Hey there, this isn't strictly probability, but I know there's a ton of really smart people in this forum. Hoping someone can help me understand a concept from Janda's Applications of No-Limit Holdem.
In the chapter "The Value to Bluff Raise Ratio," Janda discusses how many combos you must bluff on the flop to make an unexploitable river bet. In the example, one player has a range of nuts and air, and their opponent has bluff-catcher. The player with the polarized range makes pot-sized bets on the flop, turn and river. Janda says the bettor's range on the flop is 20% nuts and 80% air, so on the river they bet 30% of their flop range.
Janda begins at the river, and works backward through the hand to show how many bluff combos should be bet on the flop. When the polarized player bets on the river, they offer their opponent 2-1 odds. Therefore, their betting range should be 2/3 nuts and 1/3 air to make the other player indifferent to calling. Because this player is indifferent to calling, we can "look at our river bet from the perspective our opponent always folds when we bet...since our opponent folds every time we bet, these are all winning bets." Because the river bet is always a winning bet, there must be more bluff combos on the turn to maintain value-to-bluff ratio. Janda says to maintain the ratio, 15% bluffs should be added on the turn, so the player is betting 30% of their flop range for "value" (a winning bet on the river), and 15% bluffs which will check on the river and forfeit the pot. In summary, the player bets turn with 2/3 of their range for value (the winning river bet which = 30% of the flop range), and 1/3 as a bluff (the 15% of flop hands that will check and forfeit the pot on the river). He goes on to apply similar reasoning to add additional bluff combos to the flop betting range.
Quite frankly, none of this makes any sense to me. First, I don't understand the importance of perceiving the river bet as always winning.
Second, in my mind there is a simple example that goes against everything he wrote. Using the same game structure as his example, let's say Player A has 20 nut combos and 10 air combos on the flop. If they bet the flop, their opponent is indifferent to calling or folding, because they are getting 2-1 pot odds, and facing a range that is 2/3 nuts and 1/3 air. Player A can continue betting on the turn and river, with the same 30 combos, and retain their unexploitability. I don't see the need to add additional bluff combos, and I don't understand how Janda's method of starting at the river and working backwards justifies this.
I have been reading Applications very slowly, and I'm honestly disappointed. It's riddled with so many errors, and so poorly and haphazardly explained I'm losing faith in the content. Hoping I'm just being dumb and someone can straighten me out
edit: pages 105-7 if you have the book
Last edited by markdirt; 04-28-2021 at 02:11 AM.