---
name: xlow sizing — flat beats 0.25-Kelly on the 286-bet stream
description: Simulated flat vs 0.25-Kelly on the exact rerouted-to-Kalshi xlow backtest stream. Flat $10 ends +$619 vs Kelly's +$141 off $1k. Kelly refuses 88/286 still-profitable bets and under-stakes longshots. Bet flat ~1% units.
type: project
---

Tested 2026-07-16 via `E:\soccer\research\xlow_sizing_compare.py` on the same 286-bet
strict-xlow, rerouted-to-Kalshi stream from `kalshi_only_execution.py` (fees included,
p_win = pin_fair, price = Kalshi ask — identical to live `_kelly_stake` inputs):

| Scheme | End ($1k start) | MaxDD |
|---|---|---|
| Flat $10/bet (1%) | $1,619 | 10.3% |
| Flat $20/bet (2%) | $2,239 | 19.6% |
| Flat 1% of current bank | $1,752 | 11.3% |
| 0.25-Kelly compounding (live paper scheme) | $1,141 | 4.8% |
| 0.25-Kelly fixed $1k notional, $5 cap (auto-trade scheme) | $1,159 | 3.4% |

**Two structural reasons Kelly loses (not luck):**
1. **Kelly refuses 88/286 bets (31%)** — f<=0 where Kalshi's ask >= pin_fair, mostly the
   rerouted Poly-cheap legs. Those 88 bets still made **+6.5% ROI flat**. The xlow shape is
   the signal; Kelly's per-bet ask-vs-fair check discards validated bets. (Kelly-approved
   subset: n=198, +28.4% ROI — Kelly picks good bets, it just barely stakes them.)
2. **Kelly under-stakes longshots** — median stake $2.70 off $1k notional (consistent with
   the "[[strategy-improvement-probes]] Kelly under-bets longshots" finding). Even doubling
   Kelly to match flat's drawdown lands well short of flat's profit.

**Why:** The forward-test validation metric is flat-ROI (+17.8% fee-adj net, z+2.41); the
Kelly machinery is a leftover from the baseline strategy. On xlow it both shrinks and
censors participation, so paper/real results diverge from the validated benchmark.

**How to apply:** Size xlow bets FLAT at **1% of the day-start tracker** (user decision
2026-07-17, implemented in live_monitor `XLOW_STAKE_PCT` — the tracker only moves at the
00:05 nightly resolve, so alert-time reads ARE day-start; equal stakes within a day,
compounding across days). Do NOT skip
bets because Kelly f<=0 at the Kalshi ask — that check contradicts the validated rule. Same
in-sample caveats as [[project_kalshi_only_execution]]: magnitudes optimistic, but the flat
vs Kelly ordering is structural. This REVERSES the default assumption that Kelly sizing is
conservative-but-helpful here: its "safety" is mostly non-participation.

**FORWARD RE-TEST 2026-09-23** (646 primary-scope forward bets, same fee convention,
p = Pinnacle fair, $1k start):

| Scheme | End | MaxDD | Bets | Median stake |
|---|---|---|---|---|
| Flat 1% of bank | $1,799 | 48% | 646 | 1.00% |
| Full Kelly | $1,929 | 49% | 611 | 1.26% |
| 0.5 Kelly | $1,476 | 27% | 611 | 0.63% |
| 0.25 Kelly | $1,234 | 14% | 611 | 0.31% |

The backtest's "Kelly refuses 31%" did NOT reproduce forward: only 35 refused (5%) --
but those 35 returned +44.1% flat, so the direction holds (Kelly still discards good
xlow bets). The real finding: **flat 1% is ~full Kelly** on this edge, and fractional
Kelly is ~equivalent to a smaller flat stake, because xlow's edge sits in a narrow
5-12% band so Kelly mostly varies stake by price. The live question is stake LEVEL,
not formula: 1% (~full Kelly, 48% maxDD on an edge still at z~1.9) vs 0.3-0.5%
(~0.25-0.5 Kelly). With an estimated, not proven, edge the fractional end is standard.