In that other thread I started, it was determined that if a called hand has a 21% rake and an ante steal has no rake, then the first guy should push ten times the pot in nlh, all in, and he forces the other guy to fold all but excellent hands. The only way the caller can dissuade the pusher is by calling more often and hurting both of them.

On the other hand if the caller left his little sister in his seat and told her out loud to call with anything decent, the pusher is handcuffed and in theory must push much less often.

That's can't come up in real life. But two analogous situations come up all the time. One is in a tournament where one of the tiny stacks is sure to go broke within the next few hands, your stack is small but can last several rounds, and only one player needs to be eliminated for you to get in the money. The last remaining player against you can push with everything including hands that would normally be big losers, because you must give up on many hands that figure to be clear favorites over him.

In no limit hi lo split games the slightly inferior low draw can force out the better draw with a big bet in a three handed pot where the third person has the high locked up. Do you see why?

But again if my oponnent is stupid, rich, or vengeful, and I know he won't fold when he should, I can no longer profitably make these plays. Which brings up the question (not begs not begs not begs) as to whether there is actually some sort of optimum mixed strategy that is mathematically better than meekly accepting that your opponent, by virtue of being able to go first, or survive an all in contest can take lots of EV from you by making you fold better hands.

I actually started a thread on this subject a few years ago:
https://forumserver.twoplustwo.com/1...alled-1562868/

The conclusion was as I remember (to make it simple):

Just like you can tell your sister to call with everything, the same way your opponent can tell his sister to just jam everything every hand. This way you have no choice but to remove your sister and play normally. Your opponent always has an edge here. The situation is similar to the concept called "a game of chicken".

However, an interesting thing that I discovered in my thread was, that if one of the players theoretically had a superpower to see into the future (and the other guy knew), he would actually be at a disadvantage because of that.

I just noticed that your name was actually mentioned in that thread

Idea has been discussed a few times in a few variations, I posted a spite calling toy game back in 2013:
https://forumserver.twoplustwo.com/1...-game-1394693/

Above is based on some bubble ICM equities. There are frequently spots in tournaments where player A can make deviations from Nash that result in a very minor loss of EV compared to playing Nash and inflict a much larger EV loss to player B. If player B then adjusts their strategy to reduce that EV loss then player A is considerably better off than in the original Nash state.

I thought heads up tournament ICM shoves and calls was a completely solved and documented subject.

The more normal real world situation is that the shover had x number of potential callers, and either does or does not factor that into his shove.

Now the last potential caller in the BB, should be able to make a Nash Equilibrium call perfectly. The other potential callers between the shover and the BB have a much more complicated analysis (although I assume that has also been solved by enumerating every possible scenario).

Getting to act first is good, but if a caller gets to act last the caller should know how to break even.

The application of FTOP to three-way no-limit games is a very interesting subject, I hope you put a chapter on it in your book.

^ Linked thread is about e.g. SB vs BB after the other players on the table folded. In an actual heads up situation ICM doesn't apply.

In that other thread, two forumers now say it is actually 17 percent. I have always said it is 26 percent.

Maybe you should revisit that thread.

A potential caller should always call as often as possible without harming himself, modified for ICM of course.

How can you possibly think these questions have different answers?

Please post back in the other thread, so we don't derail this one.

(reposting this comment after I deleted it previously):


There were two different questions in that thread:

My answer to this is: 20.61%.

My answer to this is: 17,48%.


I'm confident that those are the correct results.

Your calculations however, don't seem correct to me for the reasons I mentioned in that thread (your calling range doesn't make sense, your use of card removal, the final EVs don't add up...)