InkLedger is the tool for analyzing win rates and managing position sizes — explainable math for two questions: when to act, and how much to commit.
Act I · The math of choosing
Picture the stock market as a cornfield: 25 ears of corn appear one by one, and you have just one pair of hands. At each one you must decide on the spot — pick it, or walk on, and there is no walking back. The market never lacks opportunities; but the same pair of hands can come home with very different harvests.
01
A bigger one is surely still ahead — so you walk to the end of the field. That is betting the biggest ear happens to grow last: a 1-in-25 chance, 4%. Walking on is not converging on the biggest; it is burning irreversible options.
02
You pick the first decent ear you see. But "decent" only means "biggest so far" — when the truly big one appears later, your hands are already full.
03
Walk the first 37% of the field without picking, and let the biggest ear you see set your benchmark. Then pick the first one that beats it. The math proves this maximizes your odds under these rules.
04
Sum the probability of every winning scenario and take the limit: you get P(x) = −x·ln x, which peaks at x = 1/e ≈ 36.8%. Not half. Not a hunch. 1/e.
Intuition says walking a little further never hurts. The math says otherwise: choosing has a cost, and so does missing out. A mature pick comes after seeing enough — and then having the discipline to stop comparing.
In decision theory this cornfield has a formal name: the secretary problem (optimal stopping). Let N ears arrive in random order, with the first r observed only. If the overall biggest sits at position k (k > r), you pick it only if the biggest of the first k−1 falls inside the observation window — probability r/(k−1).
Summing over positions: P(r) = Σₖ (1/N)·(r/(k−1)), for k from r+1 to N.
Let x = r/N. For large N the sum becomes an integral: P(x) = −x·ln x.
Set the derivative to zero: −ln x − 1 = 0, so x = 1/e ≈ 36.8%, and the success probability is also 1/e ≈ 37% — the global maximum.
The strategy cannot guarantee the biggest ear. But under "decide on sight, no walking back", it pushes your odds to the theoretical ceiling.
Two questions
The 37% rule answers "when to act". But after acting comes a second question — how much to commit? That one has a mathematical answer too: the Kelly criterion. And Kelly is, at its heart, position management.
Act II · The math of sizing
A special coin: 60% heads to start, 1:1 payout, and you always bet heads. But beware — halfway through, the coin gets swapped and the win rate changes. When your edge moves, should your bet size move with it? Starting bankroll $1,000; you choose how many flips.
Each round you stake a fraction f of your bankroll: a win multiplies it by (1 + f·b), a loss by (1 − f).
Long-run compound growth equals expected log wealth: g(f) = p·ln(1 + f·b) + q·ln(1 − f).
Set the derivative to zero: p·b/(1 + f·b) − q/(1 − f) = 0, which solves to f* = (p·b − q)/b = p − q/b.
Here p = 0.6 and b = 1, so f* = 20%. Whenever f* ≤ 0, the optimal move is not to bet.
Kelly maximizes the long-run geometric growth rate, not single-round expectation — that is what separates it from all-in, and what makes it a long-termist tool.
A simulation with virtual chips. Not investment advice.
Act III · From the game to real investing
In real investing they hide inside filings, valuations and the structure of your portfolio. Surfacing the odds and managing the positions — that is exactly what InkLedger does.
Turns 10-Ks and 10-Qs into plain language — business quality, financial quality, shifting risks — to help you estimate how certain a company really is.
Upload a holdings screenshot to see concentration, sector exposure and ETF overlap — the risks you are carrying without noticing.
Translates certainty into an explainable position reference: is a single name too heavy, does your exposure match your conviction.
Every conclusion shows its reasoning. No mystery scores.
Top-3 holdings weight
62%
Sector concentration
High · Tech 58%
Single-name Kelly range
8% – 14%
Reasoning
Every line traceable
Rendered from anonymized sample data. Your report reflects your own holdings.
Holding for the long term takes more than picking the right company — it takes the position discipline that lets compounding happen. Kelly and long-termism are two faces of the same idea.
The math of time
FV = C × ((1 + r)ⁿ − 1) / r
C is the monthly contribution, r the monthly rate (annual assumption ÷ 12), n the number of months.
What Kelly maximizes is exactly the exponent of this curve — the long-run growth rate. Bet too big and it drags toward zero; bet too small and it stays pinned to the floor. The whole point of Kelly and position management is lifting that slope back to where it could be. The money "left on the table" above is the price of a two-point-lower slope — after time has amplified it.
A compounding-math demo. The growth rate is your own assumption — not a forecast, not investment advice.
Your holdings data is used only to generate your own reports, and can be exported or deleted at any time.
All analysis is reference information, not investment advice.
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