Players beginning the study of Deuce-to-Seven Triple Draw will usually learn two key facts about the last draw: a pat J is a favorite to win against a single 1-card draw, and a pat 9 is a favorite against two players drawing one. Unfortunately, many players make the incorrect inference that without a hand as good as a pat Jack or a pat Nine, they shouldn’t stand pat on the last draw. But sometimes standing pat with a rougher hand is the correct play.

Snowing the Last Draw

The most obvious situation in which standing pat with a poor hand is advantageous is as a “snow.” If you stand pat on the last draw and bluff on the last round of betting, your opponent may be hard-pressed to call you with less than a made nine. A player with a strong draw such as 7532 has at most 16 outs to a nine or better--- he will complete his hand much less than half the time.

Unless your opponent loosens his calling standards or plays back at you, this play will be quite profitable. You are typically risking 2 bets, one on the third round and one on the fourth, to win a pot of 5 bets or more. Your opponent would have to call nearly 70% of the time to make this line unprofitable. However, your opponent can also combat snowing by check-raising you more often in the third round with pat hands, or counter-snowing, or bluffing (possibly bluff-raising) in the fourth round.

Against tough players, snowing should form part of a balanced strategy of value-bets and bluffs on the end. If both you and your opponent drew one on the last draw, your last-round strategy should consist of a mix of value-bets and bluffs. The same logic should be applied to the third round, where your bets or raises indicate a combination of legitimate pat hands and snows.

Here are some example hand match-ups, comparing your chance of winning by drawing to the best hand, compared with the folding equity of snowing against an opponent who needs a Nine, Ten, or Jack to call on the end. This table is calculated with a 42-card stub, ignoring discards from previous rounds.

Your Hand	Opponent’s Hand	Drawing Equity	Snowing Equity vs. 9+	Snowing Equity vs. T+	Snowing Equity vs. J+
7432/Q	8642/K	0.543	0.667	0.571	0.476
8762/K	7532/5	0.424	0.667	0.571	0.476
7432/7	8642/K	0.562	0.690	0.595	0.500
7543/3	8642/A	0.480	0.714	0.619	0.524
8765/9	7432/3	0.309	0.714	0.619	0.524

Your snow is more worthwhile if you have a poor draw to begin with (such as the last two examples, which are potential straights) or suspect that you are drawing rougher than your opponent. Paired cards also increase the strength of your snow, because your opponent is somewhat more likely, in the long run, to need that particular card to call on the end. Snowing should generally be reserved for these cases rather than employed with your strongest draws--- it is much more profitable to make a wheel against a strong second-best hand than to pick up the few percentage points in pot equity by snowing. Conversely, it is also easier to get away from a complete bluff on the end than a mediocre holding. You cannot be trapped for two bets with a pair that you snowed, when you might be with a rough made Eight or smooth Nine.

Snowing also works best in position rather than out of position. If your opponent merely calls a bet and stands pat behind you, you have probably surrendered all your equity in the pot. If you had position, you could break and try for a better hand anyway.

Drawing Correctly in Multi-way Pots

Even if standing pat with a legitimate hand does not make you a favorite to win the pot, it may still be the best option available to you. A common situation where this is the case, is drawing a T on the second draw, when you are last to act. Unless your draw is particularly good, it is usually best to bet if checked to and stand pat if they both draw one.
Suppose you have T8632 and both your opponents have one-card draws to the wheel. You are in bad shape no matter what, but drawing only makes things worse.

Your Hand	Player A’s Hand	Player B’s Hand	Equity of Drawing	Equity of Standing Pat
T8632	7432/K	7432/Q	0.245	0.285
T8632	7532/K	7432/Q	0.269	0.318
T8632	7542/K	7432/Q	0.260	0.333
T8632	7542/K	7542/Q	0.228	0.315

Unfortunately, in the cases above, even standing pat doesn’t give you an equity edge, so you’d prefer to check behind and stand pat. Betting is better, in general, because you might cause one of your opponents to fold if he’s drawing more roughly than the wheel (incorrectly, if he knew you only had a pat Ten) and make you a favorite to win. Betting may also make it somewhat less likely that an opponent will read your hand correctly and attempt to bluff you off your weak holding.

Your hand does not have to be especially rough for standing pat with the T to have a positive effect on pot equity. If you hold T7542 instead, against your opponents’ 7432/Q and 8632/A, you are 0.397 to win the pot by standing pat, but only 0.332 to win when drawing.

The 5-10% equity shift by standing pat is obviously worth more in big pots. If the pot is already very large, standing pat will be profitable even if you pay off a better hand on the river every time you are beat! However, when the pot is not this large you must weigh the chances of being outplayed on the last round (either surrendering the pot too often or calling too many value-bets) against the immediate equity gain of making a better draw. You should prefer drawing if the pot is small or if your draw may earn you a lot of bets on the last round.

As is the case for snowing, you should definitely stand pat rough if you somehow made it to the last draw with a poor hand, such as a flush or straight draw. Some examples:

Your Hand	Player A’s Hand	Player B’s Hand	Equity of Drawing	Equity of Standing Pat
T7543	7632/Q	8532/A	0.289	0.454
T8765	9632/2	8643/J	0.214	0.474
Td7c4c3c2c	8s7s3s2d/Qc	5c4s3h2h/2s	0.429	0.438
T5432	7542/7	8732/Q	0.267	0.435

Note that in all these cases you have an equity edge by standing pat, so your third-round bet will be profitable. Here are some additional examples, including a few cases where the pat Ten is a favorite to win. In fact, it is somewhat difficult to come up with a case where keeping the Ten does not increase your pot equity, though they do exist.

Your Hand	Player A’s Hand	Player B’s Hand	Equity of Drawing	Equity of Standing Pat
T7432	8752/7	7543/4	0.455	0.531
T9432	8752/7	7654/4	0.328	0.506
T8643	7432/4	8643/4	0.342	0.358
T8432	8732/8	9752/A	0.408	0.471
T8762	8432/8	7632/Q	0.291	0.350
T8642	8742/8	8742/Q	0.375	0.347

With four players on the last draw, keeping the Ten is generally unprofitable (unless your draw is quite bad.) However, keeping a Nine on the last draw usually increases your pot equity in a four-way pot, despite the fact that it is not a favorite to win.

Out of position, it is much harder to know when to stand pat. Although it is sometimes correct, you are more likely to make a mistake and end up sacrificing all your pot equity by standing pat with a Ten when somebody else has a Nine. You also suffer a disadvantage on the last round of betting, because it is less likely that the other players will check instead of value-betting.

Heads-up With a Jack

The conventional wisdom about a pat Jack being a favorite against a one-card draw is not strictly true. It is possible to come up with situations where the Jack is tied or a small dog, when the discards are considered. Also, when your draw is smooth it is superior to draw rather than stand pat though you might be the favorite either way.

For example, suppose you hold 7642A to start and have drawn a King on the first round and a Jack on the second. If your opponent holds 2478K and has discarded two sevens, his 8742 draw is dead-even against your J7642. But drawing makes you a 0.543 favorite to win.

Another example is if you hold 8542, have discarded Fours twice and then drawn a Jack. Your pat Jack is only 0.447 to win against a 7432 draw (that has discarded three Aces) and drawing is slightly better, giving you 0.454 of the pot equity.

Even in those cases where the pat Jack is superior, the player standing pat with it suffers from a disadvantage on the last round. He cannot usually bet for value (unless his opponent is playing the wrong game!), nor can he call very many bets. This playing disadvantage must be weighed against the increased equity from keeping the Jack. Triple draw player and blogger Chris Fargis has suggested treating a pat Jack out of position as a semi-snow, and betting it on the last round.

As in the previous examples, standing pat in position reduces the potential downside by making it less likely that you have made a drawing error that costs you the pot, or puts you in a tough position when you check the final round of betting. The larger the pot, the more advantageous it is to increase showdown equity.

Conclusion

Triple draw provides opportunities for mistakes in drawing as well as betting. These mistakes can be some of the most costly in limit poker. Drawing well requires knowing when to stand pat “rough” or snow the last draw. An expert triple draw player must be familiar with the principles illustrated here:

• Snow on the third draw as part of a mixed strategy, or to take advantage of weak-tight opponents.
• Stand pat when your draw is likely to be worse, and your implied odds are poor.
• Don’t sacrifice your chances to win a big pot by snowing or patting your best draws in small pots.
• Prefer to stand pat “rough” only with position, so that your last-round playing disadvantage is minimized and you don’t sacrifice your draw’s equity against a better pat hand.
• Prefer to stand pat in larger pots so that the gain in immediate equity outweighs the playing disadvantage on the last round.

(This article originally appeared in 2+2 Magazine, I believe in May 2007.)