any math guys here? i want to know something about a simple game that i sometimes play with a friend, it's called "deathrolling".
the way the game works is that first, a random positive integer n is chosen. then, the following steps are repeated until the losing condition is met:
>pick a random integer m such that 0<m<n.
>n becomes m
the losing condition is that m=1.
for example, say we play and we choose 500. i then get a random number between 0 and 500, say 3. you then get a random number, say 2. then i'm up again and i get 1 at which point i'll have lost.
i don't know the lingo so i apologize. what i want to know is the relationship between how many expected steps there will be until a game ends and the initial starting n. in other words, if i start with n, and the number of steps is m, then what does the function look like into which i can plug in any n and get out the corresponding m. obviously, 2n doesn't mean i'll have 2m steps.
the way the game works is that first, a random positive integer n is chosen. then, the following steps are repeated until the losing condition is met:
>pick a random integer m such that 0<m<n.
>n becomes m
the losing condition is that m=1.
for example, say we play and we choose 500. i then get a random number between 0 and 500, say 3. you then get a random number, say 2. then i'm up again and i get 1 at which point i'll have lost.
i don't know the lingo so i apologize. what i want to know is the relationship between how many expected steps there will be until a game ends and the initial starting n. in other words, if i start with n, and the number of steps is m, then what does the function look like into which i can plug in any n and get out the corresponding m. obviously, 2n doesn't mean i'll have 2m steps.
