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Las Vegas and game theory

This is a great example of the prisoners’ dilemma from Presh at Mind Your Decisions:

I played a poker tournament at Caesar’s Palace last night with the
following setup: The buy-in is $65, which gets you 2500 chips. There
is also the option to buy an additional 500 chips for $5 more, giving
you a total of 3000 chips for $70. At 1 cent/chip, this add-on sounds
like a great bargain compared to the 2.6 cents/chip of the regular
buy-in.

The kicker is that the house keeps the entire $5 add-on fee; none of
it goes into the prize pool.

It is the last sentence that reveals the devious set-up. The casinos are playing on individual incentives just like the police did to the suspects.

Since none of the extra money goes to the pot, the ideal solution would be for no one to buy the extra chips. The pot would stay the same and everyone’s chip stack would be equal at the start. This is analogous to both suspects staying silent in the Prisoner’s Dilemma.

And that is the rub. No one can be sure the other players will cooperate. It is therefore necessary analyze the decision based on what other’s might do:

Source

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