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
                     = 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

1 Answer 1


I haven't actually read the book, but "50% betting frequency for bluff hands" could mean that he bets his bluffs at a 50% frequency, but that doesn't not mean that they represent 50% of his total bets.

For example, if the player has 100 combos of bluffs, but bets them at 50%, he bets 50 bluff combos. If he has 100 combos of value, then his bluffs represent 1/3 of his total bets.

  • You are right and actually the example illustrates this. Thanks for your comment and allowing me to go further into the problem in the book . Kudos
    – GoitomFess
    Jul 2, 2020 at 14:36

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