Tuesday, November 10, 2009

Cold-Calling a Blocking-Raise with a Low-Draw: Scenario 2

Last week, I analyzed a tactic in Seven-Card Stud High-Low Poker I call a "blocking-raise," in which a player with a made low-hand on Fifth or Sixth Street, raises a bet from a high-hand to force out a player on a draw to a better low. The issue is whether it is correct for the player on a draw to cold-call the raise. Analysis showed that if a scoop is possible for the player on a draw, cold-calling does gain equity. The amount of equity depends on the number of outs that are still live. But what happens if no scoop is possible?

Consider a second scenario:

After Fifth Street you are in a three-way pot with the following (hole cards are in parenthesis):

You (A, 2) 6, 7, J
Bob (x, x) 3, 4, 8
Alice (x, x) K, 9, J

Action: Alice leads with a $2 bet; Bob raises to $4. It is your turn to act.

Again for computational purposes we will assume a $1-2 game with eight players dealt into the hand.

Total seen cards = 16 (Eleven that you are looking at, plus five mucked door cards).
Total unseen cards = 36.

A scoop is less likely in this case because you cannot complete a straight. Your only hope to scoop is to pair the Ace and hope it holds up against the high-hand. If your hand is completely live, your outs to make low-hand are as follows:

Outs to make a 7-high low=10 (three 3s, plus three 4s, plus four 5s)
Outs to make an 8-high low = 3 (three 8s)

Again we can divide the number of outs by 36 to arrive at Sixth Street probabilities. Your chances on Sixth Street of having a:

7-high low = 28%
8-high low = 8.3%

Again we can approximate your equity in the pot by making the following assumptions:

A 7-high will win the low-pot.
An 8-high will win the low-pot about half of the time.

Then if (P) represents the pot-size, and (E) represents the equity in the pot, then under these assumptions:

E = (0.28)P/2 + (0.083)P/4 = (0.16)P

Because you are on a draw for only one-half the pot, your equity is only one-sixth of its value. To break-even on this play you need a pot-size of about $24. Unless there was a great deal of prior action on the early streets in the hand, it is unlikely that the pot is that large. It is also unlikely that your low-draw is completely live if Bob already has a low-hand. In this scenario, without a possibility of a scoop, it is best to fold to the raise.

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