▣The Last Decimal Open the partner account
paid
Affiliate disclosure. The partner link in the masthead and in the band beside the copy on this page is a sponsored link to a partner operator, and this site may be paid if you open an account through it, at no extra cost to you. It carries rel="sponsored noopener" and opens in a new tab. The subject of this desk is the fraction a rounding leaves behind - a figure that appears on no statement - so its own interest is stated here rather than left for a footer: one link funds the site, and no operator, market, currency, price or product is named, rated or recommended anywhere on it.
The Last Decimal / The return
Which way the payout rounds

The return: the other direction

The stake is rounded on the way in and the return is rounded on the way out, and the two roundings do not have to go the same way. This page compares the same eight settled bets under two rules.

Sample spec
bets
8
down pays
64.04
nearest pays
64.07
moved
3 of 8
the unitThe smallest amount the currency can express. In a two-decimal currency it is 0.01; the increment a stake must take is coarser and published per market.
the directionWhich way each rounding goes: down on a stake and a return, up on a duty and down on a prize. It is a rule, published, and it decides who keeps the fraction.
the volumeOne unit per event is nothing once and a figure at scale: on the samples, two thousand events of the same size retain 60.00 from the digits alone.
Direct answer

A return is the stake multiplied by the price, and the product is a full-precision number that is then rounded to the currency's smallest unit. A round-down rule pays the lower unit and keeps the fraction; a round-to-nearest rule pays the closer unit. On eight invented bets five landed exactly and three moved by one unit, a difference of 0.03 in total.

Two rules, one set of bets

The same eight settled bets are cheaper under one rule than the other, and neither rule is wrong - what matters is which one the operator's published rules state.

Sample C - eight settled bets under two rounding rules
StakePriceExactRound downNearest
10.001.1411.40000011.4011.40
7.001.1428577.9999997.998.00
3.001.3333333.9999993.994.00
2.501.904.7500004.754.75
5.001.055.2500005.255.25
4.001.6667006.6668006.666.67
20.001.07521.50000021.5021.50
1.002.502.5000002.502.50
8 bets-64.06779964.0464.07
sample C - the two rules compared round down = 11.40 + 7.99 + 3.99 + 4.75 + 5.25 + 6.66 + 21.50 + 2.50 = 64.04 round nearest = 11.40 + 8.00 + 4.00 + 4.75 + 5.25 + 6.67 + 21.50 + 2.50 = 64.07 difference = 0.01 + 0.01 + 0.01 = 0.03 0.03 ÷ 64.07 = 0.047% of what the nearer rule would have paid 5 of the 8 bets were identical under both rules.

Where the three moving bets come from

The three bets that move are not the largest and not the smallest; they are the three whose product does not land on the unit. A price of 8/7 expressed as 1.142857 multiplied by 7.00 gives 7.999999, which is one hundred-thousandth of a unit below 8.00, and a round-down rule pays 7.99. A price of 4/3 slightly truncated, multiplied by 3.00, gives 3.999999, and the same rule pays 3.99. The literal price 1.6667 multiplied by 4.00 gives 6.6668 and pays 6.66. In each case the exact product sits just under a whole unit, and the direction of the rounding decides whether the player receives it.

why the product lands just under a whole unit 7 × (8 ÷ 7) = 8 exactly → but 8 ÷ 7 = 1.142857142857... truncated to 1.142857 → 7 × 1.142857 = 7.999999 → one hundred-thousandth short 3 × (4 ÷ 3) truncated to 1.333333 → 3.999999 → one hundred-thousandth short the missing fraction is not the operator's: it is the truncation of the price itself. Rounding down then decides that the player carries it.
A payout rounding and a price's display precision are two different things that meet on this page: the truncation of the price creates the fraction and the rounding rule decides who keeps it. The price's own decimals are the subject of their own page.

Read next