Due to the power of compound interest, if the bookies are giving themselves a relatively modest 10 per cent edge on the probabilities as they work them out (paying out 10% less than what they reckon to be the real odds), you're effectively increasing that edge massively with this system. If you're given 1.09 rather than 1.10 each time, you're getting winnings on 20 quid at the end of the month of 245 rather than 330. You've turned that edge of 10% into 25%.
Bookies love this system. And a brief scan of the internet shows me pretty obvious plants about it on blogs sponsored by bookies. 'Find value in compound low-odds bets,' they say. It's pretty insidious.
Whilt I agree that combining bets leverages the effect of the overround book to the punter's disadvantage, I think you've underestimated the size of the phenomenon.
For example, take two snooker matches: In match 1, between players A and B
, both have an equal chance of winning. The same in Match 2 between players C and D. In a 'fair' book, you'd be offered evens for each. In reality, there'd be an overround book, meaning you'd probably get, say, 5/6 on any of the players winning their respective matches. This would give the bookie a total book for each of the matches of 109.09% (100 × (6⁄11 + 6⁄11)) i.e. 9.09% overround.
The combined outcome of those two matches could see either of the following pairs winning: AC, AD, BC, BD. Since all four are equally likely, the true odds of any one would be 1/4 (and 3/1 against), meaning a 'fair' price of 4/1. That would result in a £10 winning £40 (10 x (3/1 + 1)). Whereas, the actual return in the overround book (using the figures in the paragraph above), would be £33.61 i.e. 10 × (5/6 + 1) × (5/6 + 1). That represents odds of 2.361/1 i.e. 29.752% (100/3.3611), which when applied to all four outcomes gives the bookie a book of 1.1901 i.e. an overround of 19.01% i.e. his edge has
more than doubled, compare to each of the singles!
On a double, the overround (0) can be calculated as 0 =
B1 ×
B2 × 100 − 100, where B1 and B2 is the whole of each respective book e.g O = 1.0909 × 1.0909 × 100 − 100 = 19.01%. Obviously, the more in the accumulator, the greater the book gets overround, calculated for a bet of y selections as
B1 ×
B2 × ... ×
By × 100 − 100.
To do as the OP hopes i.e. to turn £20 into £150 with 10/11 prices (at the longest), would take a minimum of 20 bets. If we assume a reasonable overround of 10% on each, the combined overound accross the whole is massive: something like 1.1 x 1.1 x 1.1 x 1.1 x 1.1 x 1.1 x 1.1 x 1.1 x 1.1 x 1.1 x 1.1 x 1.1 x 1.1 x 1.1 x 1.1 x 1.1 x 1.1 x 1.1 x 1.1 x 1.1 x 100 -100 = 640% i.e a total book of 740%. No wonder bookies love it!