Sure and value bets. Definitions and the odd formula

I would guess that people with reasonable expertise in this field will find this article rather unnecessary, but those who lack experience might well find some use in it.

1. As we saw in the introduction, the whole concept of betting is based on the notions of odds and probability. When looking at the quality of bets, it is possible to say there are two types of "good bets":
   
   The sure bet: this is a bet that, through a combination of wagers on the same event, but on different results (all possible results), ensures winnings. In truth, such combination of wagers are not real bets. In finance and economics, such transactions that exploit the price differences between different markets are called arbitrage.
   
   For a bet to be a "sure bet" it must satisfy the following conditions:
   1/odds 1 + 1/odds 2 + …+ 1/odds n < 1
   
   Examples:
   Federer 2.10
   Nadal 2.10
   1/2.10 + 1/2.10 = 0.952
   This is a sure bet
   
   Federer 2.10
   Nadal 1.8
   1/2.10 + 1/1.85 = 1.016
   This is not a sure bet
   
   Why are such bets possible? The reason is that bookmakers don't all use the same odds and, thus, exploiting these differences makes it possible to gain the advantage. It goes without saying that, to place a sure bet, one needs to place bets with at least two different bookmakers and so, to have multiple possibilities, it is necessary to have multiple accounts and to have a certain amount of capital to start with.
   
   A sure bet guarantees winnings and the only risk is that one of the counterparties - that is, one of the bookmakers - used does not, for whatever reason, make the payout. This is not something that happens often, but it is not impossible and it has happened. Thus, one must be very careful when one comes across odds that differ greatly from the market averages because, in some cases, the bookmakers might annul one’s bet.
   
   So, even to place a "simple" sure bet, we still need to be careful and have experience.
2. A value bet: this is a bet that, in theoretical terms, gives us an advantage in terms of odds.
   
   This means the odds at which we place our bet are better (above) the fair odds for that result or, in other words, when the probability expressed by the odds we bet on is higher than the possibility of that result occurring.
   
   For a bet to be a "value bet" it must satisfy the following conditions:
   100/odds < estimated probability, as a percentage, of the result we bet on.
   
   Examples:
   Supposed that we assign Nadal a 60% chance of beating Federer.
   
   If the odds which we bet on were 1.70, we would have:
   100/1.70 = 58.82 which is less than 60. This is a value bet.
   
   If the odds which we bet on were 1.60, we would have:
   100/1.60 = 62.50 which is greater than 60. This is not a value bet.

This is all theoretical because nobody can know, in advance and with certainty, the probability of a player (or team) winning.

So, what is this all about? Well, there are systems that can seek out such favourable bets without any guaranteed winnings. Let's have a look at a few cases.

1. Once a sure bet has been established, a punter could, drawing on his/her experience and the trends of the market odds, decide to take a risk regardless by weighting the bets in one direction to maximise the advantage. An expert punter - and one must not forget the warning earlier about odds that are way off the market averages - should be able to work out what odds are the most favourable.
   
   For example:
   Let's imagine that, in a hypothetical Champions League final, the odds for winning the cup at our favoured bookmakers are:
   Bookmaker A Inter 2.80 Milan 1.45
   Bookmaker B Inter 2.20 Milan 1.63
   Bookmaker C Inter 2.25 Milan 1.59
   Bookmaker D Inter 2.10 Milan 1.75
   Bookmaker E Inter 2.15 Milan 1.70
   Bookmaker F Inter 2.18 Milan 1.67
   
   Maximum odds (that we will bet on):
   Inter 2.80
   Milan 1.75
   
   These odds are a sure bet:
   1/2.80 + 1/1.75 = 0.928
   
   So, one could quite easily divide one's available capital as per the formula and think no more about it. This is how it’s done:
   
   Net amount that one wants to win: G
   Odds: o1 and o2
   Bets, respectively, on o1 and o2: b1, b2
   
   Having set, in advance, the amount you want to win, you must bet the following amount on option 1, odds o1:
   b2=((W*(o1-1)+W))/((o1-1)*(o2-1)-1)
   b1=((W+b2)/(o1-1)
   
   Let suppose you want to win €10
   b2=((10*(2.80-1)+G))/((2.80-1)*(1.75-1)-1) = 28/0.35 = €80 at 1.7
   b1=((G+80)/(2.80-1) = 90/1.80 = €50 at 2.80
   
   Thus, by spending €130 you would win, in either case, €140 resulting in a profit of €10.
   
   
   Yet, is this the best option?
   
   It might not be. Let's look at the odds closely. It is clear that Bookmaker A offers much higher odds for an Inter victory than the other bookmakers (i.e. the market). Clearly, this is a risky assessment. In theory, Bookmaker A might be right, but it is normally true that the average odds available on the market (i.e. the odds offered by most bookmakers) are the closest to reality. This makes one think that the really favourable odds are the 2.80 offered for Inter by Bookmaker A.
   
   In this situation, there are as many different strategies as there are schools of thought. One could try and gain the maximum benefit, but this requires the most risk. In other words, one could decide to bet everything (€130) on Inter at 2.80. To go down the "safe route" and take the value bet option, one could divide one's bets differently. One might not follow the formula for the sure bet, but - for example - one might put only €40 on Milan and not 80.
   
   For example:
   €40 x 1.75 Milan = €70 euro = €60 loss
   €90 x 2.80 Inter = €252 euro = €122 gain
   
   The derived odds are 122/60 = 2.033/1 = 3.033 in in decimal format
   
   Odds of ca. 3.03 guarantee - at least at the time the wager is placed - a value bet. However, one should remember that odds change continuously and so what is true today might not be so tomorrow.
   
   The effective difference between the two strategies is that in the riskier option, one bets on lower odds but with a larger amount (and visa versa in the second option). Many people feel that betting less to get better odds is not the best option and, clearly, you are entitled to your opinion on this. However, from a maths standpoint, there is no doubt that higher odds are always better. Yet, betting is about winning money and not getting good marks in arithmetic. Likewise, it is clearly that a 3% advantage on a series of €100 bets will be financially more "favourable" than 6% on a €20 bet. This is clearly the case if, to get 6%, we have to lower the bet from €100 to €20. The calculation needs to be done on the basis of the number of bets: five bets of 100 would produce a return of €15, while the same number of bets at 20 would only produce €6. Someone who bets 20, bets at better odds but at the end of the day that person will have less in his/her pocket than the person who bet more on lower odds.
   
   Given the difficulty of forecasting the exact probability of an event occurring, taking the path of the odds is the safer option. It is really quite hard to work out exactly how much lower the odds can be to allow a larger wager that still remains a value bet.
2. Using various algorithms (a number exist), it is possible, by analysing the data available, to work out where the advantage lies. Of course, some methods are better than others and some are more fanciful than others...but that leads us into a discussion that is well beyond this article.
3. The case of an expert punter, using his/her experience and feelings, being able to determine whether odds are favourable or not. For example, takes the odds when the market opens, that is, when the first bookmakers start to publish their odds. To win using this approach, over the long run, one needs experience, discipline and talent. Not everyone has these abilities. Indeed, they are not common (it must be said), but when they do exist, they lead not only to financial success, but also a certain sense of fulfilment.