Mathematics and Betting Thread

[redarmi]

I've been thinking about this spread betting question and it's making my head hurt, wonder if anyone can help.

On average, 0.22 penalties are scored in each champions league game so if it was a normal bet then in theory we fill our boots when offered 5/1 or better on a penalty being scored.

Assuming the time that the penalties are scored is random and evenly spread throughout the 90 minutes* how do you determine the buy or sell point at which a bet is strictly mathematically +EV?


*big assumption, I know.

Is all of the info in this post?  Not sure how it is a spread betting question so not sure if you have missed something out given you talk about buy/sell etc.

[Longines]

Is all of the info in this post? 

I thought it was...

To take it to the extremes, if the spread is 0-1 then I think we should buy as the average penalty will be scored after 45 minutes and we win 44x our stake. If the spread is 88-89 then I think we should sell for similar reasons.

However if the spread is say 16-18 I'm trying to work out if it that is +EV to either buy or sell?

[redarmi]

Ahhh so the market you are questioning is penalty minutes?  You can use poisson distribution to work out the chances of 0,1,2,3 etc penalties.  In this case there is roughly an 80.25% chance of no penalties scored, 17.65% and a 1.9% chance of two penalties.  So as a shorthand way to get there I would ignore the chances of 2 penalties and then just take the 90(minutes)  *.1765 which gives you a midpoint of 15.88.  I would then add a couple of points back for the chances of 2+ penalties and round it up to give a midpoint of 18 or so.  So if the spread was 16-18 there isn't really any value in it.  I do think that the assumptions are wrong though.  Goals are not evenly split between halves (they are generally 45/55 split) and for the same reasons penalties are more likely to come in the second half.  If anything I would think the distribution would be more skewed to the 2nd half as refs are less keen to give away early penalties I would think.  You could put together a spreadsheet to work it out but my guess would be that back of the envelope calcs like this would largely prove there was no value.  I would only be more inclined to put the work in if I was fairly sure there was value as the spread boys tend to be very good at this kind of stuff.

[TheDazzler]

At what point does playing the Euromillions become +EV?
I know that's it's ~116 million to one to win the jackpot with 1 line and as it's 2 euros a ticket you need 232 million in the jackpot (and of course you'd need to be the only winner) but there is obv all the smaller prizes to take into account. They can vary in size so I guess you can't come up with an exact number but has anyone worked this out roughly? At ~120 million jackpot, are we maybe approaching neutral EV?

[doubleup]

I'd be interested on the mathematics of bad each way races.

How much ev on the win part of the bet can we afford to give up when the place part of the bet is clearly +ev?

I do it by intuition only at the moment.

Here's a calculator

https://docs.google.com/file/d/0Byg8Wbbo5p2ucDN2WVdueENUYzA/edit?usp=sharing

you have to download it - you can't put the data in on google docs

For anyone who looks for EW opportunities and doesn't have excel, this calculator is now online

http://www.sportspreadsheet.com/EachwayCalc.html

[redarmi]

Something has been puzzling me recently and this thread might be just the place.  I generally use Kelly Criteria for my staking, or a portion of it, but these days I am doing a lot more racing bets at each way where for the win part I have a neutral or negative expectation and all of my expectation is in the win part.  How would you deal with that based on the fact that the bookies make me bet the same amount on the win as on the place element of the bet?  It is okay to work out the overall expectation and base my staking on that or is that bad?

[doubleup]

I actually posted the same Q in a couple of places and got no responses.

I would guess that you should calc the overall EV and then stake on the win odds, tho that's clearly overstaking on the win and understaking on the place.

[Doobs]

I actually posted the same Q in a couple of places and got no responses.

I would guess that you should calc the overall EV and then stake on the win odds, tho that's clearly overstaking on the win and understaking on the place.

I'd stake on the combined win and place bet.  You have worked out the EV on the combined bet.  I think it maybe should be more as the bet should have lower volatility than a win bet.  But you can counter that by saying that the 2nd bet is related to the first so you don't really want to be doubling your win stake.  Think you are probably fine just meeting half way and working it as a bet of 1.5x the win stake?  All top of my head without any maths, and never really thought about it before.

[redarmi]

Yes all makes sense and a few others have said similar to me privately.  My biggest concern is not overstaking and it is pretty unlikely I would overstake as I am pretty conservative with my staking.  Thanks for the responses.

[sonour]

Hi Doobs,

Could you help with the McCoy to ride a winner problem I struggled with on TFT please.

9/2
13/2
10/1
11/1
20/1

I think you have to invert the odds and multiply them together to get the odds of him not riding a winner and then take this answer away from 1 ?

But I'm still not sure how to do it.

I'll have another stab,

1.22 x 1.15 x 1.1 x 1.09 x 1.05 = 1.76

100 / 1.76 = 56.8 %

100 / 43.2 % = 2.31 decimal odds.

Did I do any better this time ?

Your help would be appreciated.

Thanks

[Larry David]

10/10 Correct. All about the INVERTED T Carol

But yes correct.

[doubleup]

I would do the calc in probabilities ie

1-(1/7.5) = .87

1-1/5.5 = .82

etc

then final probability 1- (.87x.82x.92x.91x.95)

but the same thing - i think the actual odds are 2.287 because there is a lot of rounding up using two decimals

[sonour]

Thanks. That was going to be my next question. I shouldn't have to convert to percentages and then back to decimal odds.
So if the decimal odds for an event occurring are say 3.5 then the decimal odds for it not occurring are :-

1 / 1 - ( 1 / 3.5 )

Is that correct ?

[doubleup]

yes that is correct.

As I said I tend to use probabilities most of the time for any sums, mostly because when some thing is over my head there is usually a formula on wikipedia or the like that uses probabilities rather than odds.

[Doobs]

All looks correct.  I tend to just bang things in spreadsheets so it is easier to calc and easier to spot mistakes.  I know I got slated for it, but it is important to realise when these maths things fall apart.  In this case I think some of the McCoy prices were clearly too short (the last one really looked an 8/1 chance to me etc).  The 3/1 bf sportsbook still looked a great bet (I got close to 2/1 after adjusting 3 prices), but I so decided the 8/11 hills on no winners was a bet too.  8/11 on a 1/2 bet is good too. Made me think they probably hadn't adjusted properly for the circumstances too.  Ofc I worked this out long after the day had finished. 

I will try and put something up about each way betting on here this week.  Keep saying I will but never get round to it.