# Roulette Probability with Coins

A question to answer a debate I have just had, Russian Roulette with coins...

We just played a game of Russian Roulette with 6 coins of different denominations as we did not have a gun.

The game was meant to be a fair game of chance to decide who would go to the shops.

Someone who was not in the game laid out 6 coins in a row, out of sight from the game players. They were different british coins with the £1 coin representing the bullet.

We took it in turns to name a number (1-6). The first person chose a number (number 2), his was not the £1 coin, this was shown to the group and he "survived".

At this point the others in the group claimed that the person who went first had the advantage as he had a 1 in 6 chance and the next person now only had a 1-5 chance. If the second person chose correctly the next only had a 1 in 4 chance etc.

If the second player had chosen number 2 (in his head) as his on his go he would now have to revise this and chose another number (1,3,4 5, or 6)

My understanding was that we all entered the roulette with the same odds (1 in 6) and that even as the game continued and the chance to survive decreased with every correct choice because we entered with the same odds no one would have an advantage over another.

Please could someone advise me (in simple terms) on the odds and fairness of this game. Is this a fair system to decide a choice eg as fair as a coin toss?

Many thanks,

Eddie

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The second player has a 1-in-5 chance if the first player survives and a 0-in-1 chance if the first player doesn't survive. So the second player's chances are $(1/5)(5/6)+(0/1)(1/6)=1/6$.
The game is fair: the fatal coin is equally likely to be in any one of the $6$ positions.