Minimax Algorithm

1Level 0 (Maximizer — your routes):
2  For each candidate route, compute the worst-case output.
3  Pick the route with the HIGHEST worst-case output.
4
5Level 1 (Minimizer — adversarial conditions):
6  For each route, model all adversarial factors:
7  - Slippage spike (2x quoted)
8  - Gas price surge (1.5x current)
9  - Bridge delay (3x median)
10  - MEV extraction (0.3% of value)
11  - Price movement (0.5% adverse)
12  Apply all simultaneously → worst-case output for this route.

1function minimax(routes: Route[]): Route {
2  let bestRoute: Route | null = null;
3  let bestMinimaxScore = -Infinity;
4
5  for (const route of routes) {
6    // Minimizer: compute worst-case output for this route
7    const worstCase = evaluateWorstCase(route);
8
9    // Maximizer: pick route with best worst-case
10    if (worstCase.score > bestMinimaxScore) {
11      bestMinimaxScore = worstCase.score;
12      bestRoute = route;
13    }
14  }
15
16  return bestRoute;
17}
18
19function evaluateWorstCase(route: Route): Evaluation {
20  let output = route.quotedOutput;
21
22  // Apply all adversarial conditions simultaneously
23  output -= route.slippage * 2.0;          // 2x slippage
24  output -= route.gasCost * 1.5;           // 1.5x gas
25  output -= route.value * 0.003;           // MEV extraction
26  output -= route.value * 0.005;           // Adverse price movement
27  output -= route.bridgeRiskPenalty;        // Bridge-specific risk
28
29  return { score: output, route };
30}

1Transfer: 1 ETH → SOL
2
3Route A (Wormhole direct):
4  Best case:  14.5 SOL (probability: 60%)
5  Worst case: 11.2 SOL (probability: 40%)
6  Expected value: 14.5 × 0.6 + 11.2 × 0.4 = 13.18 SOL
7  Minimax score: 11.2 SOL
8
9Route B (Multi-hop via Arbitrum):
10  Best case:  14.2 SOL (probability: 70%)
11  Worst case: 13.8 SOL (probability: 30%)
12  Expected value: 14.2 × 0.7 + 13.8 × 0.3 = 14.08 SOL
13  Minimax score: 13.8 SOL
14
15Expected value picks: Route B (14.08 > 13.18) ← correct here
16Minimax picks:        Route B (13.8 > 11.2)   ← also correct, same answer
17
18But what if probabilities are wrong?

1What if actual worst-case probability was 70%, not 40%?
2
3Route A actual: 14.5 × 0.3 + 11.2 × 0.7 = 12.19 SOL  ← much worse
4Route B actual: 14.2 × 0.3 + 13.8 × 0.7 = 13.92 SOL  ← barely changed
5
6Minimax doesn't need to know probabilities.
7It just guarantees Route B gives you AT LEAST 13.8 SOL.
8Period.

1Routes to evaluate: [A, B, C, D, E, F, G, H, I, J, K, L]
2
3Evaluate A → minimax score: 12.1
4Evaluate B → minimax score: 13.8 ← new best
5Evaluate C → worst-case starts below 13.8 → PRUNE (can't beat B)
6Evaluate D → minimax score: 13.2 → skip (below B)
7Evaluate E → worst-case starts below 13.8 → PRUNE
8...
9
10Result: Only 7 of 12 routes fully evaluated. Same result, 40% less work.