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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; you get $100,000 if you choose A and $1,000,000 if you choose B.

4. If their choice is B then; you get nothing if you choose A and $10,000 if you choose B.

5. Your choice is purely selfish and you do not care what happens to the other you.

6. Choices are made simultaneously and without any knowledge of the others decision.

What do you choose and why?

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".