## What's the Difference Between Level Staking and Kelly Staking?

Deciding how much to wager is at least as important as deciding what to wager it on. The simplest approach to sizing a bet is to follow what's called a level-staking approach, in which every wager is the same size, usually some fixed and small percentage of the original bankroll. Making smaller wagers, while capping potential profits, protects a punter against a run of misfortune that might otherwise 'bankrupt' him or her.

Small, fixed wagering is recommended by those gambling advisors who argue that no-one can truly know when the edge they enjoy on a particular bet is larger or smaller than is typical.

For those who believe it is possible to know when you've a larger or smaller edge for a particular wager, it makes sense to wager more when you think that edge is large, and less when you think it's small. How then might we operationalise that philosophy?

One way - an optimal way under certain conditions - is by employing an approach known as Kelly Staking, which entails wagering a proportion of your current bankroll equal to:

(pf-1)/(f-1) [assuming pf > 1; otherwise bet 0]

where p is the probability you've attached to the outcome you're wagering on and f is the price being offered to you for such a wager. In this formulation, pf is a measure of the edge you have for the current wager so you bet more when pf is larger and less when it's smaller as the philosophy requires.

To get technical for a moment, making bets of this size, in the long-run and across a series of bets offering the same 'edge' for the punter (ie with the same p and f), maximises the expected utility of gambling returns to a punter whose utility function is logarithmic in nature.

Partly because the conditions listed in the previous paragraph almost never hold in practice - especially the bit about the constant, known and positive edge for the punter - few adherents to Kelly wagering recommend wagering the full amount calculated by the equation above. By blindly using this equation it's easy to find yourself wagering one-fifth or one-third of your entire bankroll on what you consider to be a very good thing. Advocates of Kelly instead often follow a "fractional Kelly" approach in which the bet size suggested by the equation is divided by some constant.

When MoS uses Kelly staking it's even more conservative. It applies the fractional approach but also applies it to the original bankroll and not the bankroll at the time the wager is placed.