STOP CALLING

When faced with a pot sized bet on the turn defender
should never call unless one of the following
conditions are met.
The hand being represented by aggressor is worst than
defender's hand or defender is drawing live to that
hand. Don't bother drawing to 4 or 5 outs.
Or.
The aggressor is a known high frequency bluffer likely
to be bluffing more than 5/9 of the time.
In most cases just folding to large turn bets is
probably best strategy.

Critical Points.

1. One street.
2/3 Clairvoyant has 100% equity.
Clare bluffs one for every two winners. When dealt 2/3
winners Clare bets every hand and Dean should always fold.
1/2 Clare wins 1/2 pot per play.
1/3 Fair and equal game.

2. Two streets.
4/9 Clare has 100% equity.
Clare bluffs 5 for every 4 winners.
1/3 Clare wins 1/2 pot per play.
2/9 Fair and equal game.

3. Three streets.
8/27 Clare has 100% equity.
On the flop Clare should be betting 19 losers for every
8 winners.
2/9 Clare wins 1/2 pot per play
4/27 Fair and equal game.
In an equal game Clare has 46 losers for every 8 winners.
On street one she bets 19 losers for every 8 winners.
She gives on 27 losers. On street two she bets 10 losers
to her 8 winners. On street three she bets 4 losers to
her 8 winners. This overbluffing on earlier streets
is the optimal game theory strategy.

Critical Points for half pot bets.

1. One street.
3/4 Clairvoyant has 100% equity.
9/16 Clare wins 1/2 pot per play.
3/8 Fair and equal game.

2. Two streets.
9/16 Clare has 100% equity.
27/64 Clare wins 1/2 pot per play.
9/32 Fair and equal game.

3. Three streets.
27/64 Clare has 100% equity.
81/256 Clare wins 1/2 pot per play.
27/128 Fair and equal game.

Critical points for quarter pot bets.

3. Three streets.
64/125 Clare has 100% equity.
48/125 Clare wins 1/2 pot per play.
32/125 Fair and equal game.

CONCLUSIONS

When faced with a bet, the defender has three options.

A. Always call.
B. Always fold.
C. Call pot/(pot+bet) part of the time where pot is
the original size of the pot.

For years while playing limit lowball (C) seemed like
the best default action. The pots were big and the
bets were small.
Multiple streets favor the aggressor. Even in fixed
limit hold'em calling for three streets is a huge
disadvantage. The aggressor can check and give up
on some of her bluffs. She will bet all her winners
every street.
Example. 10 small bets in the pot. The defender is
faced with a small bet on the flop. Figures it will
costs two more big bets to call down. The naive pot
odds approach says 5 bets to win 15 bets. A 25% chance
of winning should be sufficient for calling down.
This neglects that the aggressor bets all the winners
three times and will check many of the losers. The
clairvoyant three street method says the defender needs
31% equity to call with plus EV and 63% winners for call
down to be equal EV.
In nolimit when facing two or more streets of betting
the defender no longer has the luxury to call. It's
too expensive.
Here's the numbers for a two person pot with two streets
and half pot bets. Defender should call pot/(pot+bet)
part of the time. That's 2/3 in this case. Providing
the aggressor is bluffing frequently. She needs to
bluff seven times for every nine winners. Are very many
players bluffing that often? Probably not. If her bluffing
ratio is less, he should always fold.
Defender must have a good reason to call. Lacking a good
reason the best default action is (B), always fold.