In Mathematics of Poker, pages 111-122 introduces the idea of half-street games.  The first example, given on page 11 as The Clairvoyance Game, has the rules as follows:

One half-street

Pot Size of P bets

Limit Betting (The only bet size possible is 1 unit)

Y is clairvoyant

Y's range is drawn randomly from a distribution of {1/2 Nuts, 1/2 Air}

However, on page 112 of Mathematics of Poker, the authors claim that:

"Y, likewise, must bluff often enough to make X indifferent to calling or folding.  When calling, X loses 1 bet by calling a value bet, and gains P+1 bets by calling a bluff:  If b is the ratio of bluffs to bets, then we have:

1 = (P+1)b ==> b = 1/(P+1)

It seems that they are making an error in setting up the indifference equation.  They have forgotten to weight the amount won from calling a bluff to the frequency that the opponent is bluffing (1-b).  The equation they start with above is equivalent to:

(P+1)b - 1 = 0 

The correct answer is b = 1 /(P+2) , right?