Why multiples are not to be taken seriously

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shakeshuck
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Joined: Fri Mar 06, 2015 2:12 pm

Why multiples are not to be taken seriously

Postby shakeshuck » Mon May 16, 2016 6:14 pm

I decided to ponder on the maths behind multiple bets this afternoon, and came to quite a revelation (as far as I was concerned, anyway). :roll: The following might be stuff you guys teach your 5-year-olds, but hopefully this will be of use to someone.

Of course if I've got this completely wrong or made a hash of it, please comment accordingly. ;)

I had a bet this morning where I had picked four near-evens selections and for a brief moment contemplated doing doubles. I quickly decided it was a bad idea, and just took singles, but later wondered if it would have been a bad idea or not. This is what came to mind:

Let's assume four coin-tosses of 50/50 odds.
The possible outcomes would be (where 0 is a loss and 1 is a win):

0000
0001
0010
0011 // two right
0100
0101 // two right
0110 // two right
0111 // three right
1000
1001 // two right
1010 // two right
1011 // three right
1100 // two right
1101 // three right
1110 // three right
1111 // four right

There are six combinations of doubles from four selections, so a bet would cost 6 pts.

Five lines contain none or one winner, so they are all losses.
Six lines contain one double. One double would return 4 pts, so a loss of 2pts would be due for each of these lines.
Four lines contain three wins. Three wins is three doubles, which would give a return of 3x4pts or 12pts, minus the 6pt cost = 6pts profit.
As there are four of these lines, the chance of hitting one of these lines is 4/16, or 25%. That equates to a 1 in 4 chance of getting an evens return (6pts profit for a 6pt outlay). Not good value at all.
Finally we have one line of four wins, that's six doubles, so a return of 6x4pts, or 24 pts, minus the cost = 18pts profit. 18pts profit to an outlay of 6pts gives us 3/1 odds, when the chance of hitting that one line is 1 in 16.

Trebles:

Using the same table as above, if we'd picked trebles we would have had four bets, or a 4pt outlay.
Four lines contain a treble, so the chance would be 4/16 to win 2x2x2, or 8pts. An 8pt win to a 4pt outlay is 2/1, again for a 1 in 4 chance of winning.
The one line of four would give us four trebles, or 4x8pts = 32pts, for a 4pt outlay. That's 8/1, but again only a 1/16 chance of hitting it.
---

Accumulators, therefore, are the only way to bet multiples if you're after betting value. ANY OTHER multiple bet should be taken as bad value and only considered if you're playing for a lottery-style win! :D

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