The Kelly Coin

The fact that we chose sports betting as a way to teach you about how much or how little to risk is no coincidence. The formula for how much to wager was derived by Bell Labs scientist John Kelly and was initially applied to gambling. The so-called Kelly Criterion has been cited by some of the world’s savviest investors such as Warren Buffett and Bill Gross. The game you just played is very similar to an experiment published in 2016 by Victor Haghani and Richard Dewey. Let us simulate a population of 1000 people, each starting with $100 and flipping the coin 100 times.

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However, the gambling community got wind of it and realized its potential as an optimal betting system in horse racing. It enabled gamblers to maximize the size of their bankroll over the long term. Today, many people use it as a general money management system for gambling as well as investing.

Kelly’s Criterion

The edge is the $100 profit divided by the $100 wager, or simply 1. The edge is how much you expect to win, on the average, assuming you could make this wager over and over with the same probabilities. It is a fraction because the profit is always in proportion to how much you wager. At a racetrack, the edge is diminished by the track take.

Whats The Kelly Criterion?

If we examine the full population of 10,000, we see an interesting pattern. The mean wealth is over $16,000, but the median wealth after 100 periods is 51 cents, a loss of over 99% of the initial wealth. 86% finishes with less than the initial wealth of $100.

You will see this through discussion of Sports Betting For Dummies what’s known as the “Kelly Criterion” which long ago I blogged a bit about. Basically a “kelly” is the optimal bet size for ONE bet with the rest in cash given a certain probability of winning and certain edge . And Whitley, R. Optimal strategies for repeated games. Gottlieb, G. An optimal betting strategy for repeated games. Harville, D. A. Assigning probabilities to the outcomes of multiple entry competitions. Data from over 4000 recent association football matches from the main English competitions show clear evidence that the rate of scoring goals changes over the course of a match.

Problems With Using The Kelly Criterion For Betting

There has to be a minimum of two legs in your bet to be classified as a parlay. The maximum number of legs in a parlay is dependent on the sportsbook you are placing the bet with. That is, if one leg loses, your entire parlay loses (that’s why you usually get big odds for adding more legs)! A parlay can combine different bet types across a range of markets as long as they are not conditional .

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When you add in calculating the volatility (ie standard deviation of $log$) then calculating confidence intervals, it gets much worse. And as a double check it might be nice to simulate a few thousand trial runs for a Monte Carlo simulation. Surely no self-respecting degenerate gambler would admit to doing something that looks so much like work.

Doubling Rate

If there is a fixed amount of bets the Kelly criterion will be suboptimal, but as the number of bets grows the optimal strategy will asymptotically reach the Kelly criterion. The Kelly criterion takes into account the fact that “gaining $25000 is worse than not losing $25000”. A game where you have a 50/50 chance of gaining $25k or losing $25k has a negative expectation in the log domain, so per the Kelly Criterion one would not bet on this game. There you have it, our overview of some of the football betting strategies that could help transform the way you bet. The starting place for the Kelly Criterion strategy is locating an event you’d like to bet on; let’s call it a straight forward match result bet.

Any time you make a decision with the goal of maximising your growth of wealth relative to a level of risk, you’re using the Kelly criterion. I haven’t understood your points further than that – minimizing risk of ruin is typically equivalent to not ever gambling at all. No gambler would agree with that, by definition of them being a gambler. To take poker, bet sizing is an important factor in play, but it has as much to do with the impression the action makes on other players as the actual underlying odds. I’ve heard risk managers talk about how people put too much faith in the mean outcome and don’t focus enough on the median outcome.

Inductively use this to compute utility at each time from knowing that at the end, money is worth itself. Look at the utility of $25.” Inductively generating that whole list prescribes laziness. I have also simulated a Fixed Fraction of my account e.g. 2% and re-basing every time I am not in a position. It performs well, but it vastly outperformed by Kelly when the traded population sets have many ‘streaks’ of winners. Legend has it that Shannon went to Las Vegas to test this idea out with Ed Thorp, making a fortune in the process of playing games they had a positive edge in.