The last decimal: what the smallest unit of money decides
A gambling account is a column of numbers, and every one of them is rounded to a unit the operator chooses. This desk explains that unit: what the smallest permitted stake is, which way a stake and a return are rounded, why the balance on the screen is not always the balance the account holds, and what the leftover fraction costs when it happens a thousand times.
- samples
- 11 invented
- smallest unit
- 0.01
- typical increment
- 0.10
- rounding direction
- set by the rules
A 0.10 increment on one invented market. The request lands at 10.33, which is between the 10.30 and 10.40 steps; it is placed at 10.30 and the 0.03 is never staked. On a 2.50 increment the same request places 10.00 and leaves 0.33.
Every money figure in a gambling account is rounded to a unit the operator sets. A stake is rounded to the market's increment, a return is rounded to the smallest unit of the currency, a balance is stored at full precision and shown at two places, and a bonus, a conversion and a duty are each rounded by a rule of their own. The unit decides what you can stake; the direction decides who keeps the tail. On the samples, the tail is a function of the digits you type rather than of the amount: a thousand stakes of 5.05 leave 50.00 behind and a thousand stakes of 5.00 leave nothing, from the same turnover.
What the samples show
The desk's whole argument is in one figure, so it is stated first and then shown eight ways. The leftover fraction is fixed in money and therefore largest in percentage terms on the smallest amounts, and it is invisible on the balance you are shown. A rule that costs 0.00875 on a conversion of 0.50 costs 1.75% of it; the same rule on a conversion of 100.00 costs nothing at all. A rule that rounds a stake down costs 0.05 on a request of 5.05 and 0.00 on a request of 5.00, so the cost is decided by the digits, not by the amount. And a balance of 99.9960 is displayed as 100.00, so the number on the screen is 0.004 larger than the number the account can pay out.
None of the samples describes a real operator, a real market or a real currency. They are eight invented sets of numbers, defined on this page, and every figure anywhere on the site is derived from them and can be re-derived from the arithmetic shown beside it.
Eight samples
Eight markets at one invented operator, one request of 10.33 placed against seven different increments and one minimum.
- markets
- 8
- increments
- 7 distinct
- largest tail
- 0.33
Eight stake requests on one 0.10-increment market, and where each one lands.
- requests
- 8
- placed
- 74.80
- tail
- 0.24
The same eight settled bets paid under a round-down rule and under a round-to-nearest rule.
- bets
- 8
- down pays
- 64.04
- nearest pays
- 64.07
Eight accounts held at full precision and shown at two places, and what the two numbers disagree about.
- accounts
- 8
- show more
- 4
- show less
- 3
Eight deposits against a 100% credit rounded down to the whole unit and capped.
- deposited
- 836.22
- credited
- 782.00
- cap
- 50.00
Eight amounts converted at one rate and rounded down to the smallest unit of the second currency.
- amounts
- 8
- worst cost
- 1.75%
- best cost
- 0.00%
A duty rounded up on five stakes and a prize rounded down on three, from the same rules document.
- stakes
- 5
- prizes
- 3
- collected
- 0.0335
Two thousand events of the same size, half of them with a tail and half of them without.
- stakes
- 1,000
- returns
- 1,000
- retained
- 60.00
Three further samples are defined on the pages that use them: sample I on the eighth decimal, sample J on the display and sample R on the price.
One request, seven increments
Sample A is the clearest place to start, because it shows that the amount you ask for is not the amount you place. One invented operator publishes seven different increments across eight markets. A single request of 10.33 lands in seven different places, and the tail it leaves behind ranges from a third of a unit to eleven times that.
| Market | Increment | Minimum | Placed | Tail |
|---|---|---|---|---|
| m1 | 0.10 | 0.10 | 10.30 | 0.03 |
| m2 | 0.20 | 0.20 | 10.20 | 0.13 |
| m3 | 0.25 | 0.25 | 10.25 | 0.08 |
| m4 | 0.50 | 0.50 | 10.00 | 0.33 |
| m5 | 1.00 | 1.00 | 10.00 | 0.33 |
| m6 | 2.50 | 2.50 | 10.00 | 0.33 |
| m7 | 5.00 | 5.00 | 10.00 | 0.33 |
| m8 | 1.00 | 2.00 | 10.00 | 0.33 |
| 8 markets | 7 distinct | - | 4 amounts | 0.03-0.33 |
Why the digits matter more than the amount
The second worked example is the desk's central finding, and it is arithmetic rather than opinion. Two thousand invented events of identical size produce a retained fraction of 60.00 or of nothing at all, and the only difference between them is the digits the player typed.