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Part 4 of 7 · Tip pool splitter series ~5 min read

How the rounding remainder is handled

This post is about two pence, and it matters out of all proportion to its value. Where the rounding remainder goes is the single clearest signal a business sends about whose money the tip pool is, and it costs about four pounds a year to get right.

Key takeaways

  • Rounding to the penny always leaves a remainder. It has to go somewhere explicitly.
  • It never goes to the business. Not once, not as a convention, not as a rounding policy.
  • It is distributed a penny at a time, in a rotation recorded on the period.
  • The rotation position carries forward, so over a year it is demonstrably even.
  • The remainder and its recipients are published, because that is what makes it credible.

Where the pennies come from

A pool of £830.30 divided across 318.4 weighted hours gives a rate with more decimal places than money has. Multiply that back for eleven people, round each to the penny, and the shares will sum to something a few pence away from the pool. That difference is unavoidable, it is usually between one and ten pence, and it has to go somewhere.

How the rounding remainder is distributedA vertical chain of five steps entered by a box labelled Shares, rounded, whose sum does not equal the pool. Step one computes the remainder as the pool minus the sum of the shares. Step two asks who is next, taken from a rotation position carried between periods. Step three gives one penny each around the rotation. Step four advances the position for the next period. Step five publishes who got them, by name, every time. A note says publishing the recipients is what stops this being something people wonder about.AWS ACCOUNTShares, roundedsum != poolCompute the remainderpool minus the sumWho is next?from the rotationRotation positioncarried between periodsOne penny eachround the rotationAdvance the positionfor next periodPublish who got themby name, every timePublishing the recipients is what stops this being something people wonder about.
Fig 1. How a few pence are distributed. Carrying the rotation position between periods is what makes the distribution even over a year rather than always favouring whoever is first alphabetically.
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Why not to the business

The remainder is trivially small and retaining it is a policy choice about whose money the pool is. A business that rounds in its own favour every week has, over a year, kept about four pounds and told its staff something quite specific about the relationship.

In several jurisdictions it is also not permitted, and in most of the rest it would be difficult to defend if anybody asked. The point is not the legal exposure — four pounds is not a legal exposure — it is that the alternative costs nothing and says the opposite thing.

Why not to the largest share

“Give the remainder to whoever worked the most hours” is tempting because it is one line of code and needs no state. It also gives the same person a few extra pence every week forever, which over a year is small and over a year is also visible, and the first person to notice will describe it as the system favouring the manager.

The rotation

How the rounding rotation distributes pennies over four weeksA horizontal row of five boxes. Week one: two pence, to Ash and Rae. Week two: three pence, to Sam, Kit and Jo. Week three: one penny, to Lee. Week four: two pence, back to Ash and Rae. Over a year: within a penny of even. A note says the position carries forward, so nobody is systematically first or last.THE ROTATION, OVER FOUR WEEKSWeek 12p: Ash, RaeWeek 23p: Sam, Kit, JoWeek 31p: LeeWeek 42p: Ash, RaeOver a yearwithin a penny of evenThe position carries forward, so nobody is systematically first or last.
Fig 2. The rotation across four weeks. Carrying the position rather than restarting each period is what prevents a fixed order from advantaging the same people every time.
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The rotation order itself can be anything stable — alphabetical, by employee number, by start date — as long as it does not change between periods and the position carries forward. Restarting the rotation each period is the bug that makes this whole mechanism pointless, because whoever is first in the order gets a penny every single week.

Publishing it

The remainder line appears on every published split: “3p of rounding went to Sam, Kit and Jo. Next period starts at Lee.” It is one sentence, nobody will ever read it twice, and its presence is the reason nobody wonders.

Next: what publishing actually looks like.

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