Math tip: secure multiple bets

Parlay bet: an unnecessary risk ?

A parlay bet, also reffered to as an accumulator bet or multi bet, is a common strategy in sports betting and is made up of two or more individual wagers. The main interest of such a strategy lies in the high odds obtained, which are calculated mathematically by multiplying the odds of each separate bet, resulting in really attractive profit opportunities.
On the other hand, the major drawback is that this betting strategy is risky because to win all the pronostics must be correct: mathematically, the probability of winning is also obtained by multiplying the probabilities of each separate bet, and the resulting overall probability can be very low.
These facts, interest and drawback, can be observe numerically using the multiple bet calculator: accumulating bets increase highly payouts, but reciprocally decrease the probability of winning.

In this article we will look at the math and calculations of multiple bets, to understand how to take advantage of the high winning potential of an accumulator bet while making it secure, that is to say while reducing the probability of losses and therefore reducing the associated risk.

Example of a treble bet: Odds, Probability and Winning

A Treble bet involves three selections on the same bet. All three outcomes have to be successful in order to achieve a return from the bet: that is the very risky part.

The multi bet calculator easily handle the caracteristics for the following treble strategy:

Stake: 10 euros
1st bet odds of: 1.5
2nd bet odds of: 1.8
3rd bet odds of: 1.7

and calculates and yields

Gain	45,9
overall odds of	4,59
Winning probability	21%

with the distribution of net gains and losses:

Gains	−10	35.9
Probabilities	79%	21%

These calculations show that the treble bet (or multis in general) now has high odds, but despite the low chance of winning : around 80% chance of losing, that is around 4 out of 5 chances!
The following math tip mathematically combines the different betting formulas seen so far: the double chance and the refunded if to secure the strategy, and of course this multi bet (treble bet) to increase the odds.

Formula to secure a multi bet

This tip consists of making an additional bet which depends on a first result: as for the idea of a martingale we will secure our overall bet by mathematically calculating this adapted additional bet.
We are therefore interested in combining three bets in a single parlay, three single bets spaced over time: we will adapt our additional bet according to the first two results.

1st step: the treble bet

In this 1st step, as previously planned, we bet 10 euros on our treble bet, with the previous odds: 1.5 and 1.8 and 1.7. We thus try to earn 45.9 euros, but with a high probability of loss.

2nd step: secure the treble bet

The idea now is to react based to the first 2 results:

if one of the two is lost, the treble is in any case definitively lost...
The probability of such a loss here is around 60% (loss only of the first 2 bets, not the 3 of the triple combination)
otherwise we can now act to secure our triple bet before the third and final result. Suppose the odds of the 3rd bet are respectively 1.7 and 2.1.
We then bet (as in the refunded if ) a new bet on the 3rd simple bet in order to reimburse us in the event of defeat.
We therefore calculate the correct stake for this:
10/2.1 − 1 ≃ 9.10
and so:
- if the 3rd bet is lost, we lose our triple (10 euros) and we win this last bet, i.e. a total profit of
  −10 + 9.10 × 2.1 −9.1 = 0
  and we are therefore staked back.
- if the 3rd bet is won, we win our treble (45.9 euros) and we lose this last bet:
  45.9 −10 −9.1 = 36.8

We therefore come to the new distribution of net gains and losses:

Gains	−10	0	26.8
Probabilities	60%	19%	21%

The treble profit is somehow reduced, but so is the risk: the probability of losing is also reduced.
In a way, we reduced 20% of the chances of losses (1 chance in 5) from −10 euros (dead loss) to 0 (neither loss nor gain). This is called mathematically securing a bet.

Secure treble bet with a surebet

To secure our treble bet, we used a refunded if mathematical method.
In fact, when we look at the odds after our first two bets we read:

if the 3rd wins, the overall rating of the triple combined is 4.59
defeat of 3rd with odds of 2.1

We are clearly in a surebet situation because

1/4.59 + 1/2.1 ≃ 0.69 < 1

Using the surebet calculator we calculate that we can bet 21.85 euros on the 3rd bet and then

if the 3rd bet is lost, we lose our treble (10 euros) but we win this 3rd bet, i.e.
−10 + 21.85 × 2.1 −21.85 ≃ 14
if the 3rd bet is won, we win our triple (45.9 euros) and we lose this last bet:
45.9 euros − 10 − 21.85 ≃ 14

In any case, whether the 3rd bet is won or lost, we will definitely earn 14 euros.

We finally have the new distribution of winnings from the treble bet secured by surebet:

Gains	−10	14
Probabilities	60%	40%

The mathematical expectation does not change, but the risk clearly does.
In practice, as sports betting does not relate to pure chance events (roulette, dice, lotto, etc.) in which case these math formulas do not change the results and the gain in the long term, these calculations and formulas of math & probability can change things. Indeed, any prediction is also subject to chance, of course, and a tipster can also be wrong, of course, but if he is wrong 2 times out of 3 on average we can easily conclude that it is necessary to change it! Here we erase uncommon pronostic errors with this type of mathematical method.
In other words, a smaller and more frequent gain (with a very positive expectation) is obtained by combining a secure betting formula and technical knowledge of the event, by studying the sporting situation (context, statistics on previous results, special conditions, etc.) and/or following the advice of a tipster.

Towards profitable and even safer bets

We can thus, with this method, mathematically modify risky bets into more secure bets while keeping a high odds.
In particular, it is possible to find many bets that are very safe, but which therefore have unattractive odds, odds of 1, 1 or 1.2 for example.
The previous method therefore makes it possible to combine these very safe low-payoff bets with a third bet with higher odds. We bet on a combo of the 3 then, at the end of the first 2 very likely winners, we bet with the 3rd: we take no risk there, and the odds of the 3rd increase those of the first 2.