calling and dealing with a difficult break or pat decision themselves.

As a word of warning, it’s important to not conflate this situation with others that may seem similar, but are actually completely different. In the example above, we were pat heading into the second draw and our opponent was drawing one. That is quite different to the times we get check-raised after making an automatic turn bet because we’re drawing one and our opponent two.

This article is specifically talking about the situation where our opponent knows we have a pat hand (or we are at least representing one) and takes an aggressive line against us. However, if it’s possible we are still drawing; our opponent’s check-raise will be made with a much wider range.

That range would contain many worse lows, sometimes even with tens and jacks, as well as some two-pair or trip holdings turning their hand into bluff. In that situation, we basically just have to pat any eight low and make our opponent show us a better hand.

However, when we were already pat heading into the second draw an opponent is generally never check-raising a hand worse than 8-7-4-3-2 for value and has fewer bluffs. Thus, against most opponents it is correct to break and try and improve your hand.

Occasionally our opponents will move us off of the best hand, but we can’t be too hard on ourselves when that occurs. It’s results oriented to consider a “bad break” a disaster. Bad break is in parentheses because in the long run breaking in that spot against most players is the optimal play. Therefore, it really wasn’t a bad break.

After all, our opponents do sometimes make sevens and strong eights, where our break allows us a chance to draw live along with the possibility of winning multiple bets on the river. That’s certainly a big upgrade from being dead in the water and possibly feeling compelled to call a river bet.

One must consider all relevant factors including the play of the hand and our opponent, and try to not let emotions cloud our thinking. ♠

Kevin Haney is a former actuary but left the corporate job to focus on his passions for poker and fitness. The certified personal trainer previously owned a gym in New Jersey, but has since moved to Las Vegas. He started playing the game back in 2003, and particularly enjoys taking new players interested in mixed games under his wing and quickly making them proficient in all variants. Learn more or just say hello with an email to [email protected].