The Monty Hall Paradox -- Are there poker applications? (NC)

[Kasane]

A thoroughly honest game-show host has placed a car behind one of three doors. There is a goat behind each of the other doors. You have no prior knowledge that allows you to distinguish among the doors. "First you point toward a door," he says. "Then I'll open one of the other doors to reveal a goat. After I've shown you the goat, you make your final choice whether to stick with your initial choice of doors, or to switch to the remaining door. You win whatever is behind the door."

You begin by pointing to door number 1. The host shows you that door number 3 has a goat. Do the player's chances of getting the car increase by switching to Door 2?

My brother posed this one to me today, and intuitively I knew the answer was "yes" -- and I attributed that knowledge to poker. I knew the host was giving me information, and it took almost no time for me to figure out what info and how it was important. It took me fifteen minutes to convince him -- and he's a fairly smart guy.

Now I'm wondering if I can more formally apply this back to poker -- but it may be trivial in that we do this all the time. Anyhoo, it's a fun puzzle.

More at wikipedia: http://en.wikipedia.org/wiki/Monty_Hall_problem

[Sean Fraley]

No, it doesn't apply to poker.

In the Monty Hall problem, the reason that switching doors increases you chance is because fundametally, there is a 33% chance that the car is behind the door you initially pick and a 66% chance that the car is behind the door that you didn't pick. The crucial factor is that when the host shows you what is behind door number three, the only thing that changed is the amount of information you have about the situation, not the situation itself. In poker, the situation actually changes every time that either

A) A new card is put into play (i.e. the flop is dealt).

or

B) A player bets or calls (i.e. your opponent shoves all-in).

While having aces over kings preflop gives you an 80% chance of winning the hand at that time, if a king hits the flop you chances go to 9%. What you chances were preflop don't matter squat.

[ybother]

maybe, a similar decison might occur in a live cash game where some flashes one card with action pending on the opponent at the river?

[KreellKeiser]

[ QUOTE ]
maybe, a similar decison might occur in a live cash game where some flashes one card with action pending on the opponent at the river?

[/ QUOTE ]

I still don't think there will be a good application of this. Exposing one card would allow you to limit their range, obviously, but the paradox doesn't really apply.

[CardSharkGames]

The Monty Hall Paradox, and how it applies to Hold'em, is discussed in the book <u>Weighing The Odds In Hold'Em Poker</u>, by King Yao.

However, the example he gives of applying it to Hold'Em is not very useful. Basically, he says that if a preflop raiser who always cb's after the flop indeed bets after the flop, it doesn't give you any new information about his hand.

Doesn't seem like we need Monty Hall to tell us that.