First off, p - q == p - (1 - p) == 2*p - 1. Second, b cancels in that equation, giving you f == 2*p - 1, which should be a constant. So maybe you typed it wrong?
To find the maximum, you should use derivatives. See http://en.wikipedia.org/wiki/Differential_calculus#Optimization. The maximum value of a differential function on an interval will occur either at one of the end points of the interval or at a point where the derivative is equal to 0. Aaron Meurer On Jun 14, 2010, at 4:35 PM, butch wrote: > Pot is $ in poker pot > > minBet is minimum amount you must bet to play > > pot odds are calculated by > b = Pot/minBet > > p is the probability of winning a poker hand: > > 0.0 <= p <= 1.0 > > q is the probability of loosing a poker hand: > > q = 1.0 - p > > f is the calculated kelly bet > > f = ( b * (p-q)) / b > > substituting b with Pot/minBet > > f = ( (Pot/minBet) ( p - q )) / ( Pot/minBet) > > Solve for max f such that > > f >= minBet and, > f <= Pot > > I did this with a loop incrementing the value for minBet until it was >> = (f + delta) > > That calculated value of "f" is the max value meeting the constraints. > > Anybody have a suggestion on how to solve this explicitly and not use > a loop? > > > > > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > For more options, visit this group at > http://groups.google.com/group/sympy?hl=en. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
