Calculating multibet odds & probability

Determining the value of a multibet is a simple exercise in which you multiply the implied odds of each match together (compute the product) and compare this to the product of your perceived odds. If your odds are shorter, then it would be a ‘good value’ (albeit long odds) bet. As an example, lets take the recent details of the multibet I placed for round 8 of the 2016 NRL season. In the table below, the team_descr is the team I tipped to win and the bookie_odds_stake were the odds at the time I placed the bet:

If we calculate the product of the perceived odds we get 5.12 and if we calculate the product of the bookie odds we get 5.85. Because 5.12 is less than 5.85 it is a ‘good value’ bet. Just a reminder, the product of odds is simply all the odds multiplied together.

As an example the product of my perceived odds is:

1.33 x 1.42 x 1.51 x 1.37 x 1.31 = 5.12

If we look at it from a probability perspective, the perceived probability of this multibet paying off is 1/5.12 which is 19.5%. The bookmakers implied probability is 1/5.85 which is 17.1%. So I perceive that there is a greater chance of this event occurring than the bookmakers, therefore I deem it a good value bet. Of course we must also consider that the probability of it paying off (according to our own perceived probability) is only 19.5%.

Value of ‘cash back’ promotional offer/s

Now lets take a look at the scenario where a ‘cash back’ offer exists.

Specifically, for multibets, Sportsbet currently has a promotion whereby if you place a 5 leg multibet (on S2016 NRL matches) and only 4 of your tips actually win then you receive cash back (up to $50). So how do I tell if that’s good ‘value’ or not?

Well, I can tell you straight up that simply receiving your cash back on 4 of 5 legs is never good value because your perceived odds will be the product of 4 legs winning vs the cash back value which is equivalent to odds of 1.00. As an example the range of perceived odds for any 4 combinations of my 5 leg multi is between 3.39 and 3.9 and the odds offered (the cash back) is only 1.00. This is obviously negative expected return. So the ‘value’ of a cash back offer is really determined by your panchant for the overall risk of the multibet.

As an example in this 5 leg multi I can tell myself:

I perceive I have around (at best) a ~30% (1/3.39) chance of at least getting my cash back and about a 20% chance of a return of 5.8. So if I bet $50 I have around a 1 in 3 chance of getting my money back and about a 1 in 5 chance of a $290 return ($240 profit). In this case I took the ‘punt’ but at least I understood my chances. In this case it paid off!

As you can see multibets are high ‘risk’ high reward, and the promotional offer does not represent good value for the odds at time of potential cash back, however provides a ‘psychological’ buffer for the punter (which is why they offer them).

In all, given this sort of promotional offer it is worth understanding your chances of money back after 4 legs so you can put the multibet into perspective.

For example if you determine you have a 1 in 4 chance of money back and a 1 in 5 chance of a ‘big’ payout you might be less inclined to bet. Conversely if (in the case that one of your legs is very long odds) you might calculate you have a 1 in 2 chance of money back and a 1 in 4 chance of a big payout. In this case the higher chance of cash back might be enough for you to take a ‘punt’

Determing the odds of 4 of 5 betting legs

The odds of 4 of 5 of the multibet legs are simply calculated in the same way as previous (its just the product of the odds of 4 of the matches). If you assume that your top 4 ‘highest’ probability matches are most likely to win, just calculate the product of these odds and this is the (perceived) odds of cash back. For my multi, the highest probability games were games 1,2,3 and 8 and if I compute the product of these I get 3.3 which is equivalent to 29.5%. So I perceive I have a 29.5% chance of getting my money back.

It gets a little more tricky if you want to evaluate the range of odds for any four bets winning. To do this you have to compute the odds for every combination of odds for the 4 of 5 matches. Combination math is a little bit off topic (if your interested see http://stattrek.com/online-calculator/combinations-permutations.aspx#examples) but when you have 4 objects from a set of 5 objects there are 5 possible combinations of odds.

The 5 possible combinations of perceived odds odds expressed as a matrix looks like:

##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1.33 1.33 1.33 1.33 1.42
## [2,] 1.42 1.42 1.42 1.51 1.51
## [3,] 1.51 1.51 1.37 1.37 1.37
## [4,] 1.37 1.31 1.31 1.31 1.31

Now If we compute the product of these combinations (re-ordered from lowest to highest) we observe the range of odds of getting our cash back after 4 legs:

## [1] 3.39 3.60 3.74 3.85 3.91

As probabilities this looks like:

## [1] 0.295 0.277 0.268 0.260 0.256

So if I assume that any combination of 4 legs is possible, the chances of getting my cash back is between 25.6% and 29.5%

Remember of course this all assumes my perceived probabilities are accurate 😉

Conclude

So now you know how to calculate the probability of a multibet based on your perceived odds and determine if its a good value bet. In the event of ‘cash back offer’, you will understand that the odds at time of cash back will never be favorable; however you will know its worth calculating the odds of to determine if the chances of cash back are favorable enough to factor into your psychology of bet placement. Finally you understand that multibets are high risk (long odds) high reward (high return) bets.