Tournament Results

Bull Difficulty

Select a bull difficulty multiplier. Standard (1.0×) treats bull the same as numbers. Harder levels reflect bull’s smaller geometric target. See Bull Analysis for the full impact study.

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. Note: average win rate is heavily influenced by margins against weak strategies. Two strategies that tie head-to-head can have different rankings if one beats weak opponents by wider margins. See Key Observations below for details.

Key Observations

• Phase Switch (PS) dominates at low-to-mid skill but drops at pro level. PS ranks #1 from MPR 0.8 through 3.0 (avg win rates: 73.6%, 62.9%, 60.9%), beating S2 head-to-head at every level. But at MPR 5.6 PS falls to #5 (59.3%), overtaken by E3 (60.4%), S2 (60.2%), E2 (60.2%), and E10 (60.0%). When players rarely miss, the phase-switching overhead loses its edge.
• E10 (ScoreSurge) and E3 (GreedyCloseAndScore) are consistently top-5. E10 ranks #2 at MPR 0.8 (63.9%), #2 at MPR 2.0 (59.3%), #2 at MPR 3.0 (59.2%), and #4 at MPR 5.6 (60.0%). E3 tracks closely: #4, #3, #4, and #1 respectively. Both strategies combine aggressive closing with opportunistic scoring, making them robust across the full skill spectrum.
• S2 rises at high skill — simplicity wins when players rarely miss. S2 climbs from #11 at MPR 0.8 (51.6%) to #8 at MPR 2.0 (57.7%) to #5 at MPR 3.0 (58.7%) and finally #2 at MPR 5.6 (60.2%). Its straightforward rule (“score until you lead, then cover”) is the best original Frongello strategy at every skill level.
• S2 decisively beats S10 at all skill levels — non-chase dominates chase. S2 vs S10 head-to-head: 57.8% at MPR 0.8, 57.6% at MPR 2.0, 58.9% at MPR 3.0, and 60.1% at MPR 5.6. The gap widens as skill increases, confirming Frongello’s original finding that chasing the opponent’s numbers is suboptimal.
• E6 (AlwaysSingle) and E7 (AlwaysDouble) are catastrophically bad. These strategies confirm that triples are essential. E6 averages just 21.6% at MPR 0.8 and collapses to 1.4% at MPR 5.6. E7 fares only slightly better (21.3% to 6.3%). At pro level, E6 wins 0.0% against 16 of 29 opponents. Refusing to throw triples is the single worst strategic decision in cricket.
• E1 (Early Bull) is highly sensitive to bull difficulty. Under standard bull (toggle above), E1 tops average rankings at 9 of 11 skill levels — but this advantage was inflated by its early bull closure on an unrealistically easy target. Under realistic bull difficulty (0.75×), E1 drops from #1 to dead last at MPR 3.6+, losing an average of 5.67 percentage points across all skill levels. See Bull Analysis for the full breakdown.
• 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.
• At low MPR levels, strategy differences diminish. When most darts miss their target, luck dominates and the gap between the best and worst strategies narrows considerably.
• Harder bull acts as a mild equalizer in unequal matchups. The weaker player consistently gains 0–2pp when bull is harder, with the effect growing at higher skill levels. Games also become 2–4% longer.

Frongello's Original Rankings

For comparison, Frongello's equal-skill simulation found the following ranking by average win rate:

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

Frongello found S2 statistically significantly better than S6 against 13 of 17 strategies at equal skill (S2 beat S6 head-to-head 51.9%). However, in his unequal-skill simulation (one player at 95% relative accuracy), S6 became optimal — using “extra darts” extends the game and favors the stronger player. Under our realistic miss-rate profiles at equal skill, the gap between S2 and S6 widens further, confirming that extra darts disrupt closing tempo when accuracy is imperfect.