Quote:
Originally Posted by HappyLuckBox
Actually, you want more bluff combos on each prior street, because a bluff combo can turn into a "value combo" on a future street.
This is a reason, but I wouldn't say it's the main one.
Every time we bet with a perfectly polarized, balanced range (bluffs always lose, value bets always win), we effectively win the pot. In this hand if the board bricks out we have 18 value combos on the river, and by betting half pot we offer our opponent 3:1, so we need to have one bluff combo for every three value combos to make villain indifferent to calling with a bluffcatcher. We can bet the river with 24 total combos, 18 value and 6 bluffs.
On the turn we will also bet half pot offering the opponent 3:1. He needs to be able to win 25% of the time to make a breakeven call. Since he always wins when we check the river, and loses when we bet the river with a balanced range, we can add some turn bluffs which will give up on the river. 8 additional combos can be bluffed on the turn which will give up on the river, so we end up betting the river (and winning) 75% of the time.
The same idea can be applied to the flop. We can add 32/3 ~= 11 flop bluff combos which will give up on the turn. This allows us to bet 18 value combos on the flop and 25 bluff combos.
This isn't the whole story, though, because our bluffs have significant equity when called and our value bets will rarely be outdrawn, so we can actually bluff even more often on the flop. IDK exactly how much more often, but we can see that there is a cap on how much we can bluff. If we bet half-pot on the flop, then the opponent's JJ or whatever can jam 3.5 PSBs to win 1.5 PSBs and our range has to be about 34.5% value to make this jam breakeven. Therefore, I would guess that having 34 bluff combos on the flop for our 18 value combos is about optimal, and when we bet the flop with this range a hand like JJ will be close to indifferent between calling, folding and jamming. Does this seem reasonable?