Theory of Poker pg 166--extra $100???

[dukenukem]

Sorry to jump ahead of the study sessions, but I have been struggling to understand something on page 166 (1999 edition) in the first paragraph under the header, "Optimum Bluffing Frequency":

"Regardless of what your opponent does, you average winning an extra $100 every seven hands."

Would somebody who has read the entire passage leading to this conclusion please explain to me where that "extra $100" comes from?

Thanks!

[DiamondDog]

I'll have a go.

There's $100 in the pot and you're deciding whether to bet or not.

Suppose you have a choice between just two strategies.

The first is what you might call the HONEST strategy.
That means you only bet when you have the best hand.
Because you're honest, your opponent knows that it's safe to fold when you bet, but that when you check, he should bet because you will now fold and he'll take it down.

Consider what happens over 7 hands.

Suppose you have the best hand on 6 occasions.
You bet 6 times and win $100 on each occasion.
The seventh time you stay honest and let your opponent win the $100.

Your EV from the seven hands is $600 and your opponent’s EV is $100.

Now consider an alternative strategy. We’ll call it the MIXED strategy because sometimes you bet with the best hand and other times you bet with the worst hand (ie. you bluff).

The probability that you’re bluffing on any given hand is 6/1 against.

Now consider your opponent’s EV over 7 hands if you adopt this mixed strategy and bet every hand.

If he calls every time his EV from the 7 hands is
6 x -$20 + $120 = 0

and if he folds every time his EV is also 0.

Either way his EV from the 7 hands has gone from $100 when you played HONEST to $0 when you play MIXED.

The reduction in HIS EV is an increase in YOUR EV.

I hope I’ve got that right.
I’m sure there’s a simpler way of explaining it.

[dukenukem]

DiamondDog, thanks for taking the time to make it clear. I'm printing this out to keep in the book at page 166!