Arbusers

I have been betting heavily online for the past few months with great success. However, I recently had my betting limits reduced on many bookmakers, leaving me with only a few places where I can currently place bets (until I acquire more accounts). As a result, I have become less selective in my betting, taking on any wager I can find. This has negatively impacted my performance.

This experience led me to ponder: what is the recommended minimum positive expected value (EV) for a bet? Is there an optimal range to target?

To investigate this, I ran numerous Monte Carlo simulations. I simulated placing 12,000 bets in a year (approximately 33 bets per day), testing various odds and EV levels to observe the growth of the bankroll over time. My findings suggest that to achieve steady bankroll growth over a year without significant drawdowns, there is a sweet spot for minimum EV based on the probability of the bet paying out:

90% probability: min +EV of 1%
80% probability: min +EV of 1.2%
70% probability: min +EV of 1.8%
60% probability: min +EV of 2.2%
50% probability: min +EV of 2.6%
40% probability: min +EV of 3.2%
30% probability: min +EV of 4%
20% probability: min +EV of 5-6%
10% probability: min +EV of 8-10%

The results indicate that the less likely a bet is to pay out, the higher the EV needs to be to avoid substantial drawdowns throughout the year. Upon further reflection, this makes sense.

Consider a bet with a 10% probability of winning. In theory, you should win about 1 out of every 10 times. However, in practice, this is rarely the case in the short term. The probability will only average out over thousands of bets. The issue arises when you encounter a bad losing streak, say in an extreme example potentially losing 40 times in a row before winning a few times consecutively. The lower the probability, the worse the potential losing streaks can be, resulting in much higher volatility. Therefore, you need more value in your bets to compensate for this increased risk.

I typically use the Kelly Criterion to scale my bets, naturally betting less when a bet has lower EV and more when it is a more lucrative opportunity. This approach maximizes long-term profit margins by default. However, I am increasingly considering skipping the "bad" bets altogether. But maybe if i do use kelly for staking, then i'm overthinking it at this point.

I would be interested to hear how other gamblers approach this issue and learn from their experiences.

Hi, do you calculate the probability based on the alarm service or yourself?

3% on high liquidity sports.
5% on low liquidity sports.

I always bet to win 1% of my bank which stays relatively constant. I profit take when it increases and my worst draw downs from starting bank are typically less than 10%.

Fractional kelly would be more profitable but I have been doing it this way for the last 5 years and I'm comfortable with it.

fusiqi wrote: ↑

Sat Aug 03, 2024 12:11 am

Hi, do you calculate the probability based on the alarm service or yourself?

I use the probability provided by the alarm service, which is based on the average probability among all bookmakers and exchanges.
However, consider this example:
If you bet frequently throughout the year on odds around 3.0 with only a 1% expected value, simulations show that there's always a possibility of being unprofitable for the year. These results are not ideal. While I'm not overly concerned about drawdowns, I don't want to place over 10,000 bets without knowing if I'll be profitable. My focus is on long-term profits. That said, these bets aren't necessarily unprofitable in the long run, as there is some expected value, albeit small. The risk of a losing year is present.

Now, if you place the same bets but with a 5% profit margin instead, the profit/loss curve looks like this:
Multiple simulations show steady growth in most scenarios, with a significantly lower risk of losing money over the same sample size.
The question then becomes: is it better to skip such low-edge bets or simply bet less on them? There might not be a definitive answer. I prefer the Kelly Criterion, so using a partial Kelly formula with a built-in maximum threshold (e.g., max 10% of bankroll on any bet) would give more weight to the best bets compared to the low-edge bets like in the first example. Those bets still have some value, just not a lot.

The Kelly Criterion optimizes bet sizing for a given expected value but doesn't necessarily determine which bets are worth making in the first place. In theory, any positive EV bet should be profitable in the long run. However, there might be a sweet spot where you should completely avoid certain bets. If you have to make over 10,000 bets to turn a slight profit, it's no better than flipping burgers at McDonald's.

When is a positive EV bet worthwhile?
In theory, any positive EV bet will be profitable in the very long run. The law of large numbers says that if you place that +EV bet an infinite number of times, you're guaranteed to come out ahead. However, in practice, bettors have finite time, money, and opportunities. Betting volume and timeline matter. If you only place 100 bets a year, a 1% edge bet might not be worth it, compared to betting 10,000 times a year. Another consideration is the opportunity cost. Even if a bet is +EV, if you have a limited bankroll, you may be better off saving that money for higher value bets. It's about allocating your capital optimally. The lower the probability of winning, the higher the risk of an extended drawdown. You need a higher EV to compensate for that risk and make the bet worthwhile. A 1% edge on a coin flip is very different than a 1% edge on a 10% probability bet.

Minimum EV as a function of betting volume and risk tolerance: The more bets you place, the lower your minimum EV can be, since you'll have more opportunities for the edge to play out over time. If you have a high risk tolerance and a large bankroll, you can afford to make more bets at a lower edge, since you can weather the variance. Conversely, if you have limited funds and opportunities, being more selective with a higher minimum EV is often advisable.

turbobets wrote: ↑

Sat Aug 03, 2024 12:51 am

3% on high liquidity sports.
5% on low liquidity sports.

I always bet to win 1% of my bank which stays relatively constant. I profit take when it increases and my worst draw downs from starting bank are typically less than 10%.

Fractional kelly would be more profitable but I have been doing it this way for the last 5 years and I'm comfortable with it.

Thanks, that's a clear answer.

Regarding fractional kelly:
I think the problem is sometimes also, depending on your system of analysis, you might not really know what your actual expected profit is. Unless you can quantify that, then kelly criterium is not really useful. Like you might know that you are profitable on the long run, but maybe not exactly the profit margin on each individual bet.

Betting on such low EV as 1% is probably not a good idea. Just because alert service says that the bet has 1% EV doesn't mean that it is actually true. You need some safety margin. The EV range that turbobets suggested is going to work well for most people.

Have you considered the favorite - longshot bias in your calculations?
Because that is exactly what it implies - the margin is heavily skewed towards the lowest probabilities outcomes. Even the tables are almost identical as yours :

More info here: football-data.co.uk/blog/favourite_longshot_bias_revisited.php

Highly recommend Joseph Buchdahl's books in case you have not read it.

About the original question - I have never calculated EV for all my bets. All I know is that my bank account is growing over the weeks/months/years. But that is about my style of play. When you bet mostly in-play - I aim for a huge margin of safety (10%), so in the end are there are 2, 3 or 1% it does not bother me at all. It is useless information. Could my results have been better had I calculated them? I don't care, too lazy to bother myself with it.

I don't use paid services, but have my automation, and sometimes I do it just for fun and the thrill. Arbs / steams on UK Championship / NBA are so hard to catch, that if I manage to get a mere 0.1% I do it. You know - an ego thing, it is a testament for my abilities, that is.

Tonton wrote: ↑

Sun Aug 04, 2024 6:33 am

Have you considered the favorite - longshot bias in your calculations?
Because that is exactly what it implies - the margin is heavily skewed towards the lowest probabilities outcomes. Even the tables are almost identical as yours :

More info here: football-data.co.uk/blog/favourite_longshot_bias_revisited.php

Highly recommend Joseph Buchdahl's books in case you have not read it.

About the original question - I have never calculated EV for all my bets. All I know is that my bank account is growing over the weeks/months/years. But that is about my style of play. When you bet mostly in-play - I aim for a huge margin of safety (10%), so in the end are there are 2, 3 or 1% it does not bother me at all. It is useless information. Could my results have been better had I calculated them? I don't care, too lazy to bother myself with it.

I don't use paid services, but have my automation, and sometimes I do it just for fun and the thrill. Arbs / steams on UK Championship / NBA are so hard to catch, that if I manage to get a mere 0.1% I do it. You know - an ego thing, it is a testament for my abilities, that is.

I'm not sure if the longshot bias has anything to do with it. Because longshot bias basically means the vig/juice is bigger on longshot events (so high decimal odds) then on the favorites (where there are low odds). But when bookmakers lay a market we bet on they are essentially doing to opposite. So when you bet on a long shot that has low chance to happen, for them there is a high probability the bet pays out.

Here i found the opposite to be true, low probability bets should have more margin to them to compensate for added risk.

When i simulate bets i always conclude i need more +EV when betting on longshots. But betting on lot of low probability events have a bigger tailrisk in some way. There are ways to calculate this, like for example if you make this many bets at these odds then there is this much risk to get a streak of this length.

sportsbookreview.com/betting-calculators/streak-calculator/

Say you bet 12000 times during a year on something with 2 decimal odds so a coinflip basically, then there is a 16.7% risk you have a losing streak of losing 15 times in a row. But say you bet on something with 3.3 decimal odds there is a 100% chance you will lose 15 times in a row. The risk of losing 28 times in a row is 15.2%. So as you can see, if you bet a lot and you like to bet on low probability events, eventually you will have a nasty losing streak.

And in reality apart from running simulations with a fixed betting amount, there is also the fact that you need to earn percentage wise more to make up losses. For example lose 50% of your bankroll you now need to make 100% to break even. So mathematically speaking long losing streaks weigh heavy on performance. Because you now have less money to work with. But this is only the case if you use something like kelly for staking. But even otherwise nobody has infinite bankroll, lol.

I could be wrong. Betting is not that simple, lol.