Two correct answers to one question
Slot machines and other games of chance have a built-in house edge, and no strategy, system or timing changes the odds. Most players lose money over time, and nobody should gamble money they cannot afford to lose. The figures in this article are hypothetical and are here only to explain how changes in rates are described.
Suppose a rate moves from 4% to 5%. Was that a 1% increase or a 25% increase? Both statements can be correct, which is exactly why this topic causes so much confusion. They answer different questions.
Percentage points: the plain difference
A percentage point is the arithmetic difference between two percentages. Going from 4% to 5% is a change of 1 percentage point, found by subtracting: 5 − 4 = 1.
Percentage points describe movement on the scale itself. They do not depend on the starting value, so a move from 40% to 41% is also 1 percentage point.
Percent change: relative to the start
Percent change describes the size of the change compared with where you began:
percent change = (new − old) ÷ old × 100
For 4% to 5%: (5 − 4) ÷ 4 = 0.25, so a 25% increase.
Same data, two descriptions: “up 1 percentage point” and “up 25%”. The second sounds more dramatic, and that is not an accident when headlines pick one.
More worked examples
- 10% to 15%: up 5 percentage points; relative change is 5 ÷ 10 = 50% increase.
- 20% to 10%: down 10 percentage points; relative change is −10 ÷ 20 = 50% decrease.
- 60% to 63%: up 3 percentage points; relative change is 3 ÷ 60 = 5% increase.
- 2% to 3%: up 1 percentage point; relative change is 1 ÷ 2 = 50% increase.
The same one-point move produced a 25% change in one case and a 50% change in another. The smaller the starting value, the bigger the percent change from the same shift. That is the central idea behind relative risk and absolute risk.
Percent changes are not symmetric
Percent changes do not undo each other the way many people expect. Start at 100. Raise it by 50% and you reach 150. Now lower that by 50% and you reach 75, not 100. To return from 150 to 100 you need a drop of one third, or about 33.3%.
This is simply because the second percentage applies to a different base. It matters whenever someone reports “up 20% then down 20%” and implies nothing changed. Starting at 100, up 20% is 120 and down 20% is 96.
Why small base values inflate percent changes
When a rate is already tiny, a very small absolute change can produce a huge relative change. A rate going from 0.1% to 0.2% is a 100% increase, yet it is only 0.1 percentage points. If a story reports “doubled”, ask what it doubled from.
The reverse also holds. A large base makes percent changes look modest even when many people are affected.
Applying it to game math
Percentages show up in discussions of slots, for example in return to player and the house edge. A hypothetical game with a return to player of 94% that changes to 96% has moved by 2 percentage points. As a relative change in the return, that is 2 ÷ 94, about 2.1%.
But the house edge, which is 100% minus the return, has moved from 6% to 4%. That is also 2 percentage points, and a relative drop of 2 ÷ 6, about 33.3%. The same change can be described as “about 2% better” or as “the house edge cut by a third”, depending on which quantity you describe. Neither tells you what will happen in a single session, because these are long-run averages, and a lower house edge is still a house edge.
This is a good illustration of how framing affects the impression a statistic gives, one of the ways advertised chances can mislead.
How to read a statistic
When you see a reported change in a rate, ask three things.
- What was the starting value? Without it, a percent change cannot be judged.
- Is the change in percentage points or in percent? A story that says “rose by 2%” might mean either one.
- What is the absolute difference? Convert it to a count of people or events if you can. A rise from 1 in 1,000 to 2 in 1,000 is 100% in relative terms and one extra case per thousand in absolute terms.
Tips for writing it clearly
- Use “percentage points” when subtracting one percentage from another.
- Use “percent” for relative changes, and say what the base was.
- Give both when the difference is large, such as “from 4% to 5%, a rise of 1 percentage point or 25%”.
- Avoid the bare phrase “a 1% increase” for a rate that moved from 4% to 5%.
Why it matters for choices
Numbers that sound large or small can nudge decisions. Reading them carefully is one of the better defenses against the framing effect and other cognitive biases. It also makes it easier to see through offers or claims that rely on dramatic-sounding relative changes.
If you gamble, treat it as paid entertainment, set a limit before you play, and stop when you reach it. If gambling is causing worry, a national problem-gambling helpline or local health service can help.