Correction · 2026-04-20
An earlier version of this page claimed Phase Switch was the #1 strategy at 9 of 11 skill levels. Two simulator bugs (MAX_TURNS=200 truncating long casual-skill games, and a matrix tally that attributed truncated games to the losing side) had inflated Phase Switch’s apparent win rate at casual and amateur skill. After the fixes, Phase Switch sits mid-pack (~#10 at MPR 2.0); E12 is the narrow top-tier leader. The discovery story below is preserved as an honest account of how the strategy was designed; the absolute numbers in older tables reflect the post-fix results.
The Problem with High Thresholds
On paper, S5 sounds like a great idea. Its threshold is 9 times the value of the highest open number — meaning it keeps scoring aggressively until it has built a massive lead before switching to covering mode. More points should mean more insurance, right?
But S5 actually loses to S2 in Frongello's round-robin tournament. S2, which switches to covering the moment it has any lead at all, consistently beats the seemingly more aggressive strategy. Why?
The answer is oscillation. S5 re-evaluates its score-versus-cover decision on every single dart. If your lead drops below the 9× threshold — which it will whenever your opponent scores — you go back to scoring mode. Then the lead climbs above the threshold again and you switch to covering. Then your opponent scores and you're back to scoring. This constant switching is deeply inefficient. You never commit to a plan, and the overhead of context-switching between strategic modes costs you darts and tempo.
The Lock-In Insight
This raises a natural question: what if the switch from scoring to covering was one-way?
Instead of re-evaluating the score/cover decision on every dart, what if you scored aggressively until a certain game-state condition was met, then committed to covering for the rest of the game? No going back. No oscillation. Once you decide to close out, you close out.
This eliminates the oscillation problem entirely. Once you've built your lead and are close enough to finishing that pure covering will get you there, you lock in and sprint to the finish line. The two-phase structure — score hard, then cover permanently — is the core of the Phase Switch strategy.
Finding the Right Trigger
The crucial design decision is: when to switch? Two conditions must both be true:
- Unclosed targets ≤ 3 — you're more than halfway done closing your seven targets.
- Marks remaining ≤ 9 — at most 9 marks left to close everything out.
This "combo condition" was discovered through systematic grid search. It captures the moment when closing out becomes realistically achievable — you're close enough that pure covering will finish the job before your opponent can catch up on points.
Why not just unclosed ≤ 3? Because 3 unclosed targets with 0 marks each (9 marks remaining) is a very different situation from 3 unclosed targets with 2 marks each (3 marks remaining). A player in the second scenario is far closer to winning than the first. The marks-remaining condition captures actual progress toward closing, not just the number of targets left.
The Grid Search
We tested 10 threshold multipliers × 3 fixed switch-at values plus 10 combo variants at pro skill level, running 50,000 games per cell. Each cell shows the Phase Switch variant's head-to-head win rate against S2.
| Threshold | sw@2 | sw@3 | sw@4 | combo |
|---|---|---|---|---|
| 10× | 53.5% | 54.0% | 53.2% | 55.0% |
| 11× | 53.7% | 54.2% | 53.3% | 55.3% |
| 12× | 53.8% | 54.4% | 53.4% | 55.5% |
| 13× | 53.9% | 54.5% | 53.5% | 55.8% |
| 14× | 53.8% | 54.4% | 53.4% | 55.6% |
| 15× | 53.7% | 54.3% | 53.3% | 55.5% |
| 16× | 53.6% | 54.2% | 53.2% | 55.4% |
| 18× | 53.4% | 54.0% | 53.0% | 55.2% |
| 20× | 53.2% | 53.8% | 52.8% | 55.0% |
| 25× | 52.8% | 53.4% | 52.4% | 54.5% |
Win rates shown are Phase Switch vs S2 head-to-head at pro skill level (MPR ~5.6), 50,000 games per cell. The best result (55.8%) is highlighted at threshold 13× with the combo switch condition.
Key observations from the grid search:
- The combo condition consistently outperforms every fixed switch-at value, regardless of the threshold multiplier. The gap is roughly 1–2 percentage points across the board.
- Thresholds between 12× and 16× all cluster in a tight range — the strategy is remarkably robust to the exact threshold chosen.
- The optimal combination is 13× with the combo switch condition, achieving a 55.8% win rate against S2 in the 50,000-game grid search (56.1% head-to-head at MPR 2.0 and 52.1% at MPR 5.6 in the 30-strategy, 20,000-game tournament).
Note: the original 50,000-game grid search ran at pro skill only. A per-MPR sweep (Apr 2026) now covers all 11 skill levels — see the Threshold Sensitivity section below.
The Threshold Depends on What You’re Optimizing
A recent fast-sim sweep (10 thresholds × 11 MPRs × 5 top opponents, 20,000 games each) shows the “optimal” threshold depends on framing. Against only the top-5 strongest opponents (S2, E2, E3, E10, E12), the lowest threshold tested (10×) wins at every MPR. Against the full 30-strategy field, higher thresholds (20–25×) win because they score more aggressively against the weak tail. The current 13× sits near the middle of both curves — a defensible default, but not the extremum for either metric.
The bigger finding: adding E12’s close-opp-closed-1 mechanic to PS (PS×E12) beats plain PS head-to-head at every skill level (51–53pp), but the combined strategy still sits mid-pack in the 30-strategy field — only reaching top-3 at competitive skill (MPR 4.0). See the PS×E12 section below.
The Strategy in Plain English
Phase 1: Scoring
Score aggressively. Don't cover until your lead is massive — 13 times the face value of the highest open number. With 20 still open, that means keep scoring until you're ahead by 260 points. Target the highest-value open number and pile on marks. Every excess mark past the three needed to close converts directly into points.
Phase 2: Closing
When you have 3 or fewer numbers left to close and need 9 or fewer total marks to close them all, switch to covering mode permanently. Close everything as fast as possible. No going back to scoring. No second-guessing. Sprint to the finish line.
The beauty is in the commitment. Once you decide to close out, you close out. No oscillation, no re-evaluation, no wasted darts switching between modes. The game ends fast.
Why It Works
1. Point Insurance
By the time Phase Switch transitions into covering mode, the player has built an enormous point lead. Even if the opponent catches up on a few numbers and starts scoring, the accumulated points provide a deep buffer. The win condition requires closing all targets and having a score greater than or equal to your opponent's — and by Phase 2, the score gap is nearly insurmountable.
2. No Oscillation
S5 goes back and forth between scoring and covering dozens of times per game. Every time the opponent scores a few points, S5's lead drops below its threshold, and it reverts to scoring mode. Then the lead climbs back up, and it switches again. This constant switching wastes darts on transitions that accomplish nothing. Phase Switch does it exactly once. One clean transition, then full commitment to closing out.
3. Endgame Efficiency
The combo condition triggers at exactly the right moment — when closing out is realistically achievable. Switching earlier wastes scoring opportunities (you leave points on the table while you still have the lead and open targets to score on). Switching later risks running out of targets to score on, or letting the opponent close the gap. The two-part condition (unclosed ≤ 3 and marks ≤ 9) identifies the inflection point where pure covering becomes the faster path to victory.
Performance Across Skill Levels (post-fix)
After the two simulator fixes, Phase Switch lands mid-pack across every skill level we tested. At MPR 2.0 it ranks roughly #10 among the 30 strategies; at pro skill (MPR 5.6) it ranks #6 with an average win rate of 58.9%. It still beats S2 head-to-head across the full skill range, but that edge does not generalize: simpler strategies like S2 and more aggressive finishers like E12 beat a wider field.
The numbers in this section as originally published (PS #1 at MPR 2.0 and 3.0, average win rates in the low sixties) were driven by the truncation bug described in the correction above. They are omitted here rather than restated, because the correct comparison is no longer “PS vs the field it was designed against” — it is “PS vs the actual field, where it sits in the middle.” See Results for the full post-fix rankings and Shape Reader for the strategy that did end up on top.
Threshold Sensitivity (per-MPR sweep)
The original 13× lead threshold was grid-searched at pro skill against S2 only. The table below shows the sweep extended to all 11 MPR levels and 10 thresholds (10× through 25×), averaged across five top-tier opponents (S2, E2, E3, E10, E12) at 20,000 games per pairing.
| MPR | 10× | 11× | 12× | 13× | 14× | 15× | 16× | 18× | 20× | 25× |
|---|---|---|---|---|---|---|---|---|---|---|
| 0.8 | 24.8 | 22.3 | 20.2 | 18.0 | 16.0 | 14.1 | 12.6 | 9.8 | 7.2 | 3.5 |
| 1.0 | 32.7 | 29.9 | 27.1 | 24.9 | 22.5 | 20.4 | 18.3 | 15.0 | 11.9 | 6.4 |
| 1.5 | 43.6 | 41.4 | 39.1 | 36.3 | 33.9 | 31.7 | 29.4 | 25.2 | 21.5 | 13.7 |
| 2.0 | 48.3 | 46.6 | 44.6 | 42.5 | 40.5 | 38.2 | 35.8 | 31.8 | 27.7 | 19.5 |
| 3.0 | 51.4 | 50.3 | 48.6 | 47.7 | 46.0 | 44.4 | 42.3 | 38.4 | 34.4 | 26.3 |
| 4.0 | 52.5 | 51.8 | 50.6 | 49.4 | 48.0 | 46.4 | 44.2 | 40.8 | 36.9 | 28.8 |
| 4.9 | 52.8 | 52.3 | 51.8 | 51.3 | 50.2 | 49.0 | 47.5 | 44.8 | 41.7 | 34.5 |
| 5.6 | 52.7 | 52.3 | 51.8 | 51.0 | 50.2 | 49.5 | 48.2 | 45.8 | 43.3 | 36.7 |
Each cell is PS win rate averaged across the 5 top-tier opponents. Best threshold per row bolded. Against this strong-opponents panel, the monotone pattern is clear: lower thresholds win at every skill. Below casual MPR, PS is outclassed by these opponents regardless of threshold — the issue is the opponents, not PS.
Against the full 30-strategy field, the picture inverts: higher thresholds (20–25×) win in average win rate because they score more aggressively against weak opponents (S1, S3, E6–E8). So “optimal” depends on framing. 13× remains a reasonable middle-of-the-road default.
PS×E12 — The Stronger Combo
Phase Switch is a phase structure (when to cover). E12 is a dart-allocation mechanic (when behind with nothing to score, finish an opp-closed target that’s one mark away before opening a new one). These are orthogonal. Combining them produces PS×E12 (13× threshold, with E12’s 1-away finish check inside PS’s scoring phase).
| MPR | PS×E12 rank | PS×E12 avg WR | PS×E12 vs PS | PS×E12 vs E12 | PS×E12 vs S2 |
|---|---|---|---|---|---|
| 0.8 | #9 | 56.6% | 51.5% | 49.0% | 50.4% |
| 1.0 | #9 | 56.8% | 52.2% | 49.0% | 50.8% |
| 1.5 | #7 | 57.1% | 51.5% | 49.0% | 51.4% |
| 2.0 | #6 | 57.6% | 52.1% | 49.8% | 51.0% |
| 3.0 | #4 | 58.4% | 52.6% | 50.6% | 52.8% |
| 4.0 | #2 | 59.3% | 53.1% | 51.8% | 53.5% |
| 4.9 | #6 | 58.7% | 51.1% | 52.1% | 52.8% |
| 5.6 | #7 | 57.9% | 51.1% | 51.5% | 52.2% |
PS×E12 is competitive but not dominant. Its best showing is at competitive skill (#2 at MPR 4.0, #4 at MPR 3.0). At casual skill the top of the field is too compressed for it to separate; at pro skill E3/E12/E2/S2 edge it out. Against individual competitors, PS×E12 wins head-to-head most matchups by less than 3 percentage points — in the same neighborhood as every other top-tier strategy.
The mechanism: the E12 opp-closed-1 check occasionally saves a dart during extended scoring phases. That small gain matters at competitive skill where every efficiency counts, but at casual skill the stochastic noise of missed darts dominates any strategy-level advantage.
Context and Related Strategies
For reference, S2 beats S1 (Frongello's weakest strategy versus his strongest comparison) by a similar margin at low skill levels. S1 is a pure covering strategy — it never scores intentionally, just tries to close everything first. S2's advantage over S1 demonstrates the value of scoring before covering: build a lead, then close out.
Phase Switch takes that principle further by making the scoring phase more aggressive and the transition to covering irreversible. But in the full 30-strategy field, PS sits mid-pack (rank #8–#9 across skill levels) because the E-series closing-first strategies beat it head-to-head. PS still beats S2 narrowly at higher skill (51.3% at MPR 3.0, 51.8% at MPR 5.6), but E12 leads every skill level.
E9 (PhaseShift): A Related Approach
The experimental strategy E9 (PhaseShift) uses a similar phase-based idea but with different thresholds for when to switch from scoring to closing. E9 ranks #7 at MPR 2.0 (58.2% avg), #8 at MPR 3.0 (58.0% avg), and #9 at MPR 5.6 (56.7% avg) — consistently strong but trailing PS at every skill level. The fact that two independently designed phase-based strategies both outperform most of the field reinforces that the core insight — a one-way switch from scoring to covering — is genuinely powerful, even if the exact trigger conditions differ.