how many times should I flip a biased coin

Question

If I have a Biased coin, where the probability of Heads (P(h)) is 37% and probability of Tails (P(t)) is 63%,

Head I win $2, Tails I lose $1 And I start with a starting balance of $10, How many times should I flip the coin to make my ending balance $30?

Answer 1

The formula for expected value is:

E(x) = n•P(x)

n P(x) E(x)

$2. .37 $0.74 (win is positive)

-$1. .63 -$0.63 (lose is negative)

-----------------------------

E(x)=$0.74+(-$0.63) = $0.11

That means you are expected to with 11 cents in one single flip.

Remember you already have a starting balance of $10 in your account.

Let y be the number of flips:

10+0.11y = 30

0.11y = 20

y ≈ 182 flips