Originally published at BetStories.com
One of the most common questions that haunt the minds of all serious and meticulous bettors relates to the success of their strategy: “How can I make sure my system is a winner?” How many bets do you need to place and come out victorious before you feel confident you lay your cash on the right, profitable system?
Some would suggest that 200 bets seem adequate, while others would need 500, yet some others would say that you cannot be absolutely sure unless you test your “modus operandi” a couple of thousand of times.
The right answer, however, is the one that we despise the most: it depends.
Nevertheless, today we will go over a simple method which should help you to gain insight about the strategy you use. Don’t be scared! I am not going to bombard you with terms like volatility, standard deviation and other statistical jargon of this kind! I know you detest those. Therefore, some images will do the work. For, a picture is worth a thousand words.
This is a random line that shows the change in a gambler’s capital when they were betting on a heads-or-tails system. Every bet was placed on even odds in favor of the heads. After 200 bets the gambler ended being a winner by about 14 units, starting with 100 units of cash. At one point, he was winning 19 units!
What would you say about that? Would it be a good strategy if we bet on fair odds (2.00) when tossing a coin? Would the above chart be convincing about a possible profitability of a system where we place our bets blindfold on heads?
Let us take a look at another bettor who lodged his bets under the same idea.
Oops! A loss of 11 units in the end, losing up to 15 units at one point! This specific bettor loses about 5% of his capital after each coin’s toss. What went wrong? Really, could betting on coin tossing be that disastrous?
The (almost) random distribution of outcomes
As we can see on the above charts, the very same system turns out to be successful to the first bettor and ill-fated to the latter.
However, this is not actually true. Account the second graph to be the extension of the first. In other words, a single bettor who was lucky enough to win on the first 200 bets is expected to sustain a loss out of his profit in the next 200 bets. This is how it goes.
In essence, this is a third bettor who placed their cash on 400 bets. Even though in the first 200 or so bets they are a winner, in the following 200 they are constantly suffering losses, finally having their bankroll reach the breakeven point.
Clearly, the three bettors experienced completely different outcomes, in random. What happens if 10 bettors make their bets on heads at odds of 2.00 in 400 different coin flips?
It’s really a mess. Do not forget that we are talking about a system that is defined by default to produce zero profit or loss. In the long run, the betting system always recovers out of extreme losses or profits. Each time we fail we lose a unit of our cash, which we retrieve the next time we are successful. Of course, a fair coin has 50% probability of falling on either its’ heads or tails when tossed in random.
Yet, on such a blind bet under the most trivial betting system in the whole world – betting blindfold on heads, or similarly betting blindfold on home teams in football – one bettor enjoyed 41% increase on his capital while another suffered 33% loss! Obviously, more others saw positive or negative results in-between.
Do 10 gamblers seem not enough to you?
Ta-dah! The same cunning strategy put to the test by 100 bettors! Now, what will be your opinion about the betting system? Treasure or trash?
None obviously, because the main rule we explained above still applies. However, a number of bettors will stubbornly insist that this system is a winner, given they are up 50 units! It must become clear that because of the outcomes’ randomness, the bettors’ bankroll will always unpredictably deviate from the positive to the negative region and vice versa.
After all, the outcome is well defined. It is not in random. We know that this method will bring neither profit nor loss. We definitely know that, because we make the wager on 50% probability with the odds at 2.00. We could be lucky to enjoy some profit after 400 bets but we could also be losing some of our capital just as easily. Yet, the most probable outcome will always tend towards the middle as expected: the perfect balance, the zero or breakeven point. Judging by the chart above, this is the point where we may feel a bit grateful of not being unlucky…
How to make sure your strategy is a winner
Based on the above, let us proceed to what is most important at the end of the day, by discussing two distinct scenarios:
- Suppose that we know our coin is tweaked to drop on heads by 80% probability
- Imagine that there is a guy so naive who would offer odds at 3.20 on heads
Of course, on both options we should bet on heads. In the first case, we expect to win on 8 out of 10 tosses of the coin (instead of 5), while in the second we should win 2.20 units on heads against losing 1 on tails. Again, we deal with two options and two scenarios. This is not about a combination of the two, betting at 3.20 on heads of a coin that will bring heads by 80% probability! In that case, what kind of stupid would we be not betting a huge chunk of our capital, sparing the “wait and see” precaution that we should normally take before we commit on a betting system??!
However, BOTH scenarios will result in the same outcome: our winrates are totally equal. Check this by simply multiplying the odds of 2.00 with the probability of 80% on heads of the first scenario and the 3.20 odds on heads with 50% probability of the second. The result is the same (1.60), which means that our (enormous) edge is 60% in both cases. Along these lines, this is the foundation of value betting.
Given that our system in both these cases is a winner, let us monitor the performance of a bettor who makes a wager on either of these two betting systems.
Fantastic! At that edge, the punter’s bankroll shows hardly any unexpected variance. This is why we normally say:
The bigger the edge, the fewer the bets we need to verify our strategy.
Let us follow closely now another group of 100 bettors.
Of course, this is phenomenal performance. Their capital increases with only a few ups and downs. No reason to spend more time on this. The system is a winner right from the first 100 bets or even less. Good luck if you think you can easily find such a system!
How many bets would we need in order to be confident of your system?
Suppose you are testing a betting system nowadays. So far, you are being very attentive and have reached 400 bets studying the outcomes. Remember: we are interested in the 400 bets that you would have put your money on, not the pool of 3,000 football (or any other sport) games out of which you have selected the 400 bets of your study.
Up to this moment, you have won 100 units by betting one unit on each game out of 400. In other words, you’ve bet 400 units and now you hold 500 units. Therefore, your performance equals to (1+100/400) 2.25, on average.
Moreover, you are being successful in your predictions exactly half of the times, which means that your forecast to the next game will be by 50% chance accurate, or that your forecast success rate is equal to 50%. This is exactly the winning probability of heads and tails when tossing a fair coin.
Let us take a look at what happens after testing your strategy 100 times.
According to the graph, we see that it may be possible to:
- Win up to 113.25 units
- Win by 98% chance
- To finish in the red by… 2% chance after betting 400 times, since only 2 out of 100 trials ended in the negative zone!
Suppose now that you test another system at 5.00 average winning odds and 23% strike rate.
Even though the anticipated edge is slightly better than in the previous example (15% instead of 13%), notice how the bankroll’s variance has changed! A good number out of the 100 tests ended up losing you cash while the capital’s volatility varies considerably. Notice how the luckiest bettor won 166 instead of 113 units on the first example, benefiting by more or less the same edge! The same applies for the unluckiest punters in both scenarios.
Therefore, based on the above we conclude that:
Opting to bet on long shots will increase the betting system’s variance on our bankroll.
The next example will be the most common betting system used. This is a system of 44% hit rate when the winning odds are 2.30 on average.
On this system, we notice that for every 100 bettors, about half of them end to be winning and half are unprofitable. We should calculate the percentage of winning trials in order to find out the exact probability of having a winning system beforehand. That is to say, if 55 trials ended in positive territory, based on these data, we have a winning system by 55%.
However, this is only one variable on the equation and besides, this is not what you are after for.
Your main goal here today is to find out how many bets you must place or test before you are absolutely confident of the profitability of your betting system. So far, as you can see, based on the aforesaid numbers, 400 bets are not enough. Let us see what happens after 2,000 bets and 20 trials.
Ouch! Someone lost 115 units, meaning that if they risked 1% of their bankroll on each selection, by now nothing is left, not even a cent! Thus the informal but well-known rule among gamblers state that:
Proper money management requires risking no more than 2% of the total betting bankroll.
It’s quite obvious that even at the given system’s profitability, betting 2% of your capital might be extremely risky. Let’s take a look now what happens if we proceed to 10 trials of… 40,000 bets each!
Yes, when your… grandchildren study the results of this method, you can rest assured that your system is a winner. All you have to do is rise from your grave and place your bets! In that case, maybe 10,000 tests prove enough, wouldn’t they?
Tough luck! After 10,000 bets your chances to be a winner are 16/20 (16 positive trials in every 20 trials). If you still consider such a percentage too low, you have better either improve your forecasts or go after higher odds, aiming at the same success rate of course!
Therefore, stop wondering when the right time to follow your betting system with real money will be. First of all, calculate the success ratio and the average odds of your winning bets. Thereafter, enter these values into the betting simulator you can find after visiting BetStories.com. Select a satisfactory number of trials (10-100) and then start raising the total number of your wagers.
You should be aware by now of the number of bets you need to test in order to feel confident of your system’s success! Or, how much you need to improve your system before investing any of your money in it.
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