Originally posted by wolfgang59 The Ultimate Creator of the Multiverse decides to have some fun with you.

He takes you and you (from an alternate timeline only a millisecond apart)
and gives you this game to play:

1. Your opponent (the other you) gets exactly the same instructions.

2. You have to choose option A or B. (As does the other you)

3. If their choice is A then; yo ...[text shortened]... simultaneously and without any knowledge of the others decision.

What do you choose and why?

Since I always get more when chosing B over A and the chance for getting nothing at all when chosing A I chose B as will my other self leaving us with 10.000 each...

Originally posted by Ponderable Since I always get more when chosing B over A and the chance for getting nothing at all when chosing A I chose B as will my other self leaving us with 10.000 each...

You hit the nail on the head with "as will my other self ..."

There are only two options.
Both choosing A or both choosing B.

Logically choose A knowing that your other self
will do so also leaving you both with $100,000

Can you and "the other you" generate independent random numbers? If you can toss a coin for a/b (and "the other you" can toss a coin which could come up the other way with a fair probability) then the average payout of you both is 277500 which beats choosing a.

If your probability of choosing a is a then (and "the other you" has an independent random number generator) then your average profit is:
a^2*100000 + a(1-a)*0 + (1-a)(a)*1000000+(1-a)((1-a)*10000
which rearranges to
profit = 10000 + 980000a - 890000a^2

to find where this is a maximum we differentiate it and set the differential to 0, which gives that the maximum profit is obtained when
a = 980000/(2*890000) = 49/89
a =~ 0.550562

where you make an average profit of just over £279,775

So it is definitely worth searching out a quantum random number generator before you make this choice.

Originally posted by iamatiger If your probability of choosing a is a then (and "the other you" has an independent random number generator) then your average profit is:
a^2*100000 + a(1-a)*0 + (1-a)(a)*1000000+(1-a)((1-a)*10000
which rearranges to
profit = 10000 + 980000a - 890000a^2

to find where this is a maximum we differentiate it and set the differential to 0, which gives tha ...[text shortened]... is definitely worth searching out a quantum random number generator before you make this choice.

Good job!!!!

I hadn't thought of that.
I should have taken more care over the amounts.

The game is of course a variation of "The Prisoner's Dilemma".