a great draw

[W. Deranged]

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...we're actually only "losing" a third of a BB on every bet that goes in on this street, and risking a third of a BB to steal BB's 2/3 of this 5 BB pot seems worthwhile to me.

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I don't get it. help?

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Let's assume we have 16 outs, which, for ease, is about 1/3 equity.

When we bet on the turn and get called, 1/3 of all the money that goes in on the turn comes back to us. That's 1/3 of 2 BB or 2/3 of a BB. So, for every 1 BB we put in on the turn, we get back 2/3 BB.

I like to think in terms of the "cost" or "real cost" of a turn bet, because I think a lot of people get too much into the "one big bet is one big bet" mode of thought and hence miss some important decisions. Betting on this turn is really not that risky because, even though we're usually behind when called, we are going to win so often.

The other part has to do with thinking about what part of the pot we are stealing. We are really only stealing the portion of the pot which the BB already has claim to. Since we already lay claim to 1/3 (that's our equity), we're really only stealing his 2/3 of the pot.

The point that emerges is that when we bet, we are not "risking 1 BB to take down 5 BB." We are really risking 1/3 BB (the effective cost of our bet) to take down 5(2/3) = 3 1/3 BB. Instead of getting 5-1 on our bluff attempt we're actually getting 10-1.

The extreme example here is when we actually have a very unlikely 50/50 draw on the turn. There, we should obviously bet every time because we are risking nothing to win the entire pot.

In other words, the effective odds we are getting on a turn semi-bluff are:

Q = P(1-x)/(1 - 2x)

Where P is pot size and x is our equity. In the neighborhood of 0 < x < .5, Q is an increasing, concave function of x where Q goes to infinity as x goes to .5.