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What the Game Is Counting

Three short lessons for parents who do not play video games: health bars and the leftover hit, level curves that add or multiply, and why a 1% drop rate feels so slow.

Spark & Whetstone · sparkwhetstone.org/learn/what-the-game-is-counting · CC BY-NC-SA 4.0. Answers are at the end, so you can try each question first.

Lesson 1. The leftover hit

A monster with 100 health points that loses 15 per hit does not fall after 6.67 hits. After six hits it has 10 left, and that still needs a seventh. Games count up to the next whole number.

Children who play meet division with a remainder every day: the answer is the quotient plus one whenever anything is left over.

Question. A shield has 50 points and each hit takes 12. How many hits does it take to break?

  1. 6 hits
  2. 4 hits
  3. 5 hits

Say it back. In your own words: why does a game round the number of hits up, not to the nearest?

Lesson 2. Curves that add or multiply

A designer decides how many points each level needs. Some add the same amount each time (100, 200, 300 …); others multiply (100, 200, 400 …). The second kind feels quick at first and then very slow.

Bonuses multiply as well. Two boosts of +20% are ×1.2 then ×1.2, which is ×1.44: +44%, not +40%.

Question. Two boosts of +50% each are used together. How much extra do they give?

  1. +100%
  2. +150%
  3. +125%

Say it back. In your own words: why do two +20% boosts make more than +40%?

Lesson 3. A one percent drop

If a rare item drops 1% of the time, each try is a separate chance. After 100 tries there is only about a 63% chance of having it, and half of all players will need 69 tries or more.

Some games add a "pity timer": a guaranteed drop by a certain try, so nobody waits forever. When the tries cost money, this is a loot box, and the maths is exactly the same.

Question. An item drops 10% of the time. About what is the chance of having it after 10 tries?

  1. About 65%
  2. 100%
  3. About 10%

Say it back. In your own words: why is 100 tries at 1% not a guarantee?

At the table: A paper dungeon

Players: Two to four, ages 7 and up. You'll need: Two dice, paper, pencils.

  1. Draw a monster with 20 health points. Each turn, roll one die: that is the damage.
  2. Before the fight, everyone guesses how many rolls it will take, and writes it down.
  3. Play it out, keeping a running total of health left. Then play again with a monster of 30.
  4. Talk about why the number of rolls is never exactly the health divided by 3.5, the average roll.

Answers

  1. 5 hits — 4 × 12 = 48 leaves 2 points, so a fifth hit is needed. 50 ÷ 12 is about 4.17, rounded up to 5.
  2. +125% — 1.5 × 1.5 = 2.25, which is +125%. The second boost also grows the first boost’s extra.
  3. About 65% — 0.9¹⁰ ≈ 0.35, so the chance of at least one drop is about 1 − 0.35 = 0.65. Ten tries at 10% is not a sure thing.