A beautiful woman has a head and a beautiful woman has a tail.
You play heads +3, -3 -2, +2.
You play mantissa -2, +2+1,-1.
Suppose the probability of our face is X, the probability of our face is 1-x, the probability of our beauty's face is Y, and the probability of our face is1-Y. In order to maximize the benefits, we should have equal benefits regardless of whether the opponent is positive or negative. The equation listed here is
3x+(-2)*( 1-x)=(-2)* x+ 1 *( 1-x)
X=3/8 when solving the equation.
Similarly, beautiful income, equation
-3y+2( 1-y)= 2y+(- 1)*( 1-y)
Y equals 3/8, and the expected income of a beautiful woman is 2( 1-y)- 3y = 1/8 yuan. This tells us that when both sides adopt the optimal strategy, the average beauty wins 1/8 yuan.
In fact, as long as the beauty adopts the (3/8, 5/8) scheme, no matter what scheme you adopt, it will not change the situation. If they are all heads, the expected return each time is (3+3+3-2-2-2)/8 =-1/8 yuan; If all the tails are displayed, then the expected return every time is (-2-2-2+1+1)/8 =-1/8 yuan. Any strategy is nothing more than a linear combination of the above two strategies, so the expectation is still-1/8 yuan. But when you also adopt the optimal strategy, you can at least guarantee the minimum loss. Otherwise, you will definitely be targeted by the strategies adopted by beautiful women, thus losing more.