**Singles Versus Accumulators**

**Reducing Bookmaker's Advantage**

It is virtually impossible to

*reduce*bookmaker's overound. However, it seems that some punters go the other way around and unintentionally make bookmaker's life actually easier!

Deluded by desire to get rich fast, they improve bookmaker's advantage. I strongly believe than simplicity is most effective in sports-betting. Let me show you my point of view on betting on Singles - why I believe they are advantageous to Doubles or Combo bets.

**Myths about Accumulators**

First of all, let us stop and think for a moment why people love accumulators so much. One of the reason might be that they treat sports-betting as a source of entertainment. It is more fun to hit big Combo coupon than to

*grind*small profits with Singles.

And to make things more complicated even from mathematical point of view Coupon seems to be, at first glance, more profitable. Below is the graph of potential profits (horizontal Y axis) for specific success rates (asix x).

For example (100 bets, average odds 2.00):

- Punter with 60% hit rate hits 60% of Singles what gives him

**+20 units**of profit because of average odds of his Single coupon 2.00

- Punter with 60% hit rate hits 36% of Doubles what gives him

**+44 units**of profit because of average odds of his Double coupon 4.00

- Punter with 60% hit rate hits 21% of Trebles (because he must hit 60% * 60% * 60% outcome) what gives him

**+72.8 units**of profit because of average odds of his Treble coupon 8.00

We can make two points here:

- For positive YIELD - the more picks on one coupon, the bigger profitability (please see again the example of 60% hit rate which is +20% yield that I wrote just above the chart)

- For negative YIELD (hit rate lower than 50%) - the more picks on one coupon, the smaller profitability.

One might make a valid point here that it is pointless to consider negative YIELD scenarios as someone who can't beat the odds would not bet at all. Let us move on here to see what is the real reasons this chart is misleading and might contain some errors in logic.

**Being Restricted To One Company Makes a Big Difference**

Firstly, one wishing to bet on Combos is always restricted to place his combo within one bookmaker. What I mean is that if one wants to create a Double coupon that contains "Arsenal versus Manchester" and "Aston Villa versus Sunderland" games, he is forced to use prices of only one bookmaker. Due to this fact, you are very likely to lose a lot of value (read: high odds).

Imagine you estimate 70% chance of winning for Arsenal and 55% for Aston Villa to beat Sunderland. You search for a bookie which offers the best

*combined*odds for these 2 events. You realize, one of the bookmakers has Arsenal with 1.52 and Nantes with 1.75. It means that:

- Your Double bet has a chance of 70%*55% = 38.5%

- Your Double bet would have odds of 1.52 * 1.75 = 2.66

- Your Expected Value for this Double bet would be

**+2.4%**

It means that in long term you will earn 102.4 EUR for each 100 EUR you wager here. You will earn 240 EUR after one hundred bets.

If you were to wager the same games as Singles, in two different companies, you would be able to get the best prices on the market. Bookmaker A has "our" Arsenal with 1.55 price and Bookmaker B has "our" Nantes with 1.82. For this scenario we expect you to:

- Earn 1.55 * 70% =

**+8.5%**for every 1 EUR spent on Arsenal

- Earn 1.85 * 55% =

**+1.75%**for every 1 EUR spent on Nantes.

For comparison purposes, we want to keep invested amounts the same for both scenarions. It has been one hundred 100 EUR bets in first scenario. Therefore, now we bet 100 times 50 EUR on Arsenal and 100 times 50 EUR on Nantes. This gives us following expected profits:

- Arsenal (70% * 100 * 50 EUR * 1.55) ***8211; (50 * 100 EUR) = 425 EUR

- Nantes ( 55% * 100 * 50 EUR * 1.82) ***8211; (50 * 100 EUR) = 87.5 EUR

- Which sums up to 512.5 EUR of profit from this 10.000 EUR hypothetical investment

We see now the price of being restricting to one bookmaker. 512 EUR earned versus 240 EUR earned for the same value bets.

If we come back quickly to our chart above we understand first error it contains. We said that for positive YIELDs we should earn more for Accumulators, not for Singles. Still I agree that if you are very good at finding value bets, you will still earn both either way -by placing Singles or Accumulators. The point is that you lose approx. 1/3 of your profit because of the fact you must use one bookmaker's prices for each event in the Coupon.

**Keeping Low Risk Profile Is Never Free**

Next fact that can also nicely show us superiority of singles is simple one - Singles have lower odds. For big coupons whose odds rise to 10.0 you are obliged to wager much less money to keep comparable level of risk of Singles betting.

Imagine we decide to bet only singles at average odds of 2.00 with 2% of our betting bank. This would keep your risk of bankruptcy to level as low as 1%. By pairing this picks into Doubles you increase odds to 4.00. Your chance of hitting this bigger coupon obviously decreases too. You are much more likely to hit some ugly streaks of 9 or more lost coupons. 2% fixed staking for 4.00 Doubles is no longer very wise. You are forced to lower our stakes to let us say 0.75%. It means that for 5% YIELD, after 1000 bets:

- You are expected to increase your bankroll by

**125%**for first scenario

- You are expected to increase your bankroll by

**37.5%**for second scenario of 4.00 Doubles.

Remember, both scenarios are calculated for the same risk levels and YIELDs. We actually just proved in last paragraph that because of restriction to one bookmaker your YIELD will be lower for scenarios with Combos.

Difference is huge already! And imagine how it would be for 3-fold or 8-fold (!) Coupons.

**Do Not Complicate Your Already Hard Life**

There is one final point I want to discuss. Namely: by betting Accumulators you increase bookmakers profit margin. Example?

A bookmaker has just set the lines for "Chelsea - Milan" and "Barcelona - Juventus" games. Odds are 1.90 - 3.25 - 3.65 for the first game and 2.20 - 3.15 - 3.00 for the other one. We can make some logarithmic calculations here to discover that it corresponds to following chances of winning (and margins in brackets)

Chelsea: 49% (93.1%)

Draw: 27% (87.75%)

Milan: 24% (87.6%)

Barcelona: 42% (92.4%)

Draw: 28% (88.2%)

Juventus: 30% (90%)

Numbers in brackets tell us how much bookmaker is expecting us to lose on average for particular outcomes. The smaller the odds, the margin is lower.

When we pair this two picks into Double coupon we get following matrix, that shows probability of each possible pair of outcomes:

How to read this table:

- Right bottom value of 7% means it is probability of two underdogs (Juventus and Milan) both winning this games

- The other example is middle 8% value which corresponds to two Draws happening in this two games.

If we multiply bookmakers' probabilities from matrix above with all possible odds from the matrix below:

...we receive the final table of bookmakers' profit expectation:

What this last matrix actually means?

- Let us remember that with Singles bookmaker expects to pay out on average only 89.8% of the total amount wagered. It means he is going to earn 10.2 EUR for every 100 EUR wagered by the punters.

- The last matrix shows how this expectation changes for people who decide to pair this two games into Doubles. Average margin in this scenario is 81%. It means he is going to earn 19 EUR on every 100 EUR wagered by the punters.

Article comes from

## Comment