A release-checked medium problem for training Games, Discrete Random Variables.
Question
You roll a fair 100-sided die with values $1-100$ on the sides and observe the value that appears. You now must guess whether the second roll will be at least as large as the first roll or not. If the second value that appears is $y$ and you guess correctly, you receive $\$y$ payout. Otherwise, you receive nothing. Assuming optimal play, find the smallest integer $t$ at which we guess that the second roll is lower than the first.
Practice focus
This Probability problem is tagged Games, Discrete Random Variables. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.