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From Mastering Small Stakes Holdem:

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What is going on in the first paragraph? Does it mean that if an opponent is laying your 2:1 pot odds, and if he is playing GTO, he will have ensured that 33% of your range is beating him (so that in the long run your opponent is indifferent to whether you call him or not, assuming you only call at the top of your range and fold at the bottom of your range)?

George
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The first paragraph is stating that you will win as often as your opponent bluffs. Strong players tend to give you pot odds that are close to their bluffing frequency. This is not always the case, but not a bad rule to keep in mind.

Also notice the key word "if" in the 3rd sentence.

If his range is 67% value hands and 33% bluffs, you will win 33% of the time.

this "if" implies that in this particular situation, the pot odds and bluff frequency match.

Clarko
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  • You mean strong players tend to give you pot odds that are close to their bluffing frequency? In any event, what is the theoretical reason they do this? – George Nov 05 '18 at 23:27
  • They do this because a strong player knows what their opponent thinks that their range is, so they give their opponent the right price to call against that range regardless of what their actual hand is. And I have edited and changed it to bluffing range :) – Clarko Nov 06 '18 at 02:02
  • @George forgot to tag you – Clarko Nov 06 '18 at 04:55
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Calling at the river I don't like talking about range. You hit or you did not. You could be in the top of you range and not hit.

You need a bluff catcher which is a pair or maybe an ace.

The math is kind of a bit out there but you should call a pot size bet 1/2 the time with a bluff catcher.

The quote does not state GTO. Mathematically if you don't know where you stand then you should bluff a pot size bet 1/3 the time.

It they are bluffing 1/3 you lose 1 pot twice and win 2 pots once. You are dead even.

paparazzo
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The GTO strategy for the opponent is to bluff 33% of the time and bet for value 67% of the time. This is because it makes us indifferent to calling vs folding since our EV is the same for either action.

One the other hand, when we call a pot sized bet on the river, we win two pot sized bets if our hand is best and lose one pot sized bet if it is not. Therefore, we need 33% equity against the opponent's range to call a pot sized bet on the river.

Qudit
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