The maths behind combination bets — or parlays

What we learned already is, that the odds we get on a certain game reflects the probability. It is actually an approximation. Because anyone at market wishes to bet „on the better side“. The side that makes him win money in the long run. We all know that in a certain game/event a lot can happen to upset the favorite. But it is also what makes us get excited about it. The bigger the surprise, the more we got to talk about. „Leicester won the Premier League“ or „Greece have become European Champions“ are much more likely to be remembered than Real Madrid winning the Champions League. We even lost count there…

So winning long term means: consistently bet on the „right side“. Get the money you bet on the side, that has the edge, that gives you the value, that fulfills the requirement of having a higher market price than the true price. From then on it makes no difference any more which kind of system you apply: single, system bets, parlay bets. You will have the edge., you will have the +EV, you will win long term. But just to make sure: you need to keep track of your records. As long as the hits you had are higher than the break-even point you are in the winning zone. If you are not (yet): keep working on it. This part you have to read elsewhere in this blog, but all of the posts here will intersect.

Still not getting to the point yet: why do we multiply the odds for a parlay bet? This is a simple mathematical law that can be applied here. It is the law that you have to multiply the probabilities for a certain combined probability in case the single events are independent of each other. Simple example: to roll a single 6 with one die the probability is 1/6. Six possible outcomes, one of the is the one we are looking for. A 6. Ok. 1/6. That simple. To roll two 6´s in a row we need (and we are allowed ..) to multiply the probabilities. It is 1/6 * 1/6 = 1/36. 1 in 36 attempts you will get two sixes in a row. The same probability we get if we roll TOW dice and hope for a double six. There are 36 possible combinations of these two dice and just one of them is double six. Watch out, though: the probability for the two dice to show 1-2 is 2/36 or 1/18. Why? Because there are TWO DIFFERENT WAYS to get a 1-2. The first die showing a 1, the other die showing a 2, and vice versa. Anyway you can and you have to multiply the probabilities.

As the European odds are expressed in that fashion to be the reciprocal of the probabilities (there are other kinds of odds to be found elsewhere in this blog) we can multiply these as well. Getting back to the dice example: if we find someone who lays a price of 6/1 (European odds) or 6.0, then this would be exactly the true price. So if we were allowed to bet on this true price and do that for two such rolls in a row we would get a price of 6*6/1 = 36/1. This is the true price for two dice showing a six each (or ruling one die twice and show two sixes).

This is why we can multiply all the odds in a parlay bet. It sounds good — but it goes down to this simple law.

We need to notice this as well: the side that does have the edge increases his profit percentage wise like that. You so to say multiply your edge and make it bigger — if you have won. Still it is the reason why the betting companies make even more money than there original edge calculated in those single odds they lay. People to those parlay bets, but usually pick the prices that do NOT give them the edge, but rather give it to the companies. It is as simple as that: if you bet for prices that would give you long term a 3% loss (because you are not good enough yet). If you make a parlay bet, then you can multiply the 97% (100% - 3%) by themselves for as many games you put into this parlay. If it were five, than you would, instead of staying on 97% would you make single bets, make your anti-edge 97%^5 = 85.87%. So you would raise your losses to 14.13% instead of those 3% initially. But this same thing holds true if you do have the edge.

So if we found bets that give us the edge and we get back 103%, then the return would be for a five games parlay 103%^5 = 115.9%. So here we increase our winnings.

Parlay are as good as any other bet. Just make sure you have the edge. There would be a few more things about it in term of turnover you can generate and distribute the impact of luck a bit better, but mathematically this is the story here. If you have good bets you can do with it whatever you want to. Parlays may sound the best percentage wise, but other factors might stand against it not mentioned here for now.