Howard Lederer's "A Simple Deuce to Seven Hand"

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"A Simple Deuce to Seven Hand" by Howard Lederer describes his reasoning about a 1000/2000 Triple Draw 2-7 hand. It's short but worth the read.

[edit] The Hand

The game is 500/1000 with 300/500 blinds. Lederer is in the cutoff with 2335Q and raises to enter. The button 3-bets and the small blind calls, as does Lederer. SB draws two, Lederer draws two, and button stands pat.

SB checks, Lederer checks blind, and button bets. SB calls and Lederer just calls with his 7K.

SB and Lederer both draw one and Lederer makes a 97532. It's checked to the button again, SB and Lederer both call.

SB draws one and Lederer breaks his Nine to draw at the wheel again. He paired threes. Checked to the button once again; he bets, SB folds and Lederer calls. Button wins the pot with 5678J.

[edit] Breaking the Nine

Lederer's reasoning for breaking the 9 is that in order to win with it, not only must it be the best hand at the time, but it also must beat SB's draw, and button's draw if he breaks. He says he's more likely to catch a 4, 6, or 8 than having all three be true.

Further, if the 9 really is ahead, it is most likely to a complete snow, and Lederer is prepared to call with anything up to a small pair on the end. (He's getting 10.5 to 1 odds that button is on a snow.)

Can we quantify this reasoning more precisely? (TODO--- it gets pretty involved when taking the third player into account.)

[edit] Heads-up

The same idea could be used when heads-up vs. a single opponent who may be snowing. If your opponent's hand range includes both many hands better than yours and hands you can easily beat by drawing, it may be better to draw.

Let's say your opponent could have either two pair or worse (a snow) or a pat 8 or better. If you hold 97542, if is obviously correct to draw because you can't beat any of your opponent's legitimate hands and can easily beat his snow. If you always call (even with a pair of 7's) then drawing can only increase your chances of winning the pot.

What if you hold 87542 instead? Is breaking correct?

If your opponent holds an 8 or better, then (using the Dead Out Calculator) we can see that there is only about a 34% chance that you are ahead already. Unfortunately, if you draw, you are only about 15% likely to win against this range. So standing pat becomes correct instead, because you decrease your chances of beating his legitimate hands (while the chances of beating his snow are the same--- or worse if you fold big pairs.)