clipka wrote:
> Warp schrieb:
>>   3) Assume two people, person A and person B, who want to decide who
>> gets
>> a price by tossing a coin.
>>
>>   Person A is a bad loser and a bully, so if he loses he says "I said
>> it's
>> two out of three". So they play it like that. If A loses again, he says
>> "I said it's three out of five", and so on, until he wins.
>>
>>   How many tosses is this game expected to last, in average?
> 
> I think that very much depends on whether the sequence is
> 
>   1 - 3 - 5 - 7 -  9 - ...
> 
> or
> 
>   1 - 3 - 5 - 9 - 17 - ...
> 
> 
I didn't look at the other puzzles, but this one sounds easy enough to
work with before sleep.

First round, A claims 'heads I win' so could win 50% of the time.
Each time B gets a tail flip, A increments how many are needed to win.

Best N out of 2N-1.

Okay, A stands to win first round 50% of the time.
Second round, A can not win because he obviously lost first round.
Third round, A has a remaining 50% chance to win if he won either
previous, a 0 if not.

Just going on brain alone, and barely any of that since it is late here.
But it seems that if the game progresses past the first round, it has a
high chance of going on forever. Same for any of the loss points after
that. Average of 1 + infinity is somewhat closer to infinity than to
one. I would say the game in unwinnable.

The other option is that Player B just needs to punch A, take the coin
and walk away. At least he wins a coin, this way.

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