2-card draws and manipulating the pot size in TD 2-7

[MarkGritter]

Having played some razz and PL O/8 recently, the matter of manipulating pot size and number of players naturally comes to mind.

A poster over on the Stud board made a very good point about not making the pot so large that it was automatically correct to call despite catching bad on 4th. The reason is: it makes bad players who chase correct, and eliminates the ability for a good player to make a good decision on 4th by folding.

An analagous situation in triple draw is a 2-card draw that misses the first draw. For what pot size is it correct to keep drawing with a quality 3-card seven draw vs. a player who drew 1 or 2 and bets into you?

If he is pat your implied odds stand at about N+2 : 2.5. Maybe N+3 : 1.5 at best if you are drawing to the nuts and can get a raise in. The odds of completing an 7 with a 3-card draw are about 7:1, and of completing an 8 are about 3.5:1. Thus the call is only automatic against a pat opponent (that needs a 7 to beat) if there are 15.5 BB in the pot already! It might be correct with only 6.75 BB if an 8 will do. But either way this is pretty unlikely.

Suppose your opponent is drawing one. He is about 45% to make this hand. You can probably still win 13% of the time by making your 7. The remaining 55% of the time you will win at least 25% (by making an 8), and let's say another 15% you win with a worse hand. This totals 0.45*0.l3+0.55*0.40 = 28%. This is odds of 2.6:1. Thus the call is 'automatic' if there are are 4.5 BB (9 SB) in the pot already.

(It might be good to look at how often you have to fold to a big bet next round as well. And of course everything gets complicated multiway.)

An exercise for the reader: calculate appropriate pot sizes given the risk that a bettor who drew 1 or 2 the first round is actually pat.

Now let's switch roles.

Suppose you raise preflop, get reraised by the SB, and cap with a 1-card draw. This puts 9 SB in the pot. So if you brick villian is correct to call with any quality 3-card draw. If you merely call, then there are only 7 SB in the pot, and villian should definitely fold (but often won't.)

If you are the small blind you should seriously consider smooth-calling rather than reraising so that you can afford to fold your bricked, OOP draw. If you smooth-call and BB folds you can fold the 5 SB pot to a 1-card draw if you brick. If you reraise and BB comes along anyway, the pot will be at least 9 SB and you will be tied to your hand.

Another example: You are in the BB with a 2-card draw. An EP player raises, and there is one cold-caller. If you smooth call there will be 6 or 6.5 SB in the pot. If you improve to a 1-card draw and your opponents do not, then they are (individually, although perhaps not considered together) incorrect to call your bet on the next round. If there is another caller or you reraise then your opponent's call on the next round is automatically correct.

On the other hand, with a quality 1-card draw it is almost certainly better to reraise after two or more players. You have an equity edge, and if you catch good then their next round calls will be a large mistake (well, bounded by 1 SB, I guess). However, when you brick, your opponents will certainly have odds to chase given the huge pot.

I found it helpful to work through this as I've been sticking with 2-card draws too far, and didn't have a good idea what pot size to look for. It is also helpful as a guide for games in which there is a lot of limping and cold-calling.

(Of course, I just dropped 45BB at the $1/$2 table tonight, so you may want to avoid any advice from me until I get back on a winning streak...)