Re: Reducing risk for a client. Is this the right solution?
My adviser presented me with a solution to counter my logic.
I don't have time to confirm it yet but just in case he is correct, please stop using my strategy until everything is clarified.
Anyway here is my advisers solution:
If you are rational risk averse, you do not play this game if you value
your life more than the other guy. PERIOD. I know this for a fact.
Let's make this simple. Say you value your life at 100 and your
opponent's life at 80.
EV playing game = 50% * -100 + 50% * 80 = -10
If your opponent also believes your life is worth 100 and his is only
worth 80.
Opponent EV playing game = 50% * 100 + 50% * -80 = 10
If anything, you want to go 2nd because if you go first and don't die,
your opponent may choose to quit the game, a source of counterparty
risk. Therefore your equity is (assuming you value your life and your
opponent's both at 100):
EV = [-100 * (1/6)] + [100 * (1/5) * (prob of opponent not defaulting on
claims)] + [rest of EV series]
This number will always be <=0, therefore at best breakeven and most
likely negative EV to go first assuming even the smallest bit of
counterparty default risk.
You say that "The highest risk of death possible is 100% lost of life
which is in the package that includes the last shot. Any rational risk
averse person will prefer any other package holding EV constant."
This thinking is seriosly flawed as you need to discount this 100% loss
of life by the probability that it will reach the 6th shot which is
about 1/6.
100% chance of dying on last shot * prob of reaching last shot =
100%*(1/6)= -16.7%
(1/6) change of dying on first shot * prob of reaching first shot =
(1/6) * 100% = -16.7%
Therefore you are indifferent to either. In fact mathematically, the EV
of the 1,2,3,4,5, or 6th shot are equal at -16.7% for the player taking
the shot and +16.7% for the player not taking the shot.
Assuming the real world and how much counterparty risk there is, I would
definitely take the 2nd shot. If it gets down to the last shot, I can
always default. In fact, I can default on the second shot gaining me
16.7% EV. Last time I checked, games of Russian Roulette aren't
enforceable.
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