Bet Sizing (Kelly)

What this page is / is not
· This page is a position-size calculator; it is not investment advice, not a gambling tip, and it does not pick opportunities for you. The doc says so in §7 (caveats) and §9 (boundaries): no investment or gambling recommendations; this algorithm does not apply to any stake involving illegal gambling, illegal fundraising or insider trading.
· The thresholds come from an internal methodology doc, 《经济盈利算法·12 下注规模算法 v1.0》 (domestic machine /opt/inventory/econ_algorithms/12-下注规模算法.md, 161 lines, finalised 2026-09-14, read-only), and have not been through any external empirical testing. The doc's §1 gives a citation for the Kelly criterion (Kelly 1956, Bell System Technical Journal, DOI 10.1002/j.1538-7305.1956.tb03809.x), but 2% / 10% / 25% / 5% / 15% / 3 losses in a row / the 1/4–1/2 Kelly reduction are practice lines the methodology set for itself; the doc itself labels “the half-Kelly / quarter-Kelly convention” as “a practice summary, an empirical rule”.

Evidence chain (the md doc has no line numbers, so these point to sections)
· EV = p × amount won − (1−p) × amount lost; EV ≤ 0 → do not bet at all → 12-下注规模算法.md §4 Step1
· b = net gain when you win ÷ net loss when you lose; f_full = (b×p − q) ÷ b; f = f_full × 0.25 ~ 0.5 → §4 Step2
· smallest of three, min(f, 5%, sleep-well ceiling) → §4 Step3; the five bands → §4 Step4
· 3 losses in a row / cumulative loss of 15% circuit-breaker → §4 Step5; the 4-column record sheet and “re-estimate p every 10 bets” → §4 Step6
· The six start conditions K1–K6 and their thresholds (basis accurate to ±15%, ≥ 10 bets available, ≤ 5% per bet, stop-loss advised after 3 losses in a row) → §3; the §6 hard rules, the preparation list and the first step → §5.2 / §5.3 / §6

Where it is not aligned / has been simplified (said plainly)
· Unconfirmed ① (mixed units): the doc's §4 Step3 puts a “ratio” (f, 5%) and an “amount” (the sleep-well ceiling) inside one min(). This page resolves it by multiplying the ratio by disposable funds to get an amount first, then taking the smaller against the sleep-well ceiling. That step is this page's implementation and the doc does not state it, so it is flagged unconfirmed.
· Unconfirmed ② (which band a boundary belongs to): the doc's band table writes “2%–10%” and “10%–25%”, so the 10% cell touches both. This page reads it as “f_full ≤ 10% goes to 🟢 standard, f_full ≤ 25% goes to 🔵 big edge”; the doc does not say which side a boundary falls on.
· Simplification ④ (floating-point tolerance): the 2% / 10% / 25% lines all carry a 1e-9 tolerance. Why: with p=0.55 and b=1, 0.55−0.45 comes out in binary as 0.1000000000000000055…, so writing fFull <= 0.10 directly would flip an input of “exactly 10%” into 🔵 big edge by mistake. The tolerance only makes inputs that sit exactly on a line land on that line; it does not change the 2%/10%/25% thresholds themselves. The EV ≤ 0 test carries the same tolerance.
· Simplification ①: the doc's §4 Step4 says the 10%–25% band should be split over 2–3 entries; this page only prints that sentence and does not break your position into 2–3 orders for you.
· Simplification ②: the 4-column record sheet in §4 Step6 (estimated p / outcome / P&L / review) is a paper discipline; this page keeps no records and stores no data and writes nothing persistent.
· Simplification ③ (input layer): the win rate accepts 0.55 and also accepts 55 (treated as 55%) —— the doc only writes p and never specifies the notation; this is this page's convenience handling, and the result says which one it used.
· Not done: the doc's §7 suggests “let an LLM turn a vague ‘I'm about 60% sure’ into a p with a basis” —— this page is pure front-end and calls no model.
· Not done: the chart plots the same formula over p = 5%–95% (with b set to your odds); that sampling is this page's own presentation and is not a field the doc outputs; the vertical axis is fixed at ±10, so parts beyond that (if your odds are small enough that f_full < −1) simply fall off the canvas.

[Evidence section · where to check each number]
① Source: internal methodology doc 《12-下注规模算法.md》v1.0 (domestic machine /opt/inventory/econ_algorithms/12-下注规模算法.md, 161 lines, read-only): the start conditions K1–K6 = §3; EV / Kelly / smallest-of-three / the five bands / circuit-breakers / record discipline = §4 Step1–Step6; preparation list and first step = §5.2 / §5.3; hard rules = §6. The literature citation appears only in §1 (Kelly 1956, Bell System Technical Journal, DOI 10.1002/j.1538-7305.1956.tb03809.x).
② Three categories
· [Verifiable] EV = p×赢 −(1−p)×输, b = 净收益 ÷ 净损失, f_full = (b×p−q)÷b, f = f_full×0.25~0.5, the smallest of three min(f, 资金 5%, 睡得好上限), the five band lines (≤0 / <2% / 2–10% / 10–25% / >25%), the circuit-breakers (3 losses in a row / 15% cumulative) —— every one of these matches §4 Step1–Step6 line by line.
· [This page's presentation choice] The p = 5%–95% curve is a page-side sampling (with your odds plugged in); the doc has no such chart, and clipping the axis at ±10 is this page's doing too.
· [No source found] The figures 2% / 10% / 25% / 5% / 15% / 3 losses in a row, and the “half-Kelly / quarter-Kelly” reduced-stake convention: the doc labels them itself, in §1 and in INDEX §4, as “practice thresholds / a practice summary, not theorems” → no external basis exists (they are internal practice lines).
③ How to check it yourself: p=0.55, win and loss both 1 → b=1, f_full = (1×0.55−0.45)÷1 = 0.10 → should land in 🟢 standard with a suggested range of f = 0.025~0.05; with disposable funds 10000 and a sleep-well ceiling of 600, the smallest of three gives an actual stake of min(250, 500, 600) = 250. Change p to 0.65 → f_full = 0.30 > 25% → should land in ⚠️ caution.