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How to Play Yes/No Proposition Bets (and "Lodden Thinks") February 18, 2011

If you're a gambling man (like I am), and fancy yourself a good estimator, here are some fun games you can play with your friends...

Game 1: Over/Under betting, auction-style

This is an even-money bet (say for $10), where the first person starts by making a claim like:

I bet $10 that the Statue of Liberty is at least 50 feet tall.
The second person has 2 choices:
  1. Accept the bet (second person wins if Statue of Liberty is actually under 50 feet tall.)
  2. Make a bolder claim by increasing the value-in-question.
The bolder claim might be:
I bet $10 that the Statue of Liberty is at least 200 feet tall.
This keeps going back-and-forth until a bet is accepted. At that point, you have to go lookup the fact in question, and resolve the bet.

The value that the bet settles at is the Over-under that combines the two people's estimates. This is assuming both players play rationally, and neither accidentally increases the value too much in one step.

Usually, there is a gentlemen's agreement that each person has to increase the value-in-question by a certain fraction. But in practice, this doesn't come up much, because if one person were to be a sissy and increase the value from 200 feet to 200.01 feet, the second person usually just leapfrogs this to a new reasonable value.

Game 2: Lodden Thinks

The show Poker After Dark has made the "Lodden Thinks" version of this game popular. The "Lodden" is Johnny Lodden, a famous poker player.

This game is exactly the same as Game 1, except that the value-in-question is something that a third person knows and will keep secret until the bet needs to be resolved.

For example, in one episode of Poker After Dark, two players bet on the age Daniel Negreanu lost his virginity.

What's interesting about this game is that the value-in-question doesn't have to be something the third-person knows - it can be that third person's estimate of some unknown value. For instance, in one episode, two players were betting on what a third-player's estimate of Hugh Hefner's age was. Before the betting started, the third player was asked to come up with an estimate, and remember it, without telling anyone. Now the other two players bet on this estimate.

It doesn't matter if the estimate is good or not, what you're really betting on is what Lodden (or whoever the third person is) is thinking. It's an interesting game because you're basically betting over who can do a better job getting into the mind of another person (hence, why poker players like this game).

The other benefit of this game is it doesn't require access to a computer to lookup the facts - you can play this game in the car (or at a poker table), for instance.

Game 3: Odds-making on Yes-No Propositions

Both of the previous games require betting on a value-in-question that is a number. But you can play a version where you bet on a yes-no propostion, such as "Will the Lakers win the next championship?"

To play this game, you have to decide on a fixed prize-pool (say $10) and each claim is a fraction of that pool that is being bet against the remaining portion.

Here's an example: the first person starts by saying

I bet $0.10 (vs. your $9.90) that the Lakers will win.
The first claim should always be chosen to be an extremely good bet. In this case, the Lakers will probably win with better than a 1-in-99 chance, so the bet above is a good bet (for the first person).

The second person obviously never takes this first bet, but instead makes a bolder claim, like:

I bet $0.50 (vs. your $9.50) that the Lakers will win.
This goes back and forth, raising the value each time, until someone accepts.

My friends and I are software engineers, so we tend to bet on weird things like "Is the domain name GreenMonkeyButt.com available?

Note that you always have to phrase the question in the way that is MOST LIKELY, so that the small initial bet is a good bet. For example, if you wanted to bet on whether the Clippers will win the NBA championship, you'd want to start the betting as:

I bet $0.10 (vs. your $9.90) that the Clippers will lose.
so that the bet amount can increase from there. Otherwise, if you start the betting as:
I bet $0.10 (vs. your $9.90) that the Clippers will win.
Then the second player might just stop right there and accept your bet (oops).

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