Math Guys? Multi-Bet Moneyline Calculation

[statdude]

Hey all,
not sure if there is a term for it. I'm trying to calculate how to split a single outcome into mutiple moneylines.

Say a single outcome has multiple possible variations, each with a moneyline, say:

A: +250
B: +650
C: +1500

What would be the way to calculate what to bet for each outcome to create a single moneyline?

So, if you won any of the three outcomes, you'd "win" an equal amount?

[Waterstpub87]

So you want the amount to bet on each to hit have the same output:

1$ on 1500, 2.30 on 650 and 6 on 250.

[statdude]

Thanks Water,
The problem here is the cost of the other bets you lost, makes your "net" winnings unequal... wit those staking numbers, you'd win $15 for each outcome. However, if A happend, you'd have to pay 3.3, but be 7 to pay for A and C, and C would be 8.3 to pay for A & B.

Event	ML	Bet	Win?	Minus	Net
A	250	6	15	3.307	11.7
B	650	2.307	15	7	8.0
C	1500	1	15	8.307	6.7

[Waterstpub87]

It is somewhere around 7.51,3.51 and 1.645 off half a cent

[VLR100]

The hard way is to solve a system of three linear equations in three unknowns (the stakes for each bet), with the desired winnings and the odds as given. The easy way is to use a website like http://arbcruncher.com or write up a formula in excel.

[Blax0r]

So you want the amount to bet on each to hit have the same output:

1$ on 1500, 2.30 on 650 and 6 on 250.

This is the best way to do it IMO; compare the sum of your bets with the known output to determine whether an arbitrage exists.

As VLR mentioned, you can set up 3 linear equations and solve for the allocations, but I prefer waterstpub's simpler, slightly more intuitive approach (I used to do it the hard way as well).

[Optional]

I think you are speaking about Dutching.

if so, here's a tool to work it out for you: http://www.oddschecker.com/betting-t...alculator.html

You can get +109 overall dutching the 3 prices you quoted.

[Ganchrow]

Hey all,
not sure if there is a term for it. I'm trying to calculate how to split a single outcome into mutiple moneylines.

Say a single outcome has multiple possible variations, each with a moneyline, say:

A: +250
B: +650
C: +1500

What would be the way to calculate what to bet for each outcome to create a single moneyline?

So, if you won any of the three outcomes, you'd "win" an equal amount?

Assuming you were to bet k units on outcome A, you'd need to bet k × d_A/d_B units on outcome B, where d_X represents the decimal odds on outcome X.

So in the example above, given a 1-unit wager on outcome A, you'd wager 3.5/7.5 units on outcome B and 3.5/16 units on outcome C, reflecting net decimal odds of (3.5*7.5*16)/(3.5*7.5+3.5*16+7.5*16) ≈ 2.077 (~ +107.7 US).

[Carl-Haakon]

Oh my god he's still here

Edit: BTW, what do you think of Conquering Risk? MDC didn't seem to think much of it, but what about you?