Game Theory: Unusual Question #3 and #4

[well]

[ QUOTE ]
Already been checked.

Jerrod and I got the same strategies, and you and I got the same value, Jerrod apparently making an arithmetic mistake.

Craig

[/ QUOTE ]

Ok, saw posts about #3 only.
You say you and I have the same value, also the same strategy?

Thanks.

[PairTheBoard]

So B raises MORE often when A has the Option?

How does that teach the poker lesson that you should often just limp in EP?

PairTheBoard

[David Sklansky]

So B raises MORE often when A has the Option?

How does that teach the poker lesson that you should often just limp in EP?

PairTheBoard

It was only the solution to number 4 by itself that I was really interested in. I posed #3 just as an introduction. And the solution to #4 has you limping a lot.

[PairTheBoard]

I agree. B does a lot of limping in both #3 and #4. I've often felt like raising in EP often just kills the action from exactly those hands I want to be playing against while getting me heads up against hands that can beat me when I do get called - especially in certain kinds of games.

As far as the difference between #3 and #4. I'm not sure I'm seeing the game theory principle for WHY B raises more often when A has the option. Do the additional raises in the range 3/4 to 5/6 somehow act to preempt A's raising power?

PairTheBoard

[Aisthesis]

I'm not convinced that any of the solutions to #4 yet are right (unless I've missed an important one among all the posts), for the following reasons:

The value-raise and bluff-raise criteria for B must be the same as in #3 because A has no additional options when B raises. So, I don't see how there can be any difference there.

The ONLY differences between the two scenarios arise when B limps. In that case, A has some weapons at his disposal in #4.

But in case #4, when B limps, A is actually faced with a decision very similar to the raise decision of B in the easy case, but there are some significant differences:

When B raised in #3 he was winning $1 when A folded to the bluff-raise but risking $2 whenever A won.

On #4, A is making $2 whenever B limp-folds but is risking only $1 if B wins.

So, basically, it seems to me that A is just getting 4 times the odds for his raise in #4 than B got on his raise in #3.

That should at least mean that A wants to make 4 times as many bluff-raises as B did. So, rather than bluffing 1/18 of his hands, he should want to bluff 2/9 of them, I would think.

Also, on the value-raise, where B was value-raising the top 1/6 of his hands, A should presumably value-raise 4 times that many, or the top 2/3 of his hands in the range [y,5/6], where y is the threshold where B limps.

A will obviously also want to value-raise on the hands [5/6,1] because he knows he will win, and B will have to call some of the time.

Anyhow, that's about as far as I've gotten with logic. Not being able to figure out how to get a value for y that way, I tried using the brute force method and oddly came up with 1/4 (!!!), but I can't believe that's correct.

Ankenman's argument that A's raising option should actually mean that B would want to fold his thinnest value-calls seemed pretty logical to me, and if for some odd reason the call-threshold should go down, surely it wouldn't go down THAT much.

Anyhow, I guess my main point is that I don't see how B's raising criteria or A's criteria for calling the raise can change in #4 because A has no additional options in #4 if B raises (at least if I'm understanding the problem correctly).

[Bozeman]

"The value-raise and bluff-raise criteria for B must be the same as in #3 because A has no additional options when B raises. So, I don't see how there can be any difference there."

This is false: value-raise criterion depend on A's option because now B will raise more hands because it preempts A's raise. And the bluff-raise criterion is set by the value-raise criterion.

I am willing to bet on the correctness of the proposed optimal strategies.

Especially in the absence of anything close to a viable alternative. This isn't rocket science,
Craig

[Aisthesis]

Expanding B's raising criteria to pre-empt A makes sense to me.

But the rest of what you say conflicts with your solution to the problem: You have B value-raising exactly the same hands in #3 and #4 (5/6 through 1).

But you have B bluff-raising more often in #4 (1/9) than in #3 (1/18). That makes no sense to me if "the bluff-raise criterion is set by the value-raise criterion."

But I definitely see your point on B making some additional pre-emptive raises. It's just a little surprizing to me that you don't then expand B's value-raises at all.

[DoggSnott]

who gives a fiddler

[PairTheBoard]

I thought this was the agreed upon correct solution. Posted by wells and agreed to by Bozman?

http://forumserver.twoplustwo.com/sh...;o=14&vc=1

It has B value raising from 3/4 up to 1 as opposed to the 5/6 up to 1 for problem #3.

Although the Raise by B meets similar conditions as in #3, the Calls do not. So it could make sense for the Calling Interval to change. Both on the low side to folds and the high side to raises. Assuming the Linked to Solution is Correct.

Also Aisthesis, I understand you to say that A's bluffing frequency should be greater than B's because of the pot odds. When A raises B has greater Pot Odds to call. Doesn't Game Theory say the raising frequency should be less in that case?

PairTheBoard

[Aisthesis]

On raising frequency, B seems to me to have exactly the same pot odds. But A is risking less to win more when he raises, since he has already put $1 in blind.

That's not Bozeman's view of optimum. He agrees with JA, who has B raising top 1/6. Cf. his comment to well's post on this: "Jerrod and I got the same strategies, and you and I got the same value, Jerrod apparently making an arithmetic mistake."

So, Bozeman thinks Jerrod's criteria are correct but that the EV for B is 17/72 on that scenario rather than 1/4.