---
name: Round-robin / parlay study — apparent edge is in-sample variance, not real; don't pursue
description: Backtested same-day round robins on strategy_bets.csv. 2/3-leg looked +ROI but it's a few clustered longshot days; not executable on Kalshi. Shelved 2026-06-06.
type: project
---

User asked 2026-06-06 "what about round robins? any profit there?" Backtested same-day round robins (all C(n,k) parlays per game_date) on `strategy_bets.csv` (365 settled singles, 26.3% WR, +18.6% flat ROI, p=0.056 — already only marginally significant).

**Raw results looked tempting but are a mirage:**
- 2-leg: 3821 parlays, 6.0% hit, +23.5% ROI, +897.9u
- 3-leg: 35769 parlays, 1.1% hit, +5.5% ROI, +1960u
- 4-leg: 286625 parlays, 0.2% hit, **-28.4% ROI, -81465u** (knife-edge collapse)

**Why it's not real (the stress test that killed it):**
- The 2-leg +897u is **54% from one day (2026-05-17, +480u)** and **top-3 days = 103% of profit** — the other 26/29 days net negative. Only 12/29 days profitable; median day -1u.
- Round-robin parlays are **non-independent**: each single is reused across many parlays, so one lucky longshot inflates dozens at once. "3821 parlays" is really ~29 clustered days; effective sample is tiny.
- Parlaying **compounds an edge that isn't statistically established** (singles p=0.056). The 4-leg -28% is what compounding a near-zero edge actually yields.
- **Not executable on the primary book:** Kalshi is a single-outcome exchange with no parlays. B365 parlays compound B365's per-leg margin, eroding the Pinnacle-CLV edge — so the synthetic odds (1/ask) used in the backtest OVERSTATE real returns.

**Variants also tested 2026-06-06 (all fail):**
- **Days with >=10 signals only:** barely moved 2-leg (+25.8%) — the filter CONCENTRATES the dependence on big lucky days (05-17 still in set, was 54% of profit), doesn't fix it. 4/5/6-leg = -28%/-61%/-83% (monotonic collapse past 2 legs).
- **Same-HOUR clustering (round robin only if >= N signals fired in the same clock hour, more execution-realistic):** kills the apparent 2-leg edge — ROI swings +12.3% (thr>=3) / **-1.5% (thr>=5)** / +18.1% (thr>=8), i.e. flips sign with the threshold on ~4% hit rates (a few hits per cell = pure noise). 3-leg -34%..-44%, 4-leg ~-90% at every threshold. **Takeaway: the whole-day +23% was coincidence-harvesting (more games/day -> more combos -> two longshots happen to coincide); tightening the window removes the wide net and the edge evaporates.**

**How to apply:** Don't pursue round robins / parlays (per-day, >=10-games, OR same-hour variants all fail). The apparent 2-3 leg gain is in-sample variance from a handful of lucky multi-longshot days, layered on a marginal edge, on a product Kalshi can't trade. Consistent with the longshot-skew theme: high-variance combinations look great in backtests because a few jackpots dominate. Stick to flat singles. Backtest was inline (not saved as a script).

**xlow variants tested 2026-07-11 (user request; strict-xlow base n=283, poly_backfill):**
- **NO-other-team singles** (buy NO on opponent at the cheap book, = our-side+draw): +7.5% ROI, z+1.26, p=0.10, 90% CI [-0.3,+16.0]. Real but derivative — dilutes the +24.1% YES edge with the zero-edge draw component (project_draw_outcome_test) and pays the opponent-leg spread. Half the per-bet edge (+3.6pp vs +6.0pp). Don't wire; not additive (same fixtures/signal).
- **YES round robins**: 2-leg +33.9% (CI [+1.6,+79.3], 12/33 days positive, BELOW the ~+54% independence math -> same-day losses correlate); 3-leg +16.7% with maxDD 1.6x total profit and top day = 101% of profit. Not executable on Kalshi.
- **NO round robins**: 2-leg +6.8% (P>0 75%), 3-leg +2.7% (P>0 55%, maxDD 5.2x profit, top day 338% of profit). Pure noise.
- Verdict unchanged and extended: flat YES singles dominate every variant on ROI, significance, drawdown, and executability. The re-expressions being positive-but-worse is robustness evidence for the base signal, not new opportunities.