Manual / Tilt Guard / Bound
Arithmetic

Size for the bad run, not the good night

A stake size is a statement about how much damage you are prepared to absorb. That is arithmetic, not confidence. Here are the numbers people usually skip.

Start from the margin, not from a feeling

A bookmaker prices a market so that the implied probabilities of its outcomes add up to more than 100%. The excess is the margin, or overround, and it is the operator's built-in edge on that market. Implied probability is just the decimal price inverted: 2.00 implies 50%, 1.50 implies about 66.7%. Add the implied probabilities of a two-way market and you will usually get something above 100%. That gap is why the long-run expected value of taking those prices repeatedly is negative, and why a strategy cannot fix a price.

None of that makes a single stake irrational. It does mean the size of the stake is the main variable you actually control, which is why it deserves a written number rather than a per-night guess.

Flat staking as a known fraction

Choose a bankroll you can lose entirely without it changing your rent, food or obligations. Stake a small fixed percentage of it — 1% is the conventional reference — for every stake, and re-read the number rather than the balance.

At 1%, twenty consecutive losses cost about 18% of the bankroll. Painful, survivable, and it leaves the process intact.

Why the ladder (martingale) fails

Doubling after each loss recovers a unit when it eventually wins, which is why it looks tidy on paper. The problem is the shape of the exposure: stakes grow 1, 2, 4, 8, 16, 32, 64 — doubling, so ten losses in a row needs a stake 1,024 times the first one, and twelve needs 4,096 times.

Stake caps, bankroll limits and long negative runs end the ladder before the recovery arrives. The size of the loss is roughly the size of the ladder, not the size of the unit.

What a drawdown actually costs to undo

Recovery is asymmetric. To get back to level after losing a fraction of the bankroll you must gain that fraction divided by what is left, so the required gain is always larger than the loss.

Drawdown and the gain needed to return to level
LossGain required to recoverWhat that usually implies
-10%+11.1%An ordinary correction
-25%+33.3%A good run, not a decision
-50%+100%Doubling, at the same prices
-75%+300%Statistically rare, and the point where chasing starts
-90%+900%The bankroll is effectively gone

On "optimal" sizing

You will see the Kelly criterion quoted as the mathematically optimal fraction of bankroll per stake. It assumes you know the true probability better than the price does. In practice an estimate is an estimate, so even its advocates usually recommend a fraction of the Kelly number rather than the full figure — and flat staking remains the simplest version of the same discipline.

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