Key takeaways
- Type charts work like intransitive cycles such as rock-paper-scissors: A beats B, B beats C and C beats A, so no single choice is best.
- Type advantage can be a damage multiplier rather than a win; in the Pokémon series, a creature takes double damage from types it is weak to and half from types it resists.
- In balanced designs with an odd number of options, each one beats exactly half of the others and loses to the rest.
- A team of one element shares one set of weaknesses; spread your team so that every opposing type is beaten by at least one member.
- In a hypothetical seven-element cycle where each element beats three others, three well-chosen elements can cover all seven.
If fire beats ice and water beats fire, a battle becomes less about raw strength than about the right match-up. The Pokémon series' type chart is the best-known example, and our own dragon battler leans on elemental strategy too. This guide explains the mathematics behind them and how to build a team that is hard to counter, using Wikipedia's articles on intransitive games and rock-paper-scissors.
The cycle at the heart of every type chart
Type systems rest on an old idea. Wikipedia defines an intransitive game as one in which pairwise contests between strategies form a cycle: if A beats B, B beats C and C beats A, the relation "beats" is intransitive, because transitivity would require A to beat C. Its prototypical example is rock-paper-scissors.
The cycle is what keeps a game interesting. If one type beat all the others, everyone would pick it. In a cycle, the best choice always depends on what the other side has.
| Your choice | Beats | Loses to |
|---|---|---|
| Rock | Scissors | Paper |
| Paper | Rock | Scissors |
| Scissors | Paper | Rock |
From winning to damage multipliers
In the Pokémon series, type does not decide a battle outright; it changes damage. There, Wikipedia explains, types interact in rock-paper-scissors-style relationships: a creature takes double damage from attacking moves of types it is weak to and half damage from types it resists, and some types have special properties beyond the damage chart. A ×2 or ×0.5 multiplier makes type advantage a strong lean rather than a guarantee, leaving room for level, skills and tactics.
What a balanced chart looks like
Wikipedia notes that rock-paper-scissors variants usually use an odd number of moves, in which each move beats exactly half of the others and loses to the other half. Versions with up to 101 moves have been published. The five-move variant rock-paper-scissors-lizard-Spock, invented by Sam Kass and Karen Bryla, gives each move two wins and two losses. More moves also make ties rarer: in an odd-numbered balanced game with n moves, the chance that two random picks tie is 1/n, so a third with three moves and a fifth with five.
Unbalanced charts behave differently. Wikipedia describes a French variant with a fourth move, the well, that beats both rock and scissors; rock has no advantage over the well, so the optimal strategy is to play paper, scissors and well a third of the time each, and never rock. A chart with a weak option effectively has fewer real choices.
A worked example: covering a seven-element chart
Suppose, as an illustration, a game with seven elements, arranged in a balanced cycle in which each element beats the next three around the circle and loses to the three before it. Number the elements 0 to 6:
- Element 0 beats 1, 2 and 3.
- Element 4 beats 5, 6 and 0.
- Element 1 beats 2, 3 and 4.
Together, elements 0, 4 and 1 beat all seven: every possible opponent is beaten by at least one of them. Three is also the minimum, because each element beats only three others and two elements could beat at most six. A team of a single element, by contrast, beats only three of the seven: it loses to three and merely ties against its own element.
The same check works for any chart, however many types it has: list what each team member beats, and look for opposing types nobody covers.
Building a balanced team
- Cover the cycle. Make sure every opposing type is beaten by at least one team member.
- Avoid shared weaknesses. Two members weak to the same type give opponents a double target.
- Keep one neutral option. A strong all-rounder is useful against a team you cannot read.
- Check the actual chart. Real games are not always perfectly balanced; some types have extra resistances or immunities, so test your team against the strongest opponents you face.
The same thinking applies outside creature battles. Tower types and what they counter applies it to tower defence.
Elements in Dragon Pet Evolve
Dragon Pet Evolve Hatch Eggs has seven elements: fire, water, earth, storm, ice, shadow and light. Its battles are turn-based and lean on elemental strategy, against wild monsters and bosses and in an arena. The listing does not publish the match-ups between those elements, so the chart in the example above is not the game's; learn the real one in play, then apply the coverage check. The Dragon Pet Evolve guide explains hatching, breeding and battles, and virtual pet games explained covers the genre's history. It is one of our anime and creative apps.
Good to know
Frequently asked questions
How do type advantages work in battle games?
Why are type charts based on rock-paper-scissors?
How many types should a team cover?
What does a 2× type multiplier mean?
Sources
- Intransitive game (opens in a new tab)Wikipedia — accessed
- Rock paper scissors (opens in a new tab)Wikipedia — accessed
- Gameplay of Pokémon (opens in a new tab)Wikipedia — accessed
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