All of Wamba-Ivanhoe's Comments + Replies

Going back to each of the finite cases, we can condition the finite case by the population that can support up to m rounds.  iteration by the population size presupposes nothing about the game state and we can construct the Bayes Probability table for such games.

For a population $M$ that supports at most $m$ rounds of play the probability that a player will be in any given round $n<=m$ is $\frac{2^n}{M}$ and the sum of the probabilities that a player is in round n from $n=1\to m$ is $\sum _{n=1}^m\frac{2^{n-1}}{M}=\frac{2^m-1}{M}$; We can let ... (read more)

I posit that the supposition that "At some point one of those groups will be devoured by snakes" is erroneous.  There exists a non-zero chance that the game goes on forever and infinitely many people win.

The issue is that the quoted supposition collapses the probability field to only those infinitely many universes where the game stops, but there is this one out of infinitely many universes where the game never stops and it has infinitely many winners so we end up with residual term of $\frac{\infty }{\infty }$.  We cannot assume this term is zero just because of ... (read more)

Calculating the odds of dying when playing the snake-eyes game with a player base of arbitrary size.

For an arbitrary player base of $B$ players, the maximum possible rounds that the game can run is then the whole number part of $Lo{g}_2\left(B\right)$, we will denote the maximum possible number of rounds as $m$.

We denote the probability of snake-eyes as $p$.  In the case of the Daniel Reeves market $p=1/36$.

Let $D_n=$  the probability density of the game ending in snake-eyes on round n then $D_n=p(1-p{)}^{n-1}$.

The sum of the probability den... (read more)

Because all scenarios have P(red) >= 50%, the combined P(red) >= 50%. This holds for both SIA and SSA. 

The statement above is only true if the stopping condition is that "If we get to the batch $B$ we will not roll dice but instead only make snakes with red eyes", or in other words $B$ must have been selected because it resulted in red eyes.

Where $B$ is selected as the stopping condition independent of the dice result, the fate of batch $B$ is still a dice roll so there exists a $B+1$ scenario. Any s... (read more)