Patrick, a loyal MR reader, writes to me:
Today, someone asked me this question. I ran through my own calculations, but wanted to know your thoughts on the matter:
I
have the Get out of jail free card in monopoly. You land in jail.
What’s the minimum you would sell the card to me for, and what’s the
maximum I would pay?
Here are the Monopoly rules on-line.
This is unfortunately entirely dependent on the board situation. It’s fairly common to enter a scenario (particularly in the late game) in which the best strategy is to stay in jail as long as possible, as each roll has a high probability of landing you on a prohibitively expensive rent, and a commensurately low probability of landing anywhere productive. Under those circumstances, the card has no value.
Landing in jail means you have 3 tries at rolling a double, and failing to do so means you have to pay $50. As there are 36 possible dice combinations, 6 of which are doubles, you have a 1 in 6 chance of throwing a double on each of your three throws. As you have 3 tries, you add the probabilities together, so 1 in 6 plus 1 in 6 plus 1 in 6, giving you a 3 in 6 or 1 in 2 chance of throwing a double on at least one of your three turns. So if the probability of paying the fine is 50% then the maximum I would pay is $25 for a get out of jail free card.
But I’ve forgotten that you could also have two attempts at rolling a double and then choose to play your get out of jail free card on the final turn, rather than attempting to throw a double and risking the $50 fine. So the chance of not requiring the get out of jail free card is 1/3 (1/6 plus 1/6, the probability of rolling a double), so I would place the value of the get out of jail free card at 67% of $25 = $16.67.
Of course this assumes that there are no benefits to being in jail, and that the only cost of being in jail is the $50 that you would incur. I haven’t taken into account the fact that by being in jail you may avoid paying rent, or that you may miss out on potential income (from chance and community chest cards) as well as being unable to purchase property and so forfeiting potential future income.
This is the sort of thing I wish we did in lectures.
Generally, the maximum you would be willing to pay for a GooJF card would be $49, since you can just pay the bank the $50, and it’s better to pay the bank than to pay another player. In a two-player game, that often means that the most you’ll pay for one is $24, since -$50 for yourself is equivalent to +$25 for your opponent and -$25 for yourself.
However, in an n>2 player game, there are board states where it might make sense to pay more than $50, simply to transfer wealth. There are two obvious cases, but there may be others. First, a very cash-poor player A holds the card and is likely to land on a property that a third party B wants. If A can’t purchase it, B will get it through auction, and the results will be very bad for you. The max in this case is limited by the max of a Second, a very cash-poor player A is very likely to owe a relatively small amount of money to player B in the near term, which would bankrupt him, but is very likely to owe a relatively large amount of money to you in the long term. The transfer is insurance against A going bankrupt to B and transferring all this property. The max in this case is based on rents and relative property values, but is probably less than $1000.
Note that Tournament Monopoly rules generally don’t allow selling the GooJF card for more than $50.
The minimum you’d be willing to sell for is $0. There is a point in the game where the expected value of remaining in jail is positive, at which point the GooJF card becomes worthless. If you manage to sell the card to someone when they are in that state, you’ll gladly take $0 in the hopes that your opponent will miscalculate
Oops. My maths obviously needs a little sharpening. Back to the library…
“I have the Get out of jail free card in monopoly. You land in jail. What’s the minimum you would sell the card to me for, and what’s the maximum I would pay?”
Trick question.
You cannot possibly sell him the card because he has it.
He would pay nothing because he already has it.
let’s ask this guy:
http://www.tkcs-collins.com/truman/monopoly/monopoly.shtml
Ian Stewart describes how to analyse Monopoly using Markov models
http://www.math.yorku.ca/Who/Faculty/Steprans/Courses/2042/Monopoly/Stewart2.html
and
http://www.math.yorku.ca/Who/Faculty/Steprans/Courses/2042/Monopoly/Stewart4.html
He shows the jail square is the most visited square.
The jail square should be the most visited square since there are more effects that land you in jail than any other special effects. You visit it when you are “just visiting” and if you land on the “go to jail”-square and if you pick the card “go to jail”. There are a couple of other squares that you land on, but not through so many circumstances.
Things like this are what frustrates me about Monopoly. It CLEARLY needs a revised version, since there are so many unbalanced parts, much like the original Axis and Allies, which benefited tremendously from the 1997 update.
Even if you’re at the point in the game where staying in jail is positive, isn’t it still better to play the card after your second turn, since you have to go out on your third roll anyway?
Assuming that you want to get out of jail (otherwise you wouldn’t try to purchase the card) you would only pay up to $49 for the get out of jail free card, otherwise you could just pay the $50, roll the dice, and be out. When you choose to do this would be entirely dependent upon how much you value moving on your next turn and how lucky you believe you are.
You would only be willing to sell the card for more than $50, or you wouldn’t have any expected net benefit. I think the exact amount would depend on the expected benefit of leaving the other person in jail, and whether in was the 1st, 2nd, or 3rd roll.
The only conditions I can think of when a person would be willing to sell their get out of jail free card for less that $50 are if you are in dire straights and desperately tying to liquidate all of your assets.
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