This week the question is: Can You Survive “The Floor”?

… Let’s consider a slightly simplified version of The Floor with nine contestants on a 3×3 square grid. Each round of the game consists of the following steps:

• One of the remaining contestants is chosen at random. (Note that each contestant is equally likely to be chosen, regardless of how many squares they currently control.)
• The set of eligible opponents for this contestant is anyone whose territory shares a common edge with the contestant. One of these eligible opponents is chosen at random. (Again, all eligible opponents are equally likely to be chosen, regardless of how many squares they control or how many edges they have in common with the opponent.)
• The contestant and their selected opponent have a duel, each with a 50 percent chance of winning. The loser is eliminated, and their territory is added to that of the winner.

These rounds repeat until one contestant remains, and that contestant is the overall winner.

You are a contestant on a new season of this 3×3 version of The Floor. The nine positions on the grid are shown below:

Which position would you choose? That is, which position or positions give you the best chance of being the overall winner?

And for extra credit:

Again, a new season of the 3×3 version of The Floor (as described above) is about to begin.

What is your probability of winning for each of the nine starting positions?

Highlight to reveal (possibly incorrect) solution:

Program. Numbers.

This time I wrote a program to investigate the possibilities. In summation these are the probabilities for a win, rounded:

A, C, G, I (a corner): 13%

B, D, F, H (an edge): 10%

E (the middle): 9%

So I should choose to start in a corner.