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Stake Allocation
Q: What is stake allocation? A: Stake allocation divides total bankroll across legs according to odds and payout structure so that returns under different outcomes are as even as possible.
Stake Allocation
Q: What is stake allocation?
A: Stake allocation decides what fraction of the bankroll should go to each leg.
Arbitrage does not split money equally across outcomes. It allocates by odds and risk structure.
For \(n\) legs:
\[ x=(x_1,x_2,\ldots,x_n) \]
with:
\[ x_i\ge0,\quad \sum_{i=1}^{n}x_i=1 \]
If total bankroll is \(M\), the stake on leg \(i\) is:
\[ \text{amount}_i=M\times x_i \]
Example:
| Leg | Odds |
|---|---|
| Over 2.5 | 2.05 |
| Under 2.5 | 1.98 |
Set the two returns equal:
\[ 2.05x_1=1.98x_2 \]
and:
\[ x_1+x_2=1 \]
Then:
\[ x_1=\frac{1.98}{2.05+1.98}=0.4913 \]
\[ x_2=\frac{2.05}{2.05+1.98}=0.5087 \]
For a 1000 bankroll, the stakes are 491.30 and 508.70.
The goal is not to maximize one outcome. The goal is to make even the worst outcome cover the bankroll.