Strategic Modeling

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Strategic Modeling
12,000 ops
Analyze strategy tournaments to generate Yomi

Strategic Modeling is a project in Universal Paperclips.

Summary[edit | edit source]

By using tournaments you spend your ops (operations) to gain a varying amount of yomi, which are in turn used to purchase various improvements. Yomi are valuable in all 3 stages of the game.

This project is unlocked once you complete Donkey Space.

Mechanics[edit | edit source]

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[[1]] The tournaments are based on many famous Game Theory related problems (such as "The Prisoner's dilemma", "Battle of the sexes", "Chicken", etc.) with the outcome rewards being generated randomly at the start of the tournament. While the "Random" strategy adds a little uncertainty, the general performance of each strategy can be predicted. The player can choose which strategy to back at any point before the tournament results are displayed.

The tournament cost is 1000 ops per strategy, and the number of rounds is the square of the number of strategies, so the potential "yomi" per "op" increases in proportion to the number of strategies learned. The length (duration, in real-time seconds) of a tournament depends on the number of rounds and so increases with the square of the number of strategies, plus a fixed delay of approximately 4 seconds when AutoTourney is enabled.

Each round is labelled as A versus B, with A and B being named as a temporary pair, a choice between two arbitrary outcomes, based on Game Theory problems, and some other cultural references. The name pairs have no effect on scoring, they are for informational purposes only.

Choice pairs are:

  • cooperate / defect
  • swerve / straight
  • macro / micro
  • fight / back down
  • bet / fold
  • raise price / lower price
  • opera / football
  • go / stay
  • heads / tails
  • particle / wave
  • discrete / continuous
  • peace / war
  • search / evaluate
  • lead / follow
  • accept / reject
  • accept / deny
  • attack / decay

Regardless of the pair labels, each tournament is set up with a randomly generated set of reward pairs, the first element in each pair for the player, the second element for the adversary.

The game grid is generated as follows:

Col. A Col. B
Row A: a,a b,c
Row B: c,b d,d

Note that the values will always be identical in Row A/Col A (e.g. 9,9) and Row B/Col B (e.g., 2,2). Furthermore, the value pair will be reversed for Row A/Col B (e.g., 6,1) and Row B/Col A(e.g., 1,6). This equalizes the rewards for the player and the adversary when each choose the same strategy.

Consider the following example:

Col. A Col. B
Row A: 9,9 6,1
Row B: 1,6 2,2

Suppose Strategy A100 is selected ("Choose Row A 100% of the time"). The tournament runs all strategies against each other and sums the total rewards earned for each strategy pair (Random v. A100, Random v. B100, etc.). As described in Strategy A100, the rewards in this situation are likely (though not certain due to variable results from the Random strategy) to be greatest for this strategy and earn the most Yomi, in this case approximately 1500 Yomi.

Through the stages[edit | edit source]

Towards the end of the first game stage, the Theory of Mind project doubles the tournament costs and rewards.

At the beginning of the third game stage, the Strategic Attachment project gives the player yomi rewards for correctly predicting the tournament outcomes: a 50,000 yomi bonus is awarded if the selected strategy earns most yomi, with 30,000 and 20,000 yomi bonuses for the second and third place strategies.

The following table summarizes for each strategy the average expected result, average Yomi earned, and average Yomi in Stage 3 with Strategic Attachment, based on a simulated run of 1 million tournaments. See the description of each individual strategy for the reward configurations where that strategy is likely to perform well.

Strategy Estimated Result Estimated Yomi Estimated Yomi with

Theory of Mind & Strategic Attachment

Win %
Beat Last 1,096.72 5,582.22 19,596.29 27.56%
Greedy 1,062.28 5,399.72 20,814.88 17.66%
Generous 936.69 4,004.06 15,134.30 13.63%
A100 895.69 3,616.73 13,647.21 14.68%
B100 894.86 3,500.66 13,166.29 13.56%
Minimax 856.31 2,905.70 10,443.26 7.40%
Tit For Tat 895.24 2,713.64 7,347.44 5.29%
Random 879.28 2,258.08 4,811.93 0.20%