Deuce-To-Seven Triple Draw Lowball: Analyzing A Turn Snow

Snowing is the act of betting or raising and staying pat with a busted hand with one or more draws to go in an attempt to get your opponent to fold before showdown. In Deuce to Seven Triple Lowball (27TD), as is the case in other draw games, the decision to turn your hand into a bluff eliminates the possibility of winning by drawing to the best hand. However, if we would otherwise fold, then there is no opportunity cost to snowing.

In this issue, we are going to examine a somewhat common situation on the turn where we were behind in the draws and fail to improve, however, instead of making a conventional fold; we opt to make a move at the pot.

Sample Hand Details

Villain opens from the cutoff, Hero defends the big blind with 2-3-8-K-Q, and both players draw two. On the first draw, we pull a jack as well as another three and check-call a flop bet. On the next draw, we again take two while our opponent improved and only takes one. Unfortunately, we fail to improve once again, collecting an ace and yet another three. We check the turn and face what is almost always an automatic turn bet from an opponent ahead in the draw.

Calling and drawing two on the last draw from out of position in this relatively small pot is not really a good option. We are only getting 4.25:1 on our call and while our “hot/cold” equity is probably close to what is required, we have reverse implied odds on the river.

However, having seen three of the treys has significant removal effects and our opponent originally opened from late position, making this an above average situation to make a move at the pot. The plan is to check-raise the turn and stand pat. If we don’t get re-raised on the turn and our opponent is still drawing, we will bet the river.

If we assume calling the turn and drawing is off the table, we only need to see if the expectation of turning our hand into a bluff is greater than zero (folding).

Assumptions

As outlined above, our plan of attack is to only continue with the bluff when our opponent just calls the turn check-raise and draws. We will fold if we get three-bet on the turn and will also refrain from betting the river when villain just calls the check-raise and pats. Of course, we don’t always have to play in this manner, but that is generally how we should proceed and are the assumptions that will be used in the calculations below.

When Villain pats in position he’s typically showdown bound as he didn’t call the check-raise in the hopes that you were making a move at the pot with a drawing hand. When our opponent is out of position, it’s a different dynamic as sometimes he will have a weak holding that is only calling the turn raise to see if you are pat. And if you are pat, he may find a fold on the river with the bottom of his range.

When the play fails, we will either lose two or three bets depending on when our opponent makes his hand. If the bluff succeeds in getting through, we will win a total of 5.25 big bets, the 4.25 big bets in the middle after our opponent bets the turn, plus the extra one he had to put in to call the check-raise.

We will first assume our opponent will pat after the second draw with any nine or better low. Since many players will break a hand like 9-7-4-3-2 and other holdings with a smooth draw underneath, this assumption makes our calculations slightly more conservative.

Estimating the Expected Value of Snowing

Suppose our opponent is holding 2-4-5-7 heading into the second draw, thus one of the cards he needs is a three which we are effectively blocking. On the second draw, our opponent can hit 12 different cards to make a nine or better low and with 39 unseen cards left, the probability of him making it is around 31%.

Regardless of if our opponent makes a seven and three-bets us, or an eight or nine that he may just call and pat, we will lose two big bets when he makes his hand on the second draw. We will lose three bets if he ultimately gets there on the last draw and will win 5.25 big bets when he misses both draws. The probabilities associated with these events are as follows:

Using those probabilities, we can then estimate the approximate big bets won or lost from incorporating the play:

(-2)(31%) + (-3)(22%) + (5.25)(47%) = 1.18 big bets

Under the current set of assumptions this is a highly profitable, albeit high-variance play with an overall success rate of around 47%.

And if our opponent calls with a jack or better on the end, our bluff will get through only 33% of the time but we will still eke out a tiny profit:

(-2)(31%) + (-3)(36%) + (5.25)*(33%) = .033 big bets

What do the numbers look like if Villain breaks 9-7-5-4-2 after the turn check-raise? This would benefit us, as it’s more likely our bluff will get through. The approximate chance the play works along with the estimated expected values contingent on what Villain bluff catches with on the river are as follows:

Even though it’s better for us if villain breaks a hand like 9-7-5-4-2, it is the correct play from your opponent’s standpoint against the entirety of our check-raising range that will also contain many real hands. As a first pass, it was just helpful to show the numbers assuming our opponent gets sticky with a nine, which he may do with a rough hand such as 9-8-7-4-2.

On your good days, your check-raise will make your opponent break something like 9-7-5-4-2 or 9-5-4-3-2 or possibly get him to immediately fold his rough draws. Since Villain opened from late position, he will more frequently have a weak one card draw to a nine (e.g. 2-7-8-9) and may just decide to muck on the turn.

On your bad days, your opponent will already be holding the case three and also may decide to three-bet the turn with a strong draw such as 2-3-5-7, which in this case, will instantly win him the pot.

All things considered, the player on the receiving end of a turn check-raise probably needs to bluff catch with a jack low or better on the end to deny his opponent the ability to print money with his snows.

Of course, potentially opening yourself up to being exploited and actually getting exploited are two entirely different things. Tight players with no creativity in them always have at least an eight or better when check-raising the turn and leading the river, and against them folding a nine or worse low on the river would be exploiting their straightforward play.

When deciding whether or not to snow, having seen many pairing cards is critical both in terms of increasing the likelihood our opponent will fail to complete his hand and also ensuring that we don’t overuse the play. Against a tricky aggressive opponent in an online game, numerous things can go wrong so if/when we make a move it should only be with significant blockers, meanwhile the bar can be set a little lower against a tight player in a live game.

As in many poker situations, we must also choose our targets carefully. We must never forget the old saying that poker is not really a game of cards played with people; it is mostly a game of people played with cards. ♠

Kevin Haney is a former actuary of MetLife but left the corporate job to focus on his passions for poker and fitness. He is co-owner of Elite Fitness Club in Oceanport, NJ and is a certified personal trainer. With regards to poker he got his start way back in 2003 and particularly enjoys taking new players interested in mixed games under his wing and quickly making them proficient in all variants. If interested in learning more, playing mixed games online, or just saying hello he can be reached at [email protected].