And to deal with the possibility of an infinite sequence of double-downs, let’s stipulate a small but positive chance each round that Quirrell will end the game and pay you even if your program chose to double down.
Or just observe that Quirrel can eventually write a program that just chooses to take the winnings.
He can, but the point is that you have to deal with the worst case; that’s why the game is being played by professor Quirrell, who is known to have ideas about what sorts of experiences are educational, rather than, say, Omega, who is many things but rarely actively malicious.
My point is, Quirrel has enough tricks in his arsenal that the quoted possibility is totally unnecessary. He can end it any time by offering a program reading either ‘self-destruct’ or ‘take winnings’. No new mechanism is necessary!
I don’t see how allowing this makes the problem any less of a worst case.
Or just observe that Quirrel can eventually write a program that just chooses to take the winnings.
He can, but the point is that you have to deal with the worst case; that’s why the game is being played by professor Quirrell, who is known to have ideas about what sorts of experiences are educational, rather than, say, Omega, who is many things but rarely actively malicious.
My point is, Quirrel has enough tricks in his arsenal that the quoted possibility is totally unnecessary. He can end it any time by offering a program reading either ‘self-destruct’ or ‘take winnings’. No new mechanism is necessary!
I don’t see how allowing this makes the problem any less of a worst case.
You’re right, of course. Thanks for pointing this out!
Now I see the point you were making. You’re right, the additional probability is not required, or rather, it’s built into Quirrell.