Also known as the Kelly criterion. If one possible outcome of an action is associated with a great enough loss, it doesn't make sense to perform the action no matter how unlikely the loss.
* turn a predictive model for financial prices into a profitable trading system
In the case where the bet loses money you can interpret Kelly as either "the only way to win is not to play" or "bet it all on Red exactly once and walk away " depending on how you take the limit.
That is a much narrower view of the Kelly criterion than the general concept.
The general idea is about choosing an action that maximises the expected logarithm of the result.
In practise this means, among other things, not choosing an action that gets you close to "ruin", however you choose to measure the result. Another way to phrase it is that the Kelly criterion leads to actions that avoid large losses.
"The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to maximizing the expected geometric growth rate"
In real life people often choose to make bets smaller than the Kelley bet. Part of that is that even if you have a good model there are still "unknown unknowns" that will make your model wrong some of the time. Also most people aren't comfortable with the sharp ups and downs and probability of ruin you have with Kelley.
I've long found that Wikipedia article woefully lacking in generality.
1) The Kelly criterion is a general decision rule not limited to bet sizing. Bet sizing is just a special case where you're choosing between actions that correspond to different bet sizes. The Kelly criterion works very well also for other actions, like whether to pursue project A or B, whether to get insurance or not, and indeed whether to sleep under a tree or on a rock.
2) The Kelly criterion is not limited to what people would ordinarily think of as "wealth". It applies just as well to anything you can measure with some sort of utility where compounding makes sense.
The best overview I've found so far is The Kelly Capital Growth Investment Criterion[1], which unfortunately is a thick collection of peer-reviewed science, so it's very detailed and heavy on the maths, too.
Which of course directly leads to Pascal's Mugging: I can simply say "I'm a god, give me $10000 or you will burn in hell for all eternity". Now if you follow Pascal's Wager or GP's logic you have to give me the money: I'm probably lying, but the potential downside is too great to risk upsetting me.
There's actually a rational explanation for that: humans don't care very much about burning in hell for all eternity, when it comes down to it.
There's actually a similar though experiment that might seem even more bizarre: I could tell you "give me $100 or I will kill you tomorrow" and you probably wouldn't give me the $100. That's because when it comes down to it, humans don't see the loss of their life as that big a deal as one might think. It's a big deal, of course, but in combination with the low likelihood, still not big enough to forgo the $100.
Pascal's wager is an example of motivated thinking - there were very real and certain consequences to him if his wager didn't demonstrate you should obey the Catholic Church.
