Proofset AcademyModule 4 · Bankroll managementLesson 4.2Free · 25 min

Fixed stake, percentage, Kelly

Once the unit has been chosen, you still have to decide how much to stake on each bet. There are three main ways to do it: always the same stake, always the same percentage, or a stake calculated from the estimated edge (the Kelly criterion). Each has its strengths, and the third hides a formidable trap.

Part 1

Three ways to stake

Fixed stake

Principle
Always the same stake: one unit, whatever else happens.
Advantage
Simple, easy to follow, impossible to “adjust” in the heat of the moment.
Limitation
Does not adapt when the bankroll falls.

Fixed percentage

Principle
Always the same percentage of the current bankroll, for example 1 %.
Advantage
Stakes go down when you lose: the bankroll never drops to zero in one go.
Limitation
The stake has to be recalculated regularly.

Kelly

Principle
The stake depends on the estimated edge on each bet.
Advantage
In theory, the best method when the true probability is known with certainty.
Limitation
Very dangerous if the probability is poorly estimated (part 4).
Part 2 · Animation

Facing a long losing streak

Let us compare a fixed stake of 1 % and a fixed percentage of 1 % over a very long losing streak, for illustration. The curve shows what remains of the bankroll, as a percentage of the starting amount.

Calculation: 1 % of the starting bankroll on each bet for the fixed stake; 1 % of the remaining bankroll for the fixed percentage. No real streak is this long at a normal success rate: the example is there to show the shape of the curves.

Part 3 · Your turn

The Kelly calculation

The Kelly criterion gives the share of the bankroll to stake, written f, from the true probability p and the odds:

f = [ p × (odds − 1) − (1 − p) ] ÷ (odds − 1)

True probability p60 %
Odds1,80
Full Kelly
Half Kelly
Quarter Kelly

Example: p = 60 %, odds 1,80. f = (0,60 × 0,80 − 0,40) ÷ 0,80 = 10 % of the bankroll. Kelly only suggests staking if p exceeds 1 ÷ odds: this is the rule from lesson 2.5.

Part 4

The trap: a small error in p

Kelly assumes that you know the true probability. But you can only estimate it. Let us go back to the odds of 1,80.

10 %

if you believe that p = 60 %. Kelly says to stake 10 % of the bankroll.

0 %

if p is actually 55 %. Kelly gives a negative figure: you should not have bet at all.

Five points of error in the probability are enough to go from “stake 10 %” to “do not bet”. And an overestimated probability pushes Kelly to stake big precisely on the bets that make no sense. That is why, at best, you only stake a fraction of Kelly, a quarter or a half, and never more than Kelly.

Part 5

Which method should you choose?

To start with

A fixed stake of one small unit. It is simple, and it stops you from raising the stake after a loss.

To protect the bankroll

The fixed percentage: stakes go down by themselves during a bad run.

Kelly, with caution

Only if the probability is measured and calibrated on hundreds of matches, and as a fraction (a quarter or a half).

In every case, the method is chosen with a cool head and does not change during a losing streak (lesson 4.4).

Key points

  • The fixed stake is the simplest, the fixed percentage the most protective against losses.
  • Kelly is only good if p is right. An error of a few points in the probability makes it dangerous.
  • Never more than Kelly, and preferably a quarter or a half.
Part 6

Test yourself

7 questions. You need 6 correct answers to pass the lesson.

0 / 7