Measuring Chance

Is there really a difference between saying "a one in a million chance" or "a one in 10 million chance" to most people? I'd argue that there isn't - to most people, this just means "it's not going to happen". But there is a very real difference - and if we're going to talk about probability, we need to have a better vocabulary to do it with. I propose two different ways to discuss probability - the Lotto, and the Flip.

So, how to establish a language for describing unlikely events in a way that makes sense to people? I've had an idea: how about Lotto? Legal now in most of the states of the US in some form, it's a game that a majority of Americans have played, and few have won, or expect to win. It also has the advantage of having a very definate probability of happening, unlike many other things we could pick (like getting hit by lightning). Why not relate unlikely probabilities to that?

Another idea would be the coin flip. When you stack the odds of flipping a coin one on the other, the odds become astronomical fast. This has one advantage over the Lotto as a measure - the number goes up the more the odds increase, unlike the Lotto measure.

The Lotto

A short description for anyone not familiar with Lotto, Keno, Powerball, or any of the other legal lottery systems in the USA: The basic game is one of guessing numbers. From a field of numbers (usually between one to forty up to one to fifty) you pick a few that you think will come up in a random drawing. Typically, games cost $1 per entry, and pay astronomical amounts if you win. There's also astronomical odds against you winning. Typical jackpots in the California Lotto are $20 million dollars. Chances of hitting the jackpot in California Lotto are 41 million to 1. Here's a sample game: I pick 6 numbers between 1 and 48, no duplicates allowed: 1, 7, 13, 17, 23, 37. There's a drawing where 6 numbers are picked at random, again, with no duplicates allowed: 1, 7, 14, 17, 23, 37. Sadly, I missed the jackpot by one number. In most states (and even most casios), this entitles you to a modestly large sum (in the five digit range, typically). For our purposes, we'll say you lost, since you're really playing to hit the jackpot, aren't you?

So, on the unlikely chance that something will happen, we can refer to the odds of it happening be one Lotto, meaning something that has a one in 40 million chance of occuring. Similarly, something of greater likelihood will be referred to as having more lottos, something less likely, less. For example: if something has a one in 4 million chance of occurring, then that's 10 lottos. Something with a 1 in 4000 chance of occurance (the approximate chance of flipping a coin heads 12 times) would have 10,000 lottos. And something that has a 1 in 400 million chance (like this web site becoming popular) would have .1 lottos.

I can see some problems with this - although people beleive that they understand that lotteries are improbable events, they haven't actually taken the information to heart - witness the continued success of state lottery programs. Another problem is that as probabilities decrease, the number increases - folks may find this counter intuitive.

The Flip

Coin flipping is something most people learn as a child. It's also our first experience with probability.

Wrap up

I did briefly consider the lightning as a unit instead (one in 5.5 million), but there are problems with that as a measure - namely, the odds for being killed by lightning vary wildly throughout the population, and it varies year by year. I'm all ears for a better idea.

One last note: I know both someone who was struck by lightning (twice!) and someone who's won lotto. So even improbable events can happen to people you know, if you know enough people. The subject of a future article.