Expected loss per KES 1,000 staked at a given bookmaker margin
Divide the margin by 1 plus the margin and multiply by 1,000. At a 5.26% margin that is 1,000 x 0.0526 / 1.0526 = KES 50 on every KES 1,000 staked. It is an average over many bets, not what any one bet or one evening will return.
The short answer
The average loss is the amount staked times the margin, divided by one plus the margin. For KES 1,000 staked at a 5.26% margin the average loss is KES 50. To find the margin of a market first, use the guide on calculating the bookmaker's margin.
"Average" has a precise meaning here: the figure results settle around after a very large number of bets at the same prices. It does not predict the next bet.
Where the formula comes from
Let S be the total of the implied probabilities of every outcome in a market, so the margin is S − 1. If the margin is shared out in proportion, the average amount returned per shilling staked (the payback) is 1 ÷ S. Whatever does not come back is the loss.
The last line follows because 1 − 1 ÷ S = (S − 1) ÷ S, and S = 1 + margin.
Step by step
- Find the margin of the market. Add the implied probabilities (1 ÷ decimal odds) of all outcomes and subtract 1. The margin calculator does the addition.
- Write the margin as a decimal: 5.26% is 0.0526.
- Divide it by 1 plus itself: 0.0526 ÷ 1.0526 = 0.0500.
- Multiply by the amount staked. For KES 1,000 the average loss is KES 50.
Illustrative example
A two-way market is priced at 1.90 and 1.90. Each implied probability is 1 ÷ 1.90 = 0.5263, so S = 1.0526 and the margin is 5.26%. Payback is 1 ÷ 1.0526 = 0.95, so KES 1,000 staked returns KES 950 on average and costs KES 50.
Check with a single bet: a KES 1,000 stake on an even chance at 1.90 wins KES 900 half the time and loses KES 1,000 half the time. The average is 0.5 × 900 − 0.5 × 1,000 = −KES 50.
The table: margin to average loss
Each row applies the formula to KES 1,000 staked. The payback column shows what comes back on average; the loss column is the shortfall.
| Margin | Total implied probability S | Average payback | Returned per KES 1,000 | Expected loss per KES 1,000 |
|---|---|---|---|---|
| 2% | 1.02 | 98.04% | KES 980.39 | KES 19.61 |
| 3% | 1.03 | 97.09% | KES 970.87 | KES 29.13 |
| 5% | 1.05 | 95.24% | KES 952.38 | KES 47.62 |
| 6% | 1.06 | 94.34% | KES 943.40 | KES 56.60 |
| 8% | 1.08 | 92.59% | KES 925.93 | KES 74.07 |
| 10% | 1.10 | 90.91% | KES 909.09 | KES 90.91 |
| 12% | 1.12 | 89.29% | KES 892.86 | KES 107.14 |
| 15% | 1.15 | 86.96% | KES 869.57 | KES 130.43 |
The margins are chosen to show the pattern and are not taken from any bookmaker. Check one row yourself: at 10%, 1,000 ÷ 1.10 = 909.09, and 1,000 − 909.09 = 90.91.
The same answer from the payback side
Casino games and some products are described by a payback or return-to-player figure instead of a margin. Regulation 20(2) of the Gambling Control (Conduct of Gambling Operations) Regulations, 2026 requires a licensee to display clearly the rules of games, odds, house edge and average return to the player, so for those games the figure is meant to be visible. Here the loss is simply 1,000 × (1 − payback).
| Average payback | Expected loss per KES 1,000 | Equivalent margin (1 ÷ payback − 1) |
|---|---|---|
| 97% | KES 30 | 3.09% |
| 95% | KES 50 | 5.26% |
| 92% | KES 80 | 8.70% |
| 90% | KES 100 | 11.11% |
The last column explains a common confusion. A 95% payback is a 5.26% margin, not 5%, because the margin is measured against the sum of the implied probabilities.
The cost follows the amount staked, not the amount deposited
The loss applies to every shilling that passes through a bet. Money that wins and is staked again pays the average cost again, which is why the amount of betting matters more than the size of the first deposit.
Illustrative example
A balance of KES 1,000 is staked in full on a 95% payback bet, and whatever comes back is staked in full again, ten times in a row. The average balance after n rounds is 1,000 × 0.95n. After 10 rounds, 0.9510 = 0.5987, so the average balance is KES 598.74 and the average loss is KES 401.26.
The amounts staked on average were 1,000, 950, 902.50 and so on, in total KES 8,025.26. Five per cent of that is KES 401.26, which matches. The cost is always the same share of what was staked; the balance simply shrinks, so later stakes are smaller.
Scaling the figure to your own stakes
The loss is proportional to the amount staked, so the table can be scaled. At a 5.26% margin (payback 95%):
| Total staked | Expected loss |
|---|---|
| KES 100 | KES 5 |
| KES 500 | KES 25 |
| KES 5,000 | KES 250 |
| KES 20,000 | KES 1,000 |
The total staked in a month is the sum of every bet, including bets placed with returned winnings. Multiply it by the cost per shilling to see the expected price of the month. The session budget planner turns a monthly ceiling into session amounts.
Why one session can look nothing like the average
An average loss of KES 50 per KES 1,000 does not mean you lose KES 50. In the 1.90 example a stake either gains 0.90 of itself or loses all of it.
Illustrative example
Ten bets of KES 100 each on an even chance at 1.90, so KES 1,000 is staked and the expected loss is KES 50. Each win adds KES 90 and each loss subtracts KES 100, so k wins give 190k − 1,000. That is positive only from 6 wins.
The number of ways to get 6 to 10 wins in 10 coin-like bets is 210 + 120 + 45 + 10 + 1 = 386 out of 1,024. So the chance of finishing ahead is 386 ÷ 1,024 = 37.70%, and the chance of finishing behind is 62.30%. The average is still −KES 50, because the losses when behind are larger than the profits when ahead.
Longer runs give luck less room against the steady cost. How wide the spread of results is, and how long losing runs last, is covered in the guide on variance and losing streaks.
What the figure does not tell you
- It is not a fee you can plan to recover. It is the average cost of a price. The actual cost of a period can be zero, or the whole stake.
- It assumes the margin is spread in proportion. A bookmaker may load it unevenly, and prices do not reveal how.
- It depends on the market in front of you. The regulations cited here require odds and terms to be clearly displayed (regulation 23(1)) but this site holds no verified data on typical margins, so use the margin of the actual market.
The relation between this cost and the chance of winning a single bet is the subject of the guide on the expected value of a bet. For a budget that treats the expected loss as a price, see setting a betting budget and limits. 18+. Gambling is addictive. Play responsibly.
Questions and answers
How much do you lose betting on average?
On average you lose the stake multiplied by the margin divided by 1 plus the margin. With a margin of 5.26% that is KES 50 for each KES 1,000 staked. The figure applies to the total amount staked, so repeated bets with the same money add up.
Is the expected loss the amount I will lose tonight?
No. It is the average over a very large number of identical bets. Tonight you may end ahead, lose a small amount or lose everything staked. The expected loss describes the price of the activity, not the result of one session.
Why is the loss not simply the margin times the stake?
Because the margin is measured against the total of implied probabilities (S), while the payback is 1 divided by S. A margin of 10% costs KES 90.91 per KES 1,000, not KES 100. For small margins the two figures are close, and the gap widens as the margin grows.
Does the expected loss change if I only bet on favourites?
Not if the margin is spread in proportion across outcomes, which is the usual assumption. Prices can load margin unevenly, and nothing in the prices reveals how it was shared, so treat the table as the central estimate.
Do I lose less if I stake smaller amounts?
Each shilling staked carries the same average cost, so smaller stakes mean a smaller expected loss in total. Staking less per bet but placing more bets leaves the total staked, and so the expected loss, unchanged.
Sources
- Gambling Control (Conduct of Gambling Operations) Regulations, 2026, rr.20(2), 23(1), accessed 2026-10-12