Risk and Reward Plays

Game Theory for Gamers: Applying Strategic Reasoning to Gaming Success

How to think several steps ahead in games: modelling what opponents want, working backwards from outcomes, and avoiding the trap of assuming they think like you.

On this page
  1. Strategy starts with the other player
  2. Level-k thinking
  3. Work backwards from the outcome
  4. Remove what is never worth doing
  5. Model what they want, not what you would do
  6. When anticipation backfires
  7. Using this in practice

Strategy starts with the other player

Playing well in isolation is a skill. Playing well against someone who is also trying to win is a different one. The best move in a competitive game is rarely best on its own; it is best given what the opponent is likely to do, and the opponent is choosing with the same question in mind.

Game theory is the study of exactly this situation. For a player, its most practical contribution is a set of habits: identify what each side wants, list what each side can do, and reason about how those choices interact.

Level-k thinking

A convenient way to describe depth of reasoning is in levels. A level-zero player acts without considering the opponent at all, perhaps by following a fixed script. A level-one player responds to what a level-zero opponent would do. A level-two player anticipates a level-one opponent’s response, and so on.

Mistakes usually come from assuming the wrong level. If you plan for a clever counter and the opponent is simply running their usual routine, you will have outthought yourself. If you assume the opponent is naive and they are not, you will be punished for predictability. Because most people reason only a step or two deep, one level ahead of the person in front of you is usually plenty. Going much deeper tends to cost time and attention without improving your read.

Work backwards from the outcome

When a decision leads to a sequence of later choices, a reliable method is to start at the end and work back. Ask what the final decision looks like for each side, and then what that implies for the choice before it.

A simple illustration: you can attack an objective now or wait. If you wait, the opponent can reinforce or counter-position. Rather than comparing “attack” and “wait” in the abstract, picture the opponent’s best answer to each. If their best answer to waiting leaves you worse off than attacking at a disadvantage would, then attacking now is the better of two imperfect options. The comparison is made by looking at the replies, not at your move alone.

Remove what is never worth doing

Some options are dominated: another option does at least as well in every situation and better in some. Spotting and discarding these shrinks the problem. This applies to opponents too. If an opponent’s option is dominated, a sensible opponent will not choose it, and you can stop preparing for it.

The caution is that dominance depends on the game as you understand it. Players sometimes label an option as pointless because they overlooked a context in which it works. Treat the judgement as provisional, particularly after a balance change or in an unfamiliar matchup.

Model what they want, not what you would do

A common error is simulating the opponent as a copy of yourself. Opponents have different goals, resources and tolerances. A player trying to survive a bracket round wants something different from one chasing a team ranking, and a streamer testing a gimmick wants something different again.

Useful evidence includes:

  • What they did in similar situations earlier, which is where opponent habits show up.
  • What they know. A decision that looks strange often makes sense once you remember what they could not see, and the effect of hidden information is easy to forget when you can see the whole screen.
  • What they gain or lose. Someone who is ahead and wants to run out the clock behaves differently from someone who is behind.

Gathering this through scouting information early gives you something to reason from, rather than guessing.

When anticipation backfires

Strategic reasoning can be overused. A few traps are worth knowing:

  • Overthinking: choosing an elaborate counter-plan when the obvious play is still the best one.
  • Assuming a pattern: reading one repeated choice as a trend when it might be coincidence.
  • Ignoring variance: planning around the most likely reply and being caught by a less likely one.
  • Treating the model as fact: the opponent’s reasoning is an estimate, and it should be updated as the match shows you more.

Updating matters most. Your prediction is a working hypothesis. When the opponent does something that does not fit, revise the model rather than defending it.

Using this in practice

None of this guarantees success; it simply improves the quality of your guesses. A short routine, practised over time, can help: state your goal, state your opponent’s likely goal, list the realistic options on each side, and check how each of your choices fares against their best reply. Then look at what actually happened and ask whether your model of them was right.

Over many matches, players who reason this way tend to be harder to read and less surprised by predictable responses. In any single game, though, luck, imperfect information and the other person’s own mistakes will still matter, and outcomes remain uncertain.

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