In reference to Robb's HH

There are spots when we value-bet where it's very thin, so thin that if we make our normal valuebet size (let's say 75%) of the pot our opponent's calling range might be so tight that we're actually value-towning ourselves.

Let's say we're playing 100nl and the pot on the river is $60, we bet $45 and our opponent calls. 6 out of 10 times he calls with a better hand, 4 out of 10 times he calls with a worse hand.

(.4*45)+(.6*-$45)= -$9

Therefore each time we bet $45 we lose $9, over 10 thin-value betting instances we lose $90. That's nearly a buy-in.

However, let's look what happens if we bet $20 into $60. The question becomes have we bet small enough to expand his river calling range to make our bet size profitable. Obviously our opponent has to call more frequently with worse hands due to either basic pot odds principles if he's a good player and a smaller/less-scary bet-size if he's a 1st-leveler.

Therefore, out of 20 river calls he now calls 13 times with worse hands and 7 times with better hands. This would be logical as his calling+winning range really should not expand at all (unless we're bluffing, which we're not in this case).

(.65*$20)+(.35*-$20)= +$6, or over 10 hands +$60

Therefore betting $20 compared to $45 is $15 more profitable in each case. All because we bet a small enough amount to gain value from our hand.

We now need to identify spots/players to employ this theory. One definitely is against a fish. The reasons for this is that they get to the river so often with a mediocre 1pr type hand that cannot stand a big river bet.

So, what's my point. My point is that against a player with too tight of a river calling range in order to go for thin value we must bet small. However, when we have the nuts like yours, it's much better to bet bigger. Yes, he got to the river with a wide range. This means that when we bet bigger we are going to eliminate a fair share of combinations from the range that might call a $5 bet. However, let's look at this:

In your hand history let's compare a $5 bet to a $20 bet. We must first assume that our opponent is going to call 100% of his combinations to a $5 bet, I think that's a fair assessment as the board texture+the river card means he's either going to have a flush or Jx or better.

The question becomes how much of his range does he have to fold to make $5 better than $20. Simple math tells of that $5 is 25% of $20. Therefore if our opponent calls $20 1/4th as often as $5 we break even.

Looking at this board texture it would be a safe assumption that a $20 bet. Let's first look at the range he might get to the river with (this is this wide because of your turn bet size):

A2s+,KTs+,Q8s+,JTs,A5o+,KTo+,QTo+,JTo,10fd's

Basically that range is any suited-ace, most off-suit aces, all broadway hands and like 10 combinations of flush draws.

On the river he won't fold Ax,KTo,KTs, and the flush draws turned flushes if we bet $20. If we bet $5 he'll call with them all of his turn range. The question now becomes have we eliminated 75%+ of his hand combinations.

Alright for fun I'll go through it:

A5o-AKo=78 combos
KTo=9 combos
KTs=3 combos
A2s-Aks=36 combos
flushes=10 combos

That's 136 combinations that are calling a $20 river bet. Therefore, for $5 bet to be better than a $20 bet his turn calling range has to have 544 combinations in it, we know it does not. Bah, a lot of typing, I might add more later.