Quote:
Originally Posted by aisrael01
Correct me if I'm wrong but in your example it's possible to prove that the expected share of the pot for the bluffcatching range is approximately 2% of the pot, despite the 51% equity share. If the polarized player shoves the flop with a range consisting of his 49% nut hands and 48.99% air hands, he can force the bluffcatching player to fold. The bluffcatching player can only win the pot the 2.01% of the time that the polarized player x/f's his air.
Working through simple yet extreme examples like this was the only way for me to understand the value of polarized ranges and how there is little value to bluffcatching against a balanced player. Your Applications book really drilled this point home and led to a Eureka moment in my poker development, so thanks for that.
A perfectly polarized range (one consisting of hands with either 0% or 100% equity), maximizes EV by betting a balanced range with an equal size on each street proportional to the pot so that effective stacks are all-in with the river bet. Such a range can actually capture much greater pot share than it's equity suggests. The range should be balanced by making the opponent indifferent between folding and calling to see if the next street gets checked.
In Janda's example the defending player should actually fold 100% of his range to any sized bet. The reasoning is that the polarized range has 100% pot share with optimal strategy, so if the defender calls any sized bet at any frequency, the polarized player can bet that sizing with his nuts only and capture greater than full pot share, while still having enough nuts left to bet a balanced range at other sizings.
It's easy to capture 100% pot by spreading the betting out over multiple streets, like Janda mentioned. The example isn't really interesting because the polarized player has so much nuts in his range that there are a lot of strategies that capture 100% pot share.
Quote:
Originally Posted by CowboyCold
Yes. Just made it up because it is bigger than zero and less than 100.
Sincere as I can be. Maybe you can help Janda explain how betting with 45% equity with no fold equity is not a losing play. I have a minor in math, but I've forgotten most of it.
I'm not sure I can explain the concepts any better than Janda has already (aisrael has made some good posts, too). Also, if you don't have Applications it's a good read. Janda is a bit too nice to shill his own book, but I don't have any financial interest in it so I don't mind. Buy it. There are some errors, so don't take it for gospel, but read it with a critical mind and it should help your poker game. He also has a newer book I have sitting on my shelf which I've been too lazy to read yet, but I hear it's also good.
I personally like to approach things by looking at simplified situations and extrapolating the concepts to real poker situations.
Lets say you have a PSB behind on the turn with 45% equity against villain's range. Every hand in villain's range has the same equity, and his overall range's equity is the same on every river. You should jam despite knowing you'll always get called, whether you're OOP or IP.
The EV of jamming is .45*3-1 = 35% of pot
If we check the opponent can bet 1.5*.55 = 82.5% of his range on the river and be balanced. When he bets such a range he captures 100% pot share. When he checks we win. Our EV is 17.5% of pot.
What I learn from this is that ranges which polarize on future streets (draws) generally profit by being able to see those streets. If we are in a situation where the opponent has a lot of high equity, un-made hands, and stacks are short, we don't want to wait until the river to get the money in, even if we are at an overall equity disadvantage and have no fold equity. Of course, real poker situations are much more complicated and real ranges include many different types of hands, and the distribution of equity across a range and across rivers isn't going to be so smooth, etc. but it gives an idea of some of the things that give us incentive to bet vs. check, IMO.