I have been following the Clairoyant Toy Game for Two players up against eachother and the play is on the River. The Solutions in the book are for eliminating dominant strategies, pure stragies , and essentially finding the optimal solution for each play; being their bluff to value ratios of betting frequency .
Since the solution is very long, I will be just asking help on determining whether the book has a mistake at a particular out of context part.
My Problem is that I believe the Bluff to value ratio is 1/2 as suggested but this ctually gives a bluffing frequency for the bluff 33%
Players Bluff Frequency
Bluff% = b/ 2b+p
Player 1 Value Frequency
Value % = 1 - (Bluff%) = b+p / 2b+p
** Players to Bluff Ratio**
Bluff to Value Ratio = Bluff % / Value % =(b/2b+p)/(b+p) / b+p/(2b+p) = b/b+p =100/(100+100) = 1/2
The Book states that ther eneeds to be a bluff for every two Value combos , so doesn this mean that the Bluff PErcentage should be 33 % instead of the 50% suggested in the book . Because all of their calculation afterwards for two pages assume it is a 50% betting frequency for bluff hands