In this game, all players start sitting at a round table, each with a coin in their hand.
At every turn, all players toss their coins together and put it on the table in front of them. Then each player looks at the coins tossed by his left and right neighbours.
If the neighbours got the same result (both heads or both tails), the player in the middle gets eliminated and doesn't get to play further.
If the neighbours got different results (one heads and one tails), the player sitting in between them survives for the next round.
All the eliminated players pick up their coins and leave the table , and the remaining players proceed to the next round.
The game is won when only two players remain seated on the table.
Those two then get the ultimate prize - the ultimate honor of getting to see the secret spaghetti recipe.
If all players are eliminated at the same time, the game is a tie and nobody gets the prize.
If the coin-toss is such that nobody gets eliminated, then the game continues normally. No tie or everyone wins thingy.
No changing of seats in between the game.
You and your friend are offered a chance to play this game and try your luck. The aim is for at least one of the two of you to survive until the end of the game.
You can choose your and your friend's seats, and you can also choose to play starting with 10, 11, or 12 players including yourself and your friend.
Which would you choose and why? Please include a full explanation.
Thanks to @GOTO0 and @randal'thor for the original idea for this puzzle. This is just another version of the original one.