How to choose a betting method based on your profile

Five testing methods put to the test

What are the chances of going broke based on your betting method?

The advantages of fixed and proportional betting

Discover the best betting method for you

To make a profit in the betting markets, a bettor needs two things: an advantage over the bookmaker and a well-disciplined betting method. In this article, Joseph Buchdahl calculates the profitability and the chances of going bankrupt in relation to five different betting methods. Read on to find out which betting method is best for you according to your betting profile.

In October 2016, Pinnacle published the article Staking: a method to improve your bets, in an attempt to demonstrate that the amount you bet is actually more important than what you bet on. Of course, without a positive expected value, no money management system will transform a losing system into a winning system. However, some betting methods are inherently more risky than others, and it pays to be able to distinguish between them.

The original article analyzed all-in betting methodologies, fixed amount, Martingale, Fibonacci and proportional amount, when studying its performance over an imaginary series of 500 binary bets (odds of 2.00), in which the bettor starts with a fund of $ 1000, risks $ 100 on the initial bet (except for the all-in bet, where he bets everything), which then varies depending on the betting method and holds 10% of the expected value – that is, he wins 55% of the time.

In this article, I will compare the same betting plans over the same series of bets. However, this time, I will use the Monte Carlo method to repeat the simulation 10,000 times and estimate the real risk probabilities that the bettor can take advantage of – the risk of going broke and the probability of making a profit.

Five testing methods put to the test

The table below summarizes the average, median and maximum betting funds achieved for each betting plan after 10,000 sets of 500 simulated binary bets, along with the implied odds of going broke and making a profit based on those series. If, at any time during a series of 500 bets, the fund is lost, that series ends.

Fund after 500 binary bets

“All-in” | Martingale | Fibonacci | Fixed amount bet | Proportional | |

Average | 0 | 8167 | 6489 | 5473 | 137 486 |

Median | 0 | 0 | 0 | 5800 | 12 234 |

Maximum | 0 | 32 400 | 19 500 | 14 000 | 37 459 336 |

% of losses | 100% | 72% | 54% | 13% | 0% |

% of profits | 0% | 28% | 46% | 87% | 87% |

It is not surprising, therefore, that betting all-in stops consistently leads to ruin. The probability of winning 500 consecutive binary bets (each with a 55% probability of success) is 1.518 x 10-130. If we could repeat a series of 500 bets per second, we still would not have enough time to achieve a winning series before the death of the universe, which is expected in approximately 10100 (ten duo-trigintillions, also known as a “googol”) of years. So, good luck! In my 10,000 series, the best winning series achieved before going broke was 17.

The obvious advantage of proportional betting over fixed betting is that, in theory, you can never go broke.

Of course, most punters do not make nonsense like betting their entire fund on a single bet. However, many try to make up for past losses by increasing the stakes to get successful bets. The Martingale and Fibonacci methods are what we call progressive betting plans. In the case of binary bets, the Martingale method doubles the stakes after each consecutive loss, restoring the stakes to the initial value after a win.

Of course, some consecutive losses can give rise to some frighteningly large stops that put the fund at considerable risk. Not as extreme as the Martingale method, Fibonacci progression increases stops after losses by following the sequence of Fibonacci numbers, where the next number in the sequence is the sum of the two previous numbers (1, 1, 2, 3 , 5, 8, 13, 21, etc.). After a victory, the chart goes down two numbers in a row. Thus, each victory recovers its previous losses.

Unfortunately, none of these betting plans offer the bettor a safe betting experience. Almost three-quarters of the time, a bettor who follows the Martingale method can expect to be out of the game before placing the 500 bets. In the case of the Fibonacci method, that probability is still more than half. The average returns granted (expected) are higher than fixed amount bets, where the bettor always bets the same stake ($ 100), but really wants to take that risk in the hope of getting them?

If we look at the data above, the most usual closing fund will be zero (as seen by the median). In addition, we have not even considered the possibility that, by progressively increasing his stakes to recover losses, the bettor will be faced with having to place a bet that is above the limits allowed by the bookmaker.

The advantages of fixed and proportional betting

It is clear that the two best strategies are fixed-stakes and proportional stakes. Proportional amount bets involve betting the same stake as a percentage (in this case, 10%) of your available fund at the time you place the bet. So, if your first $ 100 bet wins, your next stop would be 10% of $ 1100, or $ 110. Alternatively, if you lose, your second stop would be $ 90. And so on.

Fixed and proportional amount bets both have a very good chance (87%) of making a profit after 500 bets in this situation. The obvious advantage of proportional stops over fixed stops is that, in theory, you can never go broke, although in the real world, weak runs can actually lead to very small stops. In addition, your expected final fund is considerably higher, mainly due to the fact that you usually bet larger amounts compared to fixed amount stops.

There is, however, a considerable deviation in the distribution of possible funds, with higher values contributing to a much greater weight for the average. Although that average is well over $ 100,000 (and, in fact, one series provided a final fund of more than $ 37 million), the median (or typical) fund is slightly above $ 12,000. In fact, the distribution of possible funds that follow proportional amount stops is approximately log-normal, in contrast to fixed amount stops, where (discounting funds * to zero) it is normal, with the mean and median being much closer.

What are the chances of going broke based on your betting method?

Obtaining an expected value of 10% with binary bets is incredibly unlikely in the long run. Some of the most successful handicap punters in the business will not be as profitable. Perhaps we should investigate how each betting strategy will perform in the case of smaller advantages. The graphs below represent the probabilities of going broke and making a profit in relation to 6 levels of expected value: 8%, 6%, 4%, 2%, 0% (neither win nor lose) and -2% (approximately the Pinnacle margin size).

The data presented here should not be surprising at all. Progressive stakes are always the most risky, but fixed stakes are little better when the player no longer has an advantage over the bookmaker. What may be less intuitive is the observation that, for minor advantages, fixed-rate stops actually offer you a better chance than proportional-amount stops to finish a series of 500 binary bets at a profit. Why is this happening?

The reason is mainly because when funds lose capital, they tend to take longer to recover through proportional amount stops compared to fixed amount stops. Basically, this is the compensation for following a strategy that will never make you lose everything.

Proportional amount stops can potentially be more profitable and, in theory, safer than long-term fixed-rate stops, but are less likely to bring you short-term profit, especially when your advantage is small. In other words, when you win, you win a lot, but when you lose, it takes more time to recover. This can be confirmed by comparing the median final funds for the two strategies.

Expected value | Fixed amount stop | Proportional amount stop |

10% | 5800 | 12 234 |

8% | 4040 | 4962 |

6% | 2800 | 2461 |

4% | 1800 | 1492 |

2% | 1200 | 1105 |

Fixed amount stop vs. proportional: median final funds

How changing the size of the stop affects your chances of profitability

Although progressive betting strategies are inherently very risky, even a 13% risk of going broke will not be tolerated by some bettors who prefer fixed-rate betting. How do the risks change for each strategy if we reduce the size of the stop? The graphs below represent the probability of going broke and making a profit for a variety of additional initial bet sizes (8%, 6%, 4% and 2%), in which the bettor has a 10% advantage.

Understandably, reducing the stakes in relation to the size of the available fund reduces the risk of going bankrupt and increases the likelihood of profit, although the size of the final available fund will also be smaller. This is simply an illustration of the trade-off between risk and reward: if you want more profit, you have to risk more to get it; there are no shortcuts. However, for those brave enough (or foolish) to follow a Martingale strategy, even with initial stops of just $ 20, you may still face a 50% chance of losing everything before a series of 500 bets has ended. Even with initial stops of just $ 1, that probability is still 5%.

What is the best betting method for you?

A Monte Carlo analysis of different betting strategies provided the following broad observations.

1) Progressive stops, including strategies such as the Martingale and Fibonacci methods, are risky. Even when the bettor has a considerable advantage over the bookmaker, there is still a very real possibility of going broke when trying to recover from previous losses, unless he drastically reduces the size of the stakes.

If this is the case, there is no point in pursuing losses. If the bettor is good enough to beat the bookmaker, then there is no need to go after the losses anyway. And if it is not good enough, no method will be able to turn a losing system into a winning system. While it may increase the size of the expected long-term fund, it does so at the risk of “dying” trying.

2) As long as their advantage is significant or the size of their stakes is sensible, fixed amount stakes must provide the bettor with the means to guarantee long-term profitability with a minimum of risk.

3) Proportional amount bets may seem like the “holy grail” of betting methods and, in fact, have a lot of merit to deserve such a title, one of which is that you should never go broke. However, series of losses take longer to recover from fixed-amount bets. If you are in this for the long term, then proportional amount bets are probably for you. If, however, you prefer the good feeling of short-term winnings and believe you have a considerable advantage, simple fixed-rate bets are undeniably the way to go.