Exit Times

Timing the exit

Counting visits to measure time

Why two tails take longer than a head-tail

How long fair games last

Why does the expected exit time g satisfy g of x equal to one plus the sum of p of x, y times g of y, rather than the same sum without the one?

What values does the expected exit time g take on the target set A, and why?

Why is the expected exit time computable as I minus r inverse applied to the all-ones vector?

Both patterns HT and TT have probability one quarter on any two fixed flips, yet the expected wait for TT is 6 and for HT is 4. What explains the gap?

For fair gambler's ruin on zero to N, which properties does the expected duration E of x tau equal x times N minus x have?

For a gambler losing at rate q minus p per play, starting at x, why is the expected time to go broke roughly x over q minus p?

In matching pennies with 25 total coins, Bob starts with 15. Using the fair ruin duration formula, compute the expected number of flips until someone wins all the pennies.

At the two-year college, a sophomore repeats with probability 0.2, graduates with 0.7 and drops out with 0.1. Compute the expected years until a sophomore leaves, and write the answer as a fraction or decimal.

Compute the expected number of fair coin flips needed to see tails twice in a row, and write the number.