Question: Consider the problem above again. Suppose we tossed a coin T times and the resulting zt were all +1. The reward will be: (a) Show

Consider the problem above again. Suppose we tossed a coin T times and the resulting zt were all +1. The reward will be:

2") Wr (T +1) %3D .

(a) Show that the conditional expected reward as we just play one more time is:

image

(b) How does this compare with WT? Should the player then ?stop??

(c) But if the player never stops when he or she is in a winning streak, how long would the player continue playing the game?

(d) What is the probability that z, = ? 1 at some point?

(e) How do you explain this puzzle?

2") Wr (T +1) %3D .

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