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The previous section discussed how much of your wager to place on each selection in a betting market. What it didn’t discuss was how to choose your initial stake in the first place. The Kelly Criterion, which is discussed in a later section, outlines a formal methodology for choosing a stake amount, but for those who want something simpler, this section discusses some more basic staking plans.
Please note that we are highly skeptical of some of these plans. Please treat this section as being more of academic interest than practical advice.
A staking plan is a methodology for determining how much of your account balance to wager on an event. Countless plans are possible, but this section will discuss just a sampling of them, ranging from very basic to more formal strategies.
Many Internet sources will promote or sell “profitable staking plans”, but there’s no such thing as a staking plan that always works. If you make nothing but winning wagers you will succeed regardless of the staking plan. Likewise, if you make poor wagers you will fail regardless. While a good staking plan can ward off ill disciplined betting, the quality of your picks is arguably more important. To clarify, a pick could be backing team X to beat team Y in a head-to-head bet. A staking plan determines how much of your balance to bet on X now that you’ve chosen that selection. If you’re selections are poor, no staking plan in the world will work for you.
The best attribute a staking plan can have is one that prevents you from placing blow-out wagers in a desperate attempt to win back previous losses. Attempting to quickly regain parity will usually lead to an empty account balance.
Level Stakes
This plan involves wagering same amount for each bet, regardless of the results of previous wagers or the account balance.
Once you deposit funds into your account, choose an appropriate stake amount. This should be an amount that enables you to make numerous losing wagers without running out of funds. For example, if you deposit $100, you could set a stake of $5.00 per bet. Come rain or shine, you then always wager $5.00 on each selection.
The upside of this strategy is its simplicity. It also promotes discipline, because it avoids wagering a large amount on a “sure thing”, such as Australia beating Samoa in rugby union :). The downside is it doesn’t take into account the bookmaker odds. You would wager $5.00 regardless of whether the odds are 1.01 or 1001. The strategy also doesn’t take into account your perceived value of each wager.
Percentage Stakes
A slight variant on the level stakes plan is to wager the same percentage of your account balance on each selection.
Once you deposit funds into your account, choose an appropriate percentage. For example, if you deposit $100, you could set a relative stake of 5%. The very first bet will be 0.05 * $100 = $5.00. As the account balance goes up, so do the wagers, because you’re always betting the same percentage of the account balance. Likewise, as the account goes down, so do the wager amounts.
Like the previous strategy, this plan is highly disciplined. The obvious upside is that it will make your initial deposit go a long way due to the smaller wagers as your account dwindles. Note, however, that if your account balance trends downwards, your funds won’t last indefinitely, because you will reach a point where the calculated bet is less than the minimum accepted wager (normally $1.00). If you set a percentage of 5%, then for an account balance below $20 you will wager $1.00 instead of the calculated stake amount.
This strategy suffers from the same downsides as the level staking plan, as discussed earlier.
Square Root Stakes
This plan works very much like the percentage plan above, except it incorporates more aggressive wagering once your account balance exceeds the deposit amount.
Once you deposit funds into your account, choose an appropriate percentage. For example, if you deposit $100, you could set a relative stake of 5%. The very first bet will be 0.05 * $100 = $5.00. Whenever the account balance is below $100, you wager 5% of the account balance on each selection. However, if the account balance exceeds your deposit, take the square root of the difference between your balance and $100, and add it to 5% of your account balance.
Suppose you deposit $100, set a 5% wager level, and grow your account balance to $125. Your next wager will be √ ($125-$100) + ($125 * 0.05) = $5 + $6.25 = $11.25.
This strategy is the same as the percentage plan when your account balance dips below your deposit amount, but it wagers larger amounts when you’re performing well. The strategy remains conservative during tough times and becomes aggressive once you have your head above water.
Martingale Strategy
The martingale strategy is a well known betting system that was popular in 18th century France. The strategy attempts to recover previous losses should you be on a losing streak. Whenever you have a winning bet the system resets back to a base level.
The analysis below uses the following notation:
p – the base profit, in dollars, that you are trying to achieve per bet.
w_{i} – the wager amount, in dollars, after being on a losing streak of i bets.
q_{i} – the decimal odds of the corresponding wager above
Let w_{0} denote the base level wager. This is the wager amount used when we first start the strategy and when the previous wager was a winning bet. We calculate the wager as follows: w_{0} = p / (q_{0} – 1). Should this bet win it will return a profit of p.
Suppose you have an account balance of $500 and you set a base profit of $5.00. The first wager will be w_{0} = $5.00 / (q_{0} – 1). For example, if the odds are 3.50 the wager will be w_{0} = $5.00/2.50 = $2.00. Alternatively, if the odds are 1.50 the wager will be w_{0} = $5.00/0.50 = $10.00.
As you can see, the higher the odds, the smaller the wager, and vice versa.
If your bet wins, then the system resets and you reuse the formula w_{0} = p / (q_{0} – 1). You then continue in this manner until you make a losing bet.
If your bet loses, the next wager should return p and recover your loss from the previous bet (w_{0}). The next wager is calculated using the formula w_{1} = (w_{0} + p) / (q_{1} – 1).
If the next wager wins, the system resets to w_{0} = p / (q_{0} – 1). However if it loses you now have two losing bets in a row. The next wager will aim to win p and recover the losses from the previous two wagers (w_{0} and w_{1}). Hence, w_{2} = (w_{0} + w_{1} + p) / (q_{2} – 1). This continues until you snap your losing streak.
In the simplest case, suppose every bet is made at odds of 2.00. The first wager is w_{0} = $5.00 / (2 – 1) = $5.00. If it loses the second wager will be w_{1} = ($5.00 + $5.00) / (2 – 1) = $10.00. If the second wager loses the third wager will equal w_{2} = ($10.00 + $5.00 + $5.00) / (2 – 1) = $20.00. If your losing streak continues the next bets will be $40, then $80, $160, $320, and onwards, until you win.
You can immediately see that the wager amounts increase exponentially. This makes the strategy extremely dangerous because you can quickly end up having to make additional deposits to place the next wager.
You may think the chances are slim for making six incorrect wagers in a row at 2.00 odds. While this is true, if you repeat this strategy often enough, the probability of making six consecutive incorrect wagers at least once is very high.
The only way this strategy can work in the long run is if you have access to unlimited funds. Given that this is never possible, this strategy will always lead to ruin if employed for long enough. For this reason, we do not recommend the martingale strategy.
Reverse Martingale Strategy
The reverse martingale strategy, also known as the anti-martingale, is a type of positive progression, or “streak bet”. It uses the same mathematics as the martingale strategy, except it increases the stake amount if you win, rather than if you lose. In the preceding formulae, the variable i denotes the length of the winning streak, rather than losing streak. The reverse martingale strategy in its purest form is actually terrible, but a revised version can be somewhat reasonable.
As before, you set a base profit of p. Whenever you have a losing wager the following bet equals w_{0} = p / (q_{0} – 1). Conversely, if a wager wins, then you increase the next wager to w_{1} = (w_{0} + p) / (q_{1} – 1).
Suppose you have a starting balance of $100, set p = $5.00, and only place wagers at 2.00 odds. If you won four bets in a row and then lost the fifth bet, the outcome would be:
Bet # | Stake | Result | Account Balance |
---|---|---|---|
1 | $5.00 | Win | $105.00 |
2 | $10.00 | Win | $115.00 |
3 | $20.00 | Win | $135.00 |
4 | $40.00 | Win | $175.00 |
5 | $80.00 | Lose | $95.00 |
6 | $5.00 | … | … |
If employed without limit this strategy is absurd, because at the end of any winning streak you would be left with a $5.00 loss.
One variant on this strategy is to place a limit on the winning streak. Once this cap is reached the system resets to the base level. Using this strategy with a cap of 3, the outcome for the above selections would be:
Bet # | Stake | Result | Account Balance |
---|---|---|---|
1 | $5.00 | Win | $105.00 |
2 | $10.00 | Win | $115.00 |
3 | $20.00 | Win | $135.00 |
4 | $5.00 | Win | $140.00 |
5 | $10.00 | Lose | $130.00 |
6 | $5.00 | … | … |
This revised reverse martingale strategy places a cap on your bet amounts, making it far more reasonable than the standard martingale and reverse martingale strategies.
Another variant to the reverse martingale is to increase the bet amount by a fixed figure that doesn’t depend on your previous wagers. Using the above example with 2.00 odds, a $5.00 increment, and no cap, the outcome would be:
Bet # | Stake | Result | Account Balance |
---|---|---|---|
1 | $5.00 | Win | $105.00 |
2 | $10.00 | Win | $115.00 |
3 | $15.00 | Win | $130.00 |
4 | $20.00 | Win | $150.00 |
5 | $25.00 | Lose | $125.00 |
6 | $5.00 | … | … |
With this strategy a loss doesn’t necessarily wipe out you previous winnings.
Fibonacci Sequence
Fibonacci numbers are the integers in a sequence that starts with 0, 1, and each successive number equals the sum of the two preceding numbers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…
For the Fibonacci staking plan we will remove the first two numbers and use the following sequence:
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…
We set a base unit wager, which we will denote b. A good base is $1.00 because this is the minimum accepted wager with many bookmakers. Each successive wager will equal b multiplied by a certain number in the Fibonacci sequence. The number chosen will depend on the success of the previous bet. The number used as the base multiplier goes one step forward with each loss and two steps back with each win.
The first wager equals 1*b. If it wins then the next wager is 1*b. If it loses then the next wager is 2*b. If we lose two bets in a row the third bet will be 3*b. If we lose three bets in a row then the fourth bet will be 5*b. If this bet wins then the following bet will be 2*b (two steps back). You then continue on in this manner, increasing or decreasing your bets using the Fibonacci numbers as stake multipliers.
Like the martingale strategy, this staking plan suffers from the drawback of having wager amounts that grow exponentially if you get into a losing streak. To reduce risk, you can set a level at which your stake multiplier resets back to 1. This cap could be based on your account balance relative to your chosen base unit, b. For example you could cap the sequence at 21. If you wager 21*b and lose, you would return to 1*b rather than jump to 55*b for the next wager.
Staking Plan Application in Practice
We offer a free Excel staking plan calculator spreadsheet which doubles as a betting tracker. This tool provides recommended stakes using the level stakes, percentage stakes and square root stakes plans discussed above as well as for the Kelly Criterion. It also calculates your hypothetical profit had you strictly followed each of the four staking plans.
Staking Plans for Simultaneous Bets
The above strategies are straightforward if you only place one wager at a time, however there’s no guidance on what to do when you place simultaneous wagers. For example, suppose you employ Percentage Stakes with a 5% rate and a $100 account balance. If you want to place five wagers at the same time, do you wager $5 on each bet? Or do you wager $5 on the first, then $95 * .05 = $4.75 on the second, $4.51 on the third and so on? Both options are risky, particularly if you place a large number of wagers at one time. With the first option you will have $25 at risk, which represents 25% of your entire account balance. The second option isn’t much better, putting 22.62% of your funds at risk. When placing a large number of simultaneous wagers, this approach leads to unintentionally high risk taking, which defeats the purpose of employing a staking plan that is designed to impose discipline.
The next section discusses the application of selected staking plans to simultaneous bets.
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