Question

You have $B in your bank account. You are asked if you would like to participate in a bet in which, if you win, your bank account will become $W. However, if you lose, your bank account will contain only $L. You win the bet with probability pw. How large should pw be to accept the bet? (

Answer 1

Pw = ( B - L ) / ( W-L )

Step-by-step explanation:

pW + pL = 1 ------ ( 2 )

Expected value after placing bet = W*pW + L*pL ------ ( 2 )

pL = ( 1 - pW ) from equation 1

rewrite equation 2

W*pW + L*( 1 - pW ) ------ (3)

The condition to accept bet is ; W*pW + L*( 1 - pW ) > $B

= W*pW + L - LpW > $B ( factorize )

= ( W - L ) * pW + L > $B

hence the value of Pw = ( B - L ) / ( W-L )