The home of intelligent horse racing discussion

# Staking – maths problem.

Home Forums Tipping and Research Systems Staking – maths problem.

Viewing 6 posts - 1 through 6 (of 6 total)
• Author
Posts
• #6857

Hello fellow punters!

I have a maths problem I’m trying to solve as it’s not my strong point. I’m trying to work out how to divide up a stake to maximise profit between two runners when I know the odds of each runner and the % likelihood that each will win.

An example: two horses are racing, the first at 2 (decimal odds) and the second at 3 (decimal odds). I would get my stake back in winnings if the first horse came in, and double my stake back if the second horse came in.

No say if I have an independent way to work out how likely it is that each horse wins…

If I know that the first horse has a 60% chance of winning, I want 60% of the maximum profits it is possible for me to make to come from that horse.

I also want 40% of these potential maximum profits to come from the second horse.

That way, the stake matches the probability of a win in each case.

… This is not simply a matter of splitting the stake 60-40, as the odds are different in each case.

The basic equation is:

Profit from any horse = profit from that horse winning minus stake on the other horse.

If a stake of, say 100, is split between the first and second horse, how would I do that to make sure that my profit is the biggest it can be so that not only does it cover the other stake, but it also reflects the probability of that horse winning?

I’m usually okay with Excel etc, but this one has me stumped today!

thanks,
Parkpost #146354

Hi there

To be honest, I haven’t a clue how to set up a formula to work out what you want.

By using the "Goal-Seek" function in Excel, the program uses trial & error to work out the required stakes

This works out as follows:

Horse A (60% chance of winning)

Stake = 61.54
Winnings = 61.54
Losses = 38.46
Profit = 23.08

Horse B (40% chance of winning)

Stake = 38.46
Winnings = 76.92
Losses = 61.54
Profit = 15.38

Summary

Profit from Horse A winning = 23.08 (60% of total below)
Profit from Horse B winning = 15.38 (40% of total below)

Total Profit (theoretical) = 38.42 (if say, they dead heat and you place a bet with a bookie who pays double result)

A couple of things:

1. Kelly staking is probably the best way of maximising profits where you "know" a horses chance of winning.

2. If you "know" 1 horse has a 60% chance of winning and another horse has a 40% chance of winning then you should put your life savings on them because no other horse can win the race.

#146364

There is a spreadsheet available that might be of assistance to you and is very cheap.

I will "pm" you with the web address.

Regards – Matron #146403

parkpost,

Maybe the simplest approach is to stake in proportion to the probability of each horse winning and aiming to return a fixed amount from your bets. This might not achieve exactly what you want in terms of variable profit, but it is an easy way of proportionate staking.

For example, to return Â£1000 from horses A(evens) and B(2/1).

A evens = 50%(or 0.5) probabilty
B 2/1 =33%(or 0.33) probability

Stake required = expected return divided by probability

A = 1000/0.5 =Â£500

B = 1000/0.33 =Â£333

If A wins it covers your stake on B and gives you Â£166 profit
If B wins it covers your stake on A and gives you Â£166 profit

#146457

parkpost,

An interesting conundrum, but I think the example figures you have supplied are potentially a little misleading.

In effect, you have the same edge about each horse, so it doesn’t matter at all how you calculate your stakes. This edge is 20%.

The easiest way to think of it is that a successful Â£100 bet on the “60%,Evs” horse should according to the odds return Â£166.67, but will actually return 20% more, i.e. Â£200.

Similarly a winning Â£100 bet on the “40%,2/1” horse should return Â£250, but will return Â£300 which again is 20% more.

To illustrate the effect of different staking plans for your example, it is useful to explore some options open to you, made easier by the nice round numbers you have used, meaning that we can look at the outcomes of just 10 races (we could use 5 but 10 is simpler to work with) as being representative of how your investment will pan out. For each option, it is assumed that Â£100 is staked on each race.

Option 1 â€“ Equally-split stakes (Â£50, Â£50)
6 races are won by Horse 1 â€“ total stake is Â£100, return is Â£100 = profit is Â£0 (x6)
4 races are won by Horse 2 â€“ total stake is Â£100, return is Â£150 = profit is Â£50 (x4)
Overall: (6 x Â£0) + (4 x Â£50) = Â£200 profit

Option 2 â€“ Back Horse 1 only (Â£100, Â£0)
6 races are won by Horse 1 â€“ total stake is Â£100, return is Â£200 = profit is Â£100 (x6)
4 races are won by Horse 2 â€“ total stake is Â£100, return is Â£0 = loss is -Â£100 (x4)
Overall: (6 x Â£100) + (4 x -Â£100) = Â£200 profit

Option 3 – Back Horse 2 only (Â£0, Â£100)
6 races are won by Horse 1 â€“ total stake is Â£100, return is Â£0 = loss is -Â£100 (x6)
4 races are won by Horse 2 â€“ total stake is Â£100, return is Â£300 = profit is Â£200 (x4)
Overall: (6 x -Â£100) + (4 x Â£200) = Â£200 profit

Option 4 – Proportionally-split stakes v.1 (Â£66.67, Â£33.33) (rounded, & as per Kelly criterion)
6 races are won by Horse 1 â€“ total stake is Â£100, return is Â£133.33 = profit is Â£33.33 (x6)
4 races are won by Horse 2 â€“ total stake is Â£100, return is Â£100 = profit is Â£0 (x4)
Overall: (6 x Â£33.33) + (4 x Â£0) = Â£200 profit

Option 4 – Proportionally-split stakes v.2 (Â£60, Â£40) (as per Artemis’ & db’s posts)
6 races are won by Horse 1 â€“ total stake is Â£100, return is Â£120 = profit is Â£20 (x6)
4 races are won by Horse 2 â€“ total stake is Â£100, return is Â£120 = profit is Â£20 (x4)
Overall: (6 x Â£20) + (4 x Â£20) = Â£200 profit

Obviously, but notably, the overall total reflects the 20% edge, with Â£200 profit generated from Â£1000 staked.

Having thought through this problem, the actual calculation you need for examples which are not so precisely symmetrical would be an adapted version of the Kelly Criterion which davidbrady mentioned, an explanation of which can be found on Wikipedia.

If you are interested in this, I have spent a few minutes constructing an Excel sheet which would calculate the split-proportions for up to 10 horses in a race. PM me your email address and Iâ€™ll ping this off to youâ€¦

Regards,
NV

#146677

Thanks for all your replies to my post – they’ve certainly helped me.

cheers,
parkpost Viewing 6 posts - 1 through 6 (of 6 total)
• You must be logged in to reply to this topic.