Friday, August 17, 2012

It's All Odds

I came across this article about how we should think about all things in terms of odds, not just gambling. The premise is that very few things in life are certain, so we should consider our probability in being correct rather than assuming absolute knowledge or ignorance. The writer make a great case why we should think of these probabiliies as odds rather than the traditional percentages.

Here is a great refresher on odds from the article:

Let’s have a quick refresher on what “odds” are. We all know what a probability is (or at least, we’re familiar with the term!). Odds can be seen as ratios of probabilities. Just as we use P(A) for the “probability of A,” we may talk about O(A), the “odds of A” (where A is some apparently sensible proposition).

In terms of probabilities, O(A) = P(A)/P(~A). So for example, if there is a 66% probability of rain tomorrow, then O(rain) = 0.66/(1-0.66), or more easily 66:33, which finally reduces to 2:1 (usually read “two to one in favour”). The “:” is basically just a division sign, so O(rain) can be stated as “2 to 1” or as simply “2.” Although odds can be expressed as ratios of probabilities, they are best understood on their own terms altogether. In this case, “odds of 2 to 1 in favour of rain tomorrow” means something like “days like this are followed by twice as many rainy days as non-rainy days, to the best of my knowledge.”

Odds are even more familiar from the racetrack, where a bookie might give “10 to 1 on Longshot, to win.” What this means is that if the bookie is selling stakes for $5 each, then a single $5 stake will get you (10+1)*$5 = $55 if you win (i.e., a gain of $50 plus your $5 stake back), while a loss will simply lose you your $5 stake. (Of course, in order to make money, the bookie must think that the realodds on Longshot are even longer than 10 to 1.)

Obviously, this all applies to cards, but also life in general. Check out Rationally Speaking for more.


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