Tool
Random Percentage Allocator
Split 100% randomly between entries — uniformly over the simplex, not by normalising.
Random Percentage Allocator
Split a whole — a hundred percent, a bill, a prize pot — into random shares that add up to exactly the total, with an optional floor so nobody gets zero.
The naive way to do this is to draw a random number for each part and then divide by the sum. That produces shares that add to the total and are emphatically not uniformly random: they cluster near the average, and a genuinely lopsided split becomes nearly impossible.
This uses sorted cut points instead, which gives a uniform distribution over every valid split. The difference is visible after about five runs.
How the Random Percentage Allocator works — and why it's fair
To split a whole into k parts, the tool drops k−1 random cut points into the interval, sorts them, and takes the gaps between consecutive cuts as the shares. That is the standard method for sampling uniformly from a simplex, and it produces every valid combination of shares with equal density.
The normalise-independent-draws approach fails for a reason worth understanding, because it looks obviously correct. Each share becomes a random draw divided by a sum that includes it, and sums of independent draws concentrate — the more parts you have, the more tightly every share is pulled toward 1/k. For a four-way split of 100, normalising produces shares that are almost always between 15 and 35, while a genuine uniform split regularly produces a 3 and a 60.
The sorted-cuts method has no such pull. Any set of shares summing to the total is as likely as any other, which means extreme splits appear at exactly the rate they should. Running it a few times and seeing a 2 next to a 55 is not a malfunction; it is the distribution the naive method was hiding from you.
The minimum-share control reserves a floor for every part before any cutting happens. With four parts and a floor of 10, forty units are set aside immediately and only the remaining sixty are randomly divided. The result is still a uniform split of what is divisible, with the floor added back to each part — so the distribution is uniform, just shifted and compressed.
The floor makes the operation impossible above a certain point, and the tool says so rather than adjusting anything. Four parts with a floor of 30 needs 120 units and you have 100; there is no valid answer, and inventing one by silently lowering the floor would be worse than refusing.
The shares always sum to exactly the total, by construction — the gaps between the cuts partition the interval with nothing left over. That is a property of the method, not a correction applied at the end.
When the Random Percentage Allocator is fair — and when it is not
What it does guarantee
- Every valid combination of shares is equally likely — the split is uniform over the simplex, not clustered near the average.
- The shares sum to exactly the total by construction, with no rounding correction applied afterwards.
- The minimum-share floor is genuinely reserved before cutting, so no part can fall below it.
What it does not
- Uniform does not mean even. Extreme splits are supposed to happen, and they will.
- There is no notion of deserving. The tool cannot express that one part should tend to be larger.
- Displayed shares are rounded to one decimal place, so the printed figures can appear to sum to slightly off the total even though the underlying values do not.
Two worked examples
Four parts of 100, no floor
- Three cut points are drawn in [0, 1), sorted, and the four gaps become the shares.
- A typical run: 12.4, 41.8, 8.3, 37.5 — summing to exactly 100.
- Normalising four independent draws instead would almost never produce an 8.3 next to a 41.8.
Four parts of 100 with a floor of 10
- 40 units are reserved immediately, one floor per part.
- The remaining 60 is split uniformly and added on top, so every share lands between 10 and 70.
- A floor of 30 would need 120 units — the tool refuses and says why rather than lowering the floor.
Splits worth randomising
Prize pot division for a team win is the cleanest case: everyone contributed, nobody agrees on how much, and a random split with a floor is a settlement everyone can accept because nobody chose it. The floor is what makes it acceptable — a genuinely uniform split can hand someone 2%.
It is also a good teaching device for the difference between uniform and even, which is one of the most persistent confusions in everyday probability. Ten runs of a four-way split produce a spread that no amount of explaining achieves as quickly.
Randomised budgeting and constraint exercises use it deliberately: allocate a fixed budget randomly across categories and see what the resulting plan would actually look like. It is a way of stress-testing assumptions rather than a way of budgeting.
For a split where the parts should have deliberately different expected sizes, weight the entries with the weighted random picker and use its percentages directly. For deciding who pays the whole thing rather than dividing it, the split-the-bill randomizer does exactly that.
Frequently asked questions
Why not just draw a number for each part and normalise?
Because sums of independent draws concentrate. Normalising pulls every share toward the average and makes genuinely lopsided splits nearly impossible.
How do sorted cut points fix that?
The gaps between k−1 sorted uniform cuts are uniformly distributed over all valid splits. Nothing pulls them toward the average because nothing is being summed and divided.
Do the shares always add up exactly?
Yes, by construction — the gaps partition the interval with nothing left over. Displayed values are rounded to one decimal, so the printed figures can look slightly off.
What does the minimum share do to the randomness?
It reserves a floor per part before cutting, then splits what remains uniformly. The distribution is still uniform, just shifted upward and compressed.
Why did it refuse to split?
Because your floor multiplied by the number of parts exceeds the total. There is no valid answer, and silently lowering the floor would be worse than saying so.
Can I use it for money rather than percentages?
Yes — set the total to the amount. The method is unit-agnostic; only the rounding for display assumes one decimal place is useful.
Why did one part get almost nothing?
Because that is what uniform means. If you want a guaranteed minimum, set the floor — that is exactly what it is for.
Is this the same as the split-the-bill tool?
No. That one picks a single person to pay everything; this one divides a whole into random parts. Different questions, different mechanics.
How many parts can it handle?
As many as you list. The cut-point method scales linearly, so a twenty-way split is no harder than a four-way one — though the shares get small.
Related tools
Split the Bill Randomizer
One person pays the lot — and over enough dinners it evens out. Mostly.
Weighted Random Picker
Give each entry its own odds — and see the exact probability table before you draw.
Random Decimal Generator
Uniform decimals in a range, with the precision you choose — and the rounding explained.