William Poundstone wrote an extensive popular account of the history of Kelly betting. The behavior of the test subjects was far from optimal:. If losing, the size of the next bet gets cut; if winning, the stake increases. For simple bets with two outcomes, one involving losing the entire amount bet, and the other involving winning the bet amount multiplied by the payoff odds , the Kelly bet is:. If the gambler has zero edge, i. There is no explicit anti-red bet offered with comparable odds in roulette, so the best a Kelly gambler can do is bet nothing.
For even-money bets i. In this case, as is proved in the next section, the Kelly criterion turns out to be the relatively simple expression. Thus, using too much margin is not a good investment strategy when the cost of capital is high, even when the opportunity appears promising. Heuristic proofs of the Kelly criterion are straightforward. This gives:. For a rigorous and general proof, see Kelly's original paper  or some of the other references listed below.
Some corrections have been published. The resulting wealth will be:. After the same series of wins and losses as the Kelly bettor, they will have:. This illustrates that Kelly has both a deterministic and a stochastic component. If one knows K and N and wishes to pick a constant fraction of wealth to bet each time otherwise one could cheat and, for example, bet zero after the K th win knowing that the rest of the bets will lose , one will end up with the most money if one bets:.
The heuristic proof for the general case proceeds as follows. Edward O. Thorp provided a more detailed discussion of this formula for the general case. In practice, this is a matter of playing the same game over and over, where the probability of winning and the payoff odds are always the same.
In a article, Daniel Bernoulli suggested that, when one has a choice of bets or investments, one should choose that with the highest geometric mean of outcomes. This is mathematically equivalent to the Kelly criterion, although the motivation is entirely different Bernoulli wanted to resolve the St.
Petersburg paradox. An English-language translation of the Bernoulli article was not published until ,  but the work was well-known among mathematicians and economists. Kelly's criterion may be generalized  on gambling on many mutually exclusive outcomes, such as in horse races. Suppose there are several mutually exclusive outcomes.
The algorithm for the optimal set of outcomes consists of four steps. One may prove  that. The binary growth exponent is. In this case it must be that. In mathematical finance, a portfolio is called growth optimal if security weights maximize the expected geometric growth rate which is equivalent to maximizing log wealth.
Computations of growth optimal portfolios can suffer tremendous garbage in, garbage out problems. Ex-post performance of a supposed growth optimal portfolio may differ fantastically with the ex-ante prediction if portfolio weights are largely driven by estimation error. Strategy for wagering. Gulf Professional Publishing. Retrieved See: Gambling games. Gambling mathematics Mathematics of bookmaking Poker probability. See: Gambling terminology. Casino game Game of chance Game of skill List of bets Problem gambling.
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The more of your selections you get right, the more you win and the returns can be huge. Let me assure you that it is completely viable. Arbitrage betting is all focused on exploiting the variation in odds across different bookmakers. Each bookie applies their own statistical approach to setting odds for an event. As a result, you will occasionally find games where both outcomes are priced in a manner that promises a profit — regardless of who wins.
Sunderland to win is priced at 1. By strategically adjusting your stakes you can guarantee a profit:. Matched betting guarantees you a profit. I thought so. So how does it work? Well, matched betting only works when a free bet is available. First things first, you need to find a free bet — most bookies offer these on sign up. A lay bet is simply saying I think team X will not win thus covering a loss and draw. You now have all three outcomes covered. Of course, you need to calculate the relevant stake to lay whilst your amount at risk — called the lay liability — is higher than the stake as it needs to cover potential losses because of how betting exchanges work.
Today, Kilmarnock host Dundee United. Your free bet, which in this instance will be via SkyBet, is to back the home side i. I think Kilmarnock will win. The odds are 2. You can lay the bet i. I think Kilmarnock will fail to win with Smarkets at 2. The only other thing to consider is that most free bets require you to place a qualifying bet. Follow the same back and lay process as above and you will make a very minimal loss — usually pence — which will be more than covered in the second bet.
Why would a bookie do that? Price boosts, however, are intended to pull in new money and are only on handpicked events meaning the industry will remain in a healthy position. This example explains how it is done:. In the opening Premier League fixtures, Everton travel to face Tottenham with a current price of 4. New customers only. Sticking to what you know is also generally a good idea. But the fact everyone does this quickly drifts the odds into poor value bets, though. And any betting strategy that works always keeps value in mind.
So what can we do about this? Knowing all the tools at your disposal is step number one. This short guide was written with the intermediate punter in mind — someone who knows the basics but wants to improve. Because betting on corners in football is often overlooked, it can offer great value.
However, betting on corners may require some creative spreadsheet work. Well, you can find head-to-head statistics and detailed records for scores easily. An aggregate stat page on corners is kind of hard to find, though. Firstly, teams that use wide attacking formations tend to register high corner counts. Some teams with a deep defence tend to quickly kick the ball out rather than risk corners, for instance.
The devil is in the details when it comes to corner spread betting in soccer. Most of the time, it feels like a complete coin toss. For example, players which have a heavy record of bookings for the season will tend to be more careful.
This seems counterintuitive for soccer betting, which is usually based around using previous information to determine future outcomes. Therein lies the beauty of betting on bookings, however. Even bookmakers rely mostly on previous performance to price these markets. However, the most important factor for these is actually match importance. These contain an exceedingly low number of bookings because no player wants to risk disqualification.
Of course, this is just one example of how you can use small football betting markets to find interesting opportunities. Remember — be creative! In the soccer betting community, backing underdogs is often seen as a quick way to lose your money. However, there are ways of turning this to your advantage. This means that betting late is actually an advantage.