Explaining Probability with Gambling

This post is quite random (and has nothing to do with the other science discussion going on in the blogosphere - I can't believe I seriously just used the word blogosphere). In my academic snobbishness I've tried to explain certain probability concepts to various people at various points in time (this post is not particularly directed toward any of them). I think I came up with a great way of doing it, although I have a feeling that either it has been done before or it just seems good because I agree with what I'm trying to explain - or most likely both. I'm posting this both in case others find it useful/interesting and to see if others agree with its validity.

Anyway... I think people often vastly misjudge probabilities and they often assign a priori probabilities to events that have already occurred. So here's my new tool for figuring out if something is improbable. Ask yourself if someone else would be willing to take a bet on the unlikely event - if it helps actually bet a small amount of money with someone else. If you are offering even odds then if the event is truly very unlikely the other person should enthusiastically take the bet (assuming it is not too significant a sum - I'll spare you the tangent on risk adverseness).

I think this is most useful in clarifying that the probability of an event that has already occurred is 100%. Let's say that on my birthday I sit down in the lunch room at a table with 3 other people, all of whom also have the same birthday. Creepy -seems very improbable. Ok - now I turn to someone at another table and say hey this is super unlikely - want to bet that it will happen? No way he's taking the bet - it already happened! He'd just be handing me his money.

Now let's say that I'm still in the betting mood so I bet the person that something similarly creepy will happen at some point in the future. He'd say - No way! Even if we could establish what creepy means, of course something creepy is going to happy to me - coincidences happen to people all the time and what kind of gambler gets into a bet that can take any amount of time?

Ok, lets say I make it more specific and say that I predict that in two years, again on my birthday I will sit down with exactly 3 other people and that those 3 other people will share my birthday. Well, getting better, although the person would have to believe a promise that I will not do it on purpose (and they would have to know that I do not regularly sit with the three people I am with right now). If they are careful with their money they may also make sure there are no other underlying factors - such as if the table is close to the birthday cake tray. I also imagine they would insist on observing the event, even if they trust me they would probably recognize that the memory is a funny thing (this case is fairly clear cut, but if any part of the unlikely event involves me thinking something, such as if the bet was to have a feeling I would sit next to the people, then the bettor would be very cautions to make sure I didn't reinterpret a stomach rumble for a prediction after the fact - he'd probably make me write down the feeling as soon as it occurred). Once we've established these points, I would guess the other person would jump on the bet - cause let's face it under those conditions I'm probably going to lose.

Yes this situation may have gotten too unlikely. Perhaps I think that I often sit next to people whose birthdays have numerical relations to my birthday. Well, there are a lot of days and a lot of numerical relations. Setting up a bet will force me to define which relations count and what the acceptable time frame is. Also be careful - if I got too detailed, especially with something numeric someone may take me on an even money bet even if the event has a 40% chance of occurring - if I want to really guarantee that it is unlikely - I should give them the odds I am looking for (if I think it is one in a million I should give them those odds - although maybe in that case we wouldn't really bet).

Try it out. If possible really bet - if you don't bet the other person won't have the motivation to really question the probability. If you do try it out let me know how it goes.