Bonus Ball x Bonus Ball spread bet

[Shyetd1969]

If I were to have a spread bet with someone on the outcome of Wednesday Bonus ball multiplied by Saturday Bonus Ball, what should I quote them? The minimum outcome is 1 x 1 = 1 and the maximum outcome is 49 x 49 = 2,401 so the spread would be between 1 and 2,401.
Would I then quote 24.5 x 24.5 = 600.25 or 49 x 49 divide 2 = 1,200.5

regards Shyetd

[jake-the-peg]

:c)

Not as easy as that

Some numbers are more probable because they can be arrived at by various combinations

1 can only be reached by a 1 and a 1

24 can be obtained by an 8 and a 3, a 12 and a 2, a 24 and a 1 a 6 and a 4 etc.

Where as 53 is a prime number above 49 and cannot be obtained at all.

To make your life complete there is no mathematical way to predict prime numbers.

I'd imagine your punter has already worked out the most probable result

You must do the same

[Tim123]

If you are playing the long game, the spread should be the average value which if my maths is right is 625.

The distribution of values is not symmetrical, so if your punter goes for higher than 625 they will win more, but win less often than if they go for lower.

[jake-the-peg]

Imagine it from throwing two dice

6x6 =36 half of that is 3x3 or 9 to 1

in fact the most probable out come is either 6 or 12 with 4 options or 9:1

but if you take a 4 sided dice the most probable is 4 with 3 possibilities or 3/16 which is less than 2x2 or 4 to 1

I suspect as the number grows the number of possibilities for the most probable number will grow factorially compared to the growth of the number of sides.

But I'd have to give it a lot more thought - you could get stung here the odds of the most probable number coming up might be a lot shorter than you think

[Tim123]

Jake,

I thought we were talking about a spread bet, not betting on a particular number coming up.

If the bet is £1 on 'higher than 625', 49 on both balls wins £1,776 (less actually as the spread won't be zero) and 1 on both balls loses £624. Vice versa for the 'lower than 625' bet.

However, there is more likelyhood that the product of the two numbers will be less than 625, so in the long run, you won't make money with either bet.

[jake-the-peg]

OK I'm not quite sure what the bet would be on but I've modelled it on a spreadsheet.

for a single combination the best numbers are 120,180,240 and 360 each with 12 ways of obtaining them so odds of just under 200 to 1

The odds of getting a value above 600 are actually about 10/24 rather than the 12/24 that you might expect.

[R1Geezer]

with spread betting the quote is a range eg 600-650. If you think higher you buy, lower you sell, so you have to come up with the best range. So I assume you intend to offer a spread in that form. As jake points out, certain totals are nore common, others not possible, but really we are concerning ourselves with lower/higher here. I'm trying to figure that out now. Any thoughts Jake?

[R1Geezer]

Ok I wrote a program to generate all the possible totals, then I sorted the output and the median value is 473. so to cover the middle with a spread you should first decide on the width of spread, ie in book terms, their margin and then split each side so for a 50 wide spread go 448-498. then they can buy or sell either side of that. if you wanted to take advantage of the situation you could offer to pay out above say 900 and you could claim to be being generous because the max is actually 2401! in reality you'd win around 75% of the time! Good question. Now boss is keen I do some actual work!

[R1Geezer]

sorry to cover the middle 50 you need to spread 456-486

[Tim123]

The median is only useful if the ditstibution around it is symmetrical. In a spread bet, you aren't just betting higher or lower than the spread figure and getting even money if you are right. Your win or loss depends on the difference between the spread figure and the result.

If someone offers you a spread figure of 473, bet on the result being higher (is that buying or selling?), and in the long run you will take them to the cleaners. Sure you will lose as many TIMES as you win overall, but the AMOUNT you win will be higher than the amount you lose.

[Shyetd1969]

wow guys ... many many thanks .... I knew there was more to this that meets the eye ... have a go now with your friends and colleagues and see the money come in.

[R1Geezer]

Yes, Tim has a good point, the actual half way spread would need to be higher, not sure how to work out where though.