Staking Plans: A way to improve your betting

In the is Blog post we shall:

•    Find out why staking methods are important when betting

•    Learn about the most common staking plans

•    Find out which staking plan fits you

As we shall discover there is a chance that the amount we bet can just as important as the bet itself. We have analyzed five popular staking methods to demonstrate this point.

Ed Thorp, who was a professional blackjack player for many years and is still a successful author, learnt how to be successful at BlackJack, namely by counting cards. Many would say he was too successful, as in the end his skill at the tables of the biggest casinos in Las Vegas is what led to practices demise. Over the years it has led to the use of many decks on each table, and sparked a war against card counting to such as extent that it is now virtually impossible to do.

In addition to his professional gambling, he published two books on the subject, attributing most of his success to the betting method developed by mathematician John Kelly Jr. As he said: Betting strategy is responsible for maybe one third of your earnings. Staking strategy is responsible for up to two thirds of it.

Of course, it is easy to say that the staking method is important. But what makes such a method so useful in betting? We documented the extend of success five betting methods had after a series of 500 bets.

Assuming that there is a 55% chance of winning a two way bet, for example "Heads or Tails" and the initial bet is £100 for each method  (except for the "all-in" method, in which £100 are stakied right from the start). Each method begins with a £1000 bankroll and the simulation is allowed to run for 500 bets (or until the £1000 bankroll is lost).

One of the methods performed much better returning much higher profits than the others, while with some others the capital was lost very quickly. Let’s see which is which!

Method 1: Bet everything, every time

This is placing your entire capital on each bet. The advantage of this method is that you initially can have great returns, quickly. The downside is of course that once you lose, that is it, Game Over! And this will inevitably happen sooner or later.

Method 2: Fixed bet

This is placing a fixed amount on each bet without changing it, regardless of whether it is a win or a lose. For this study, the stake was £100 per bet. Using this method you dramatically reduce the chance of going bankrupt but unfortunately, at the same time, profits are limited to a slow and steady increase.

Method 3: Martingale

This involves betting twice the amount after each losing bet in order to cover the losses with the next bets winnings. This gives a faster increase in capital than fixed bet (as you double the bet to cover any losses). If successive losses occur, however, as the required bets continue to double, you will quickly need to bet very VERY large amounts in an effort to cover the losses. This is very likely to result in your Bankroll busting out (or you reach the house limits) before too long.

Method 4: Fibonacci

Using the Fibonacci sequence means that after each lost bet you increase your stake amount using the winnings of the next bet. This method has similar disadvantages to the Martingale method, but it reduces how quickly the bet increases in the event of continuous losses (and therefore it also reduces the rate of your winnings).

Method 5: Proportional bets

This is where you invest a portion of your capital depending on the value (odds you have over the true odds) of your bet. In this simulation we used the Kelly criterion for proportional betting. With this method, your bet must be your value divided by the odds. In this example, as the value is 10% and the yield is 2.00, 10/1 is 10.

Therefore, 10% of the capital of £1000 results in a bet of £100 initially. In the case where this bet is successful, the next bet will be 10% of the new capital of £1100, which is £110. This means that profits increase faster than in the fixed betting system, while losses reduce when you hit a downturn.

Which method is the best?

As you can see from the above descriptions, proportional bets have an advantage over the other methods. Imagine you are down to your last £100. You will now only be betting £10 a time and you will stay in the game for much longer than with a fixed betting system, where the last £100 would potentially be your last bet.

Betting your whole bankroll at any time can result in big profits, including right from the very first bet, winning an amount which other methods may only win after seven or more bets. The winnings are impressive, but you must remember the extreme risks, at any time you can be bankrupt, an event which is incredibly unlikely using other methods.

The probability of reaching 500 bets with a 55% probability of being correct is basically impossible and should not be seriously considered as a strategy (although you would have won £67 Billion by the 27th round).

Fibonacci and Martingale are progressive betting methods which have advantages but again any large sequence of losses greatly increases the required bet size, and thus the rate of ruin.

At the 83rd round of our simulation we had 11 lost bets in a row. These defeats zeroed the capital for Fibonacci and Martingale and in the case of Martingale we would have to bet over £400k to make up for our losses, a huge amount considering that the capital reached just £6300 at its highest point. For Fibonacci, the maximum bet required was £33,500, but again the capital had peaked at just £4,100.

Apart from the proportional bets, the only method that avoided bankruptcy was that of fixed betting, which made slow but steady profits. At the 83rd round, the fixed bet strategy had increased the bankroll to £3400. It didn’t go bankrupt, but it didn’t show impressive results either after 95 bets. After 500 bets, the fixed bets yielded only £6400, while the Kelly criterion had risen to £18,275.

(It should be remembered that this simulation is based on the assumption that we have the edge in our favour. Without that all these results would change.)

Which method should you use?

The above simulation shows that different staking plans can have very different results, even if the results of the bets remain the same. The difference between going bankrupt and winning € 18,275 after 500 bets was simply choosing the right betting method.

It is important to remember, however, that there is no ideal method or secretly profitable betting system. Although the Kelly criterion was used in the above simulation, there may be more sophisticated methods for different types of bets. It is important to find out what type of staking plan fits your game best, usually through research and running simulations.

It is also important to remember that the Kelly criterion only works if you know what the true chances of success are when you calculate your bet stake. If your value is calculated incorrectly, you will have problems.