Tournament Results

Skill Level

Select a skill level to view the tournament results at that MPR (Marks Per Round). Higher MPR corresponds to more skilled players who hit triples more consistently.

Tournament Matrix

Each cell shows the row strategy's win rate (%) against the column strategy. Values above 50% (green) indicate the row strategy wins more often. The matrix is symmetric: if A beats B at 55%, then B beats A at 45%.

How to Read the Matrix

• Green cells (>55%) — The row strategy dominates this matchup, winning more than 55% of games.
• Yellow cells (~50%) — An even matchup where neither strategy has a meaningful advantage.
• Red cells (<45%) — The column strategy dominates, and the row strategy loses more than 55% of games.
• Diagonal cells — Always 50% since a strategy playing itself wins half the time by definition.
• Hover — Move your cursor over any cell to highlight the full row and column for easier cross-referencing.

Rankings

Strategies ranked by average win rate across all opponents. The average excludes self-play (the diagonal), so it reflects head-to-head performance against every other strategy in the tournament.

Key Observations

• Phase Switch (PS) ranks #1 at high skill levels (MPR 4.0+). At lower skill levels it remains competitive but S2 edges it out in average win rate between MPR 1.5–3.0. Its advantage grows with player skill.
• S2 remains the best of the original 17 Frongello strategies. Its simple rule ("score until you have any lead, then cover") holds up even under realistic miss rates.
• Chase strategies (S10–S13, S14–S17) generally underperform their non-chase counterparts. Frongello's original finding that chasing is suboptimal holds across skill levels, with the gap widening as skill increases.
• Extra darts (S6–S9) provide a small boost over basic (S2–S5) at higher skill levels. When you hit triples frequently, redirecting leftover darts to scoring adds up. At low skill levels, the benefit disappears because the extra darts miss more often.
• E1 (Early Bull) is a surprise performer. By closing Bullseye earlier in the sequence (after 17 instead of last), E1 consistently ranks #1 at mid-range skill levels (MPR 2.0–4.0). The other experimental strategies (E2–E4) cluster near S2 performance without a clear edge.
• At low MPR levels (high miss rates), strategy differences diminish. When most darts miss their target, luck dominates and the gap between the best and worst strategies narrows considerably.
• At high MPR levels, strategy matters more. The gap between S1 (close only, never score) and PS widens as skill increases, because skilled players can actually execute the strategic intent of their approach.

Frongello's Original Rankings

For comparison, Frongello's paper found the following ranking:

S2 = S6 > S10 = S14 > S3 = S7 > S11 = S15 > S1 > S4 = S8 > S12 = S16 > S5 = S9 > S13 = S17

In Frongello's results, the "extra darts" and "chase" parameters had no effect within their groups — strategies with the same threshold but different extra-darts or chase settings performed identically. Under realistic miss rates, these parameters begin to differentiate, which is why our results show small but consistent gaps between S2 and S6, and between S10 and S14.