Monday, November 2, 2009

Cold-Calling a Blocking-Raise with a Low-Draw: Scenario 1

A tactic, that Seven-Card Stud High-Low (Stud-Eight) players frequently encounter, is what I call a “blocking-raise.” This is a raise intended to force out a player on a low-draw. Usually, a player who has just made a low-hand, and wants to force out a player drawing to a better low, executes this kind of raise. Blocking-raises occur most often on Fifth or Sixth Streets, when a player has completed a weak low—such as an 8-high—and wants to force out a player showing two undercards, but no other low-cards. Any player, with only two exposed low-cards, cannot have a low-hand until the river. In this post, I will analyze a scenario to determine if cold-calling a blocking-raise is a correct response. As is usually the case in high-low poker, whether or not a scoop is possible, has large effect on the expected value for a play.

For these computations, I will assume a $1-2 game with eight players dealt into the hand. Hole cards are in parentheses.

After Fifth Street you are in a three-way pot with the following:

You (2, 3) 4, 5, 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.
Total seen cards = 16 (Eleven that you are looking at, plus five mucked door cards).
Total unseen cards = 36.

If your hand is completely live, your outs are as follows:

Outs to make a straight=8 (four As plus four 6s)
Outs to make a better low = 4 (four 7s)
Outs to make comparable low = 3 (three 8s)

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

Straight = 22%
7-high low = 11%
8-high low = 8.3%

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

A straight will scoop.
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 = (0.22)P + (0.11)P/2 + (0.083)P/4 = (0.296)P

You expect about 30% equity in the total pot after the action is completed. If you cold-call the $4-raise and Alice closes the action with a call, the total pot-size needs to be at least $13 for your equity to equal the $4 call. We know that the antes and Fifth Street action alone is equal to $13. If there was any prior action on Third and Fourth Streets, the pot is larger than $13. Cold-calling the raise is a profitable response. Not only is the current pot-size large enough, but also the implied pot-size from action on Sixth and Seventh Streets is greater still. And you get a second chance to make the hand if you miss on Sixth Street. Depending on the exposed Sixth Street cards, a cold-call might still be favorable.

However, it is rare that your hand is completely live. The kinds of missing outs make a big difference in your pot-equity. If the 7s and 8s are dead, but the straight draw is live, your pot-equity falls to 22%. That means you need to take down an $18 pot to make a $4 investment worth it. But, if your straight-draw has missing outs, your pot-equity is considerably reduced. Suppose you only have four outs left for your straight, but the 7s and 8s are live. Now your pot-equity is 18.5%. You need a pot in excess of $21 to break-even. That could be a stretch. You might only get that kind of action if the high-hand can beat a low straight, in which case you have only half the equity that you thought you did.

Also keep in mind, that if Alice jams you, that is not close the action by calling, she might be unafraid of a low straight because she can already beat one. The kind of player Alice is has a big effect on your equity. Some players with high-hands are timid in response to a possible low-hand because they are afraid of being freerolled. These players will call the low-hand down, unless they can beat a low straight, in which case they will raise. Other players are more afraid of giving free cards than being freerolled, and will jam anyone raising with a low-cards, even if all they have is one or two pair. In that case your scoop possibility is still live.

Next week we’ll look at a scenario in which scooping is not a possibility.

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