Hi guys,

After seeing a lots of threads where people asked about the best gambling strategy, I thought I could share a bit of my knowledge on these questions in order to hopefully bring some insights to those who are not aware of it yet.

Please bear in my mind that the comments I will make are not my personal point of view on the topic of gambling, which is simply a form of financial investment, but only a recap of what is generally admitted among researchers in economics and by extension in the financial industry.

Also note that I will only talk about betting on real events like sport games (typically sports betting or trading on prediction markets).

**Are there some martingale techniques that allow a gambler or an investor to make money at a single bookie?** As you probably know, there is none, simply because the bookmaker sets the rules for its bets in order to favor its own profit over its players' profit. This is generally achieved by setting a margin (overround).

**All right, so that means there's no way I can make a profit in gambling?**Well, not really. You can actually make a profit out of gambling but you have to rely on other things than a simple technical procedure like a martingale.

Basically, there are two key aspects to take into account:

- Information (e.g. teams' relative strengths)
- Bankroll management (i.e. What percentage of your betting budget is it reasonable to bet)

I'll come back with details on these two aspects later on.

I said there is no martingale that guarantees you a profit at a single bookie but there is actually one that can do it if you bet at several bookies.

Most of you probably know it: it's called sure betting or simply arbitrage in financial terms.

The idea behind sure betting is the same as the one behind arbitrage. When you want to make an arbitrage on a financial market, you need to find two markets where the price of the same stock or whatever financial product is different. In such a case, you buy the stock on the cheaper market and you sell it on the more expensive one, thus ensuring a sure profit (the price difference).

Sure betting works similarly: you need to find at least two different bookies that will give odds high enough to ensure a sure profit. To be more specific, suppose you want to bet on a two-way game opposing A vs B. If odds_A denotes the (decimal) odds in favor of A and odds_B denotes the (decimal) odds in favor of B, then you need to find those odds such that: 1/odds_A + 1/odds_B < 1.

For example, if odds_A = 2 and odds_B = 2.1 then 1/2 + 1/2.1 = 0.976... < 1. Then, to make a sure bet, you just wage w*1/odds_A on A and w*1/odds_B on B where w is any number you want (the higher w, the higher your sure profit). When the game is decided:

- if A wins: you get odds_A*(w*1/odds_A) - w*1/odds_A - w*1/odds_B = w*(1 - 1/odds_A - 1/odds_B) > 0
- if B wins: you get odds_B*(w*1/odds_B) - w*1/odds_A - w*1/odds_B = w*(1 - 1/odds_A - 1/odds_B) > 0

In fact, when you bet money on the victory of A, it's like you "buy A" and when you bet money on the victory of B, it's like you "sell A" since it is the opposite of supporting the victory of A. Thus, you buy and sell the same product on two different bookies but at a different price, hence the profit.

**Information**Information is just a general way of saying that you need to know the teams, players and games you are betting on.

While everybody knows that, it is often a good idea to push the concept a bit further and analyze the odds to see whether there is a betting opportunity (also referred to as value betting by gamblers).

When you see the set of odds offered by a bookie on a market (assuming that it did not receive any bets yet), it actually tells you what the bookie thinks about what is likely to happen in the game. Taking the same example as before with A and B, odds_A and odds_B can be break down into this:

- odds_A = 1/(overround * p_A)
- odds_B = 1/(overround * p_B)

where p_A and p_B are the respective implicit probabilities of A winning and B winning and overround is the margin of the bookie (>1) and can be calculated by:

overround = 1/odds_A + 1/odds_B. Putting, those formulas together, you have an easy way of calculating the implicit probabilities of the game, according to the bookmaker:

- p_A = (1/odds_A) / (1/odds_A + 1/odds_B)
- p_B = (1/odds_B) / (1/odds_A + 1/odds_B)

For example, if odds_A = 1.35 and odds_B = 3.05, then p_A = (1/1.35)/(1/1.35 + 1/3.05) = 69.3% and p_B = (1/3.05)/(1/1.35 + 1/3.05) = 30.7%.

Hence, if you have the same opinion, in other words the same probabilities, as the bookie for this game, the average net profit you would get out of this game by betting on A would be:

p_A * odds_A*w + p_B * 0 - w = w*(1/overround - 1) < 0 (and similarly for a bet on B)

which shows that in these conditions, it's not rationally a good idea to bet. Of course, you could still bet if you are "sure" that A or B is going to win but that's not a rational argument but I am leaving it aside for the sake of the discussion.

However, you can hold a different view on what's going to happen in the game, i.e. have a different opinion. Bookies are not error-proof as several university studies showed it over the years. Thus, if you think A has a chance of winning of q_A and B has a chance of winning of q_B, then your average net profit betting on A would be:

q_A * odds_A*w + q_B * 0 - w = w*(q_A/(p_A*overround) - 1) (and similarly for a bet on B)

In such a case, if q_A is high enough, i.e. you think A has much more chance of winning than what the bookie actually suggests, then you could achieve a profit (in average).

To be more specific, this will be the case if q_A/(p_A*overround) - 1 > 0 i.e q_A > p_A*overround = 1/odds_A. Of course, the more the overround is low (low margin), the more likely you are to find such opportunities at a bookie.

**Bankroll management**Bankroll management is a much more complicated topic. The most well-known method of managing your betting amounts is the Kelly criterion.

It basically tells you how much you should bet on a particular outcome given the probabilities of the game and your betting budget as well. It aims at getting you the maximal possible increase of your bankroll over the time.

Another pro for using a bankroll management technique is that it forces you to avoid betting unreasonable amounts that could bankrupt you. Because if you are in that case, it is much more difficult to recover from your losses as you are dead broke and you do need money to bet.

I could elaborate more on the technical aspects of the Kelly criterion but I don't know if you guys are interested or not.

So, on top of my head, these are the most important facts to know when betting in order to avoid major fails.

If you have any questions or possibly don't agree (

), let me know!