p = 0.0 to 1.0 or the probability of winning. q = 0.0 to 1.0 or the probability of loosing.
p + q = 1.0 or the probability of winning or loosing. So, p = 1 - q and q = 1 -p. there is nothing wrong with this that I can see. On Jun 14, 8:54 pm, "Aaron S. Meurer" <[email protected]> wrote: > 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. > Seehttp://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 calculatedkellybet > > > 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 > > athttp://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.
