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 grid search (55.5% in the 20,000-game tournament).
The Plateau
One of the most remarkable findings: the Phase Switch strategy is extremely robust. Any threshold between 12× and 20× combined with the combo switch condition wins 55–56% against S2. You don't need to fine-tune the threshold — the one-way switch mechanism itself is the key innovation. The decision to commit, not the exact moment of commitment, is what drives the advantage.
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
Phase Switch's advantage over S2 depends heavily on skill level. At low MPR, the two strategies are nearly indistinguishable — S2 actually has a slight edge. As skill increases, Phase Switch pulls ahead decisively:
| MPR | PS Win% vs S2 | Edge |
|---|---|---|
| 1.0 | 49.2% | −1.6pp |
| 1.2 | 49.9% | −0.2pp |
| 1.5 | 49.1% | −1.8pp |
| 2.0 | 49.5% | −1.0pp |
| 2.5 | 49.7% | −0.6pp |
| 3.0 | 50.6% | +1.2pp |
| 3.6 | 51.0% | +2.0pp |
| 4.0 | 52.1% | +4.2pp |
| 4.9 | 54.0% | +8.0pp |
| 5.6 | 55.5% | +11.0pp |
20,000 games per matchup. "pp" = percentage points above/below 50%.
At low skill levels (MPR < 2.5), high miss rates introduce so much randomness that strategic decisions matter less — S2's simpler approach performs equally well or slightly better. The crossover happens around MPR 3.0, where Phase Switch begins to pull ahead. From there the advantage grows steadily, reaching +11pp at pro level (MPR 5.6). The more reliably a player can execute their intended throw, the more Phase Switch's aggressive early scoring pays off.
S2 vs S1 for Context
For reference, S2 beats S1 (Frongello's weakest strategy versus his strongest comparison) by a similar margin. 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 versus S2 represents a comparable strategic improvement — moving from "best known" to "actually optimal." Just as S2 improved on S1 by adding a scoring phase, Phase Switch improves on S2 by making the scoring phase more aggressive and the transition to covering irreversible. Each step adds a layer of strategic sophistication that translates directly into win rate.