Help me with maths / betting

December 15, 2005 5:46 AM

Need someone to do a bit of maths for me:

There is a stupid TV show that I bet on. It is called celebrity come dancing where couples ballroom dance. Anyway I bet on Zoe Ball & Ian Waite at 14/1 earlier in the year. There are now three couples left and the odds are as follows:Colin Jackson & Erin Boag 4/6; Darren Gough & Lilla Kopylova 11/4; Zoe Ball & Ian Waite 3/1. How much should I bet on the other two couples to guarantee the best return whatever happens in this weeks final. Maths was never my thing ( as i am sure you can tell).

posted by priorpark17 to science & nature (9 comments total)

To guarantee the best return bet nothing. You'll get 100% of your additional stake back, and whatever you'd have got from your earlier bet anyway.

To get the best expected return put all your additional money on who you think is most likely to win.

There ain't no tricking the system by spreading your money about I reckon.

(caveat: I haven't bothered to try to prove this mathematically)
posted by edd at 6:13 AM on December 15, 2005

To elaborate on edd, the bet takers will presumably have worked out the odds so that they favorwork out in their favor meaning that your best bet, given no special information, is to not bet at all.
posted by signal at 6:19 AM on December 15, 2005

Assuming that the lines are properly handicapped, your best bet is to stay pat on your existing position, since any other bets will just trade your expected profits for reduced variance.

That being said, I believe you could arbitrage your current position by betting 5 units on Colin/Erin, and 2 1/4 units on Darren/Lila.

If I did my math correctly (check it), that would give you a result of:

Colin/Erin win: 0.1 units profit (3.35 - 2.25 - 1)

Darren/Lila win: 0.1875 units profit (6.1875 - 5 - 1)

Zoe/Ian win: 5.75 units profit (13 - 2 1/4 - 5)

For a worst case scenario of a 0.1 unit profit.
posted by I Love Tacos at 6:42 AM on December 15, 2005

Also, people are cheating.
posted by alasdair at 6:49 AM on December 15, 2005

I Love Tacos is on the right track.

Since the odds improved on the bet you made, you can bet against your current position to even out the variance. Note that there will probably be some loss in expected return - your best bet (as mentioned above) for expected return is to take no further position.

I would call betting on the other two a "hedge" more than an "arbitrage", since you are hedging against the downside in your current position, not taking advantage of a current mis-pricing.

A perfect hedge (assuring you of the same return, regardless of outcome) would be to bet:

4 units on D/L
9 units on C/E

where I assume that your original bet was 1 unit on Z/I (at the 14/1 odds).

This assures you of 1 unit profit (+ or - a bit), regardless of who wins.

You can adjust your hedge by making bets on D/L and C/E in the same ratio (4:9) but for less total if you would still like some exposure (and upside potential) to Z/I. For example, if you hedged halfway, betting

2 units on D/L
4.5 units on C/E

you would make 7.5 units if Z/I won, and be even if they lost.
posted by aquafiend at 7:35 AM on December 15, 2005

I would also note that if your betting units are large, you might want to consider booking the Darren/Lilia bet elsewhere. There are better prices available.
posted by I Love Tacos at 8:37 AM on December 15, 2005

If you go to Betfair.com you can just lay the stake on Zoe Ball and Ian Waite and that will make the maths a whole lot easier for you.
posted by daveirl at 2:00 PM on December 15, 2005

If you go to Betfair.com you can just lay the stake on Zoe Ball and Ian Waite and that will make the maths a whole lot easier for you.

Am I missing something, or is this a totally useless answer?
posted by I Love Tacos at 4:41 PM on December 15, 2005

Thank you taco & aqua that has helped a lot. I can't choose between you for best answer and dont know if I can choose two best answers. Thanks again. PS I was in "Technical Drawing" when the rest of the class was in maths. Whatever happened to TD?
posted by priorpark17 at 11:45 PM on December 15, 2005