Wednesday, May 30, 2007

19.3 Game Implications.

On this static model the defender starts with nearly a 85%
probability of having the best hand and still was only
able to call three bets less than 10% of the time. With
barely over 15% winning cards the clairvoyant wins over
40% of the pots.
In dynamic models of real poker hands the defender usually
has less than 50% chance unless she hits the flop big.
I believe even in the dynamic case pot/(pot+bet) calling
frequency is still correct. Provided calling is still
a viable option. Often a new board card is so detrimental
to defender, his linear hand strength(LHS) becomes too low
to consider calling.
His best response is to call if and only
if F(y) > B/(2B + 2).

Where B is the bet and 2 is the pot.
This is from 5.1 pp13-14. Case 1 on page 14.
This is a paper by Thomas Ferguson.
www.math.ucla.edu/~tom/papers/poker1.pdf
The raiser's distribution is often stronger than
the defender's. Often it's the raiser always bets and
the defender always folds.
For the defender it becomes fold when LHS is too low.
Certain hands are 'clear' calls. There's an inbetween
region where defender should sometimes call and other
times fold. Call with pot/(pot+bet) frequency with these
hands. Unlike the [0,1] toy games defender shouldn't
always choose the hands with the highest LHS. LHS only
measures probability of finishing with the best hand at
showdown. He favors drawing hands with potential to be
betting or raising hands. There may be some other vector
which measures chip winning potential better. Call with
the highest pot/(pot+bet) on that chip vector.
The defender is at such a great disadvantage that it may
be wrong to ever cold call an opening raise. He will be
facing a c-bet by opener raiser over 50% of the time and
will get a piece of the flop at most 35% of the time.
There just doesn't seem to be any percentage in calling.

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