Its a theoretical concept that is applicable to this situation.

You check good hands to balance your checking range.

For villain to make a profitable call his call needs to "be best" 1/3 of the time. This is derived from the size of the pot, in my example hero makes a pot size bet, so if we assume there is no further action then villain could call 3 times, make the correct call only once, and break even.

That is theoretically incorrect. Even HU, if we assume the psb is all-in then if villain folds 2/3rds of the time and calls once then he is not break even unless he wins 100% if the time when he calls, which he won't. And multiway, you are ignoring all the factors I have mentioned earlier and many others.

think you are misreading his post

^ +1

I guess I missed the phrase "with no further action", prob as I saw that bit that said the concept was applicable to this situation where there are streets left. It's hardly the point though.

If the pot is 5-way and the first guy donks the pot and you, being next to act, reckon to be good 1/3 of the time against the better then you think a call is break even? It's would be if everyone else folded and you knew they would, but they will call if it's in their interest - so you can't call.

We're not arguing about that (at least I'm not), just that this part is all wrong :

We're sort of going around in circles here and I think it's bc we're mixing a lot of separate issues.

So ideally when we talk about a polarized betting range vs a bluff catching range we're already assuming that no other range has strong hands in it. This holds true no matter how many players in the pot because that's the limitation we set in the conditions.

Those limitations, however, do not hold true in normal play regardless of the number of players. If a single opponent has a range that can still contain some really strong hands, we can't valuebet or bluff as much as we could in our abstracted game.

So it's not that the number of players that changes the conditions directly, it's the consequence that there is a higher likelihood we face really strong hands that reduces our value bets and bluffs. That would hold true regardless of the number of players.

Lol you guys have a point. I think I thought that the other comment was about villain having no read so was protecting against hero making a profit by bluffing by calling x%. In that case it is relevant that there are cards to come as you may not always win with the x% you call.

Nobody has set any conditions about the other players, or has said that it's a nuts or air scenario, so we cant apply simple HU nuts or air principles to a situation that is multiway and anything but a nuts or air scenario.

Re the last comment, having to worry about other players changes things a lot unless you impose some heavy conditions. I guess if all other players can only have bluff catchers then once you call they probably can't call, but that's not the scenario here and it's a big restriction to make in most cases.

I was assuming any time we talk about nuts/air vs bluff catchers it's just shorthand for the results of the abstracted game that illustrates our point. This is true regardless of how many players in the pot.

I'm agreeing that it's a big restriction to make REGARDLESS of the number of players. The condition that makes it a terrible restriction is that we're assuming it's nuts/air vs bluff catchers which is idealized in a lot of scenarios, even if they are heads up, not because we make that assunption multiway.

umm no, I was refering to villain folding 2/3 of the time against a psb. Dunno where you get that from. The minimum defense freq against a psb is 50%.

Also villain is not breaking even if he calls 1/3 of the time and win 100% when he calls. Folding is 0 ev and calling with 100% equity is +ev.

Re the first point, that's why said x%. If it was a half sized bet then that rationale gets you to calling 2/3 but the point was about when you can apply that rationale and not what x is.

Re the second point, I don't know what point you are trying to make. If you are trying to make villain neutral over whether to bluff or not and you call 50%, say, then fine when on the river. But if there is a card to come and you call the same 50% then villain potentially has a profitable bluff if any of those bluffs that get called can end up winning.

I'm just saying post #52 is all wrong

Villain isn't breaking even in the river situation you described, his ev is 1/3 pot.

The last part of your post is correct and the minimal defense frequency is different on the earlier streets. You have to keep in mind it's still slightly +EV for villain to check/checkback with bluffs on the turn so it's normal that his bluffs bets are slightly +EV as well.

I think the lead is terrible for so many reasons. You can't get 3 streets of value, hand rarely improves on later streets, you are somewhat capped.

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Donking flop doesn't cap you at all, at least not necessarily.