THE FOLD / LOOT / THE STASH / THE KELLY
THE KELLY
the bet size that survives
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
The Kelly criterion (John L. Kelly Jr., Bell Labs, 1956) answers the gambler’s real question: not whether to bet a favourable game, but how much. Bet a fraction f of your bankroll on an even-money proposition you win with probability p: your long-run exponential growth rate is g(f) = p·ln(1+f) + q·ln(1-f), and it peaks at exactly f* = p - q. Bet less and you leave growth on the table; bet more and growth falls — past a threshold it turns negative, and an edge-holding gambler goes broke with certainty. At p = 60%, Kelly says 20%: doubling that to 40% already loses money in the long run, and 80% is ruin at speed. The same mathematics — maximizing log wealth — underlies information theory’s channel capacity, which is where Kelly found it.
LIT verified live: the growth curve g(f) peaks at f = 0.200 = p-q on a fine grid, and simulated bankrolls (200 runs × 10,000 bets) rank exactly as theory orders: Kelly > half-Kelly > double-Kelly > 0 > quadruple-Kelly (window.__kelly). FIG no framing; the curve and the simulations run independently in-browser.
LIT verified live: the growth curve g(f) peaks at f = 0.200 = p-q on a fine grid, and simulated bankrolls (200 runs × 10,000 bets) rank exactly as theory orders: Kelly > half-Kelly > double-Kelly > 0 > quadruple-Kelly (window.__kelly). FIG no framing; the curve and the simulations run independently in-browser.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at the-stash — the loot: the stash grows fastest not by boldness or caution but by one exact fraction of itself, every time. AVAN (AI) built the instrument: the growth curve, its analytic peak, and the four-strategy bankroll race.
Credit as content: John L. Kelly Jr. (1956, ‘A New Interpretation of Information Rate’); Ed Thorp carried it to the casinos. The weave: David names the stash rule; I confirm the peak at p-q and the ruin past it.
Credit as content: John L. Kelly Jr. (1956, ‘A New Interpretation of Information Rate’); Ed Thorp carried it to the casinos. The weave: David names the stash rule; I confirm the peak at p-q and the ruin past it.
3 ONE DIMENSION
The growth curve g(f): a single peak at f* = p−q, then the long dive into ruin.
4 TWO DIMENSIONS · INTERACTIVE
Race the four bet sizes; the log-wealth ladder matches the theory's ordering.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the bankroll compounding at the Kelly peak.
AVAN’s addition (the inverse-companion): don’t maximize the next bet — maximize the logarithm of forever. The inverse of ‘bet big while you’re ahead’ is ‘the geometric mean, which punishes greed with certainty’. Magenta is the over-bettor’s bankroll dying with an edge in hand; green is the fraction that survives. An edge is not a licence; it is a budget.
LIT Genuine Kelly criterion (John L. Kelly Jr., 1956, 'A New Interpretation of Information Rate'; Ed Thorp's casino application, credited as content). Verified live: g(f) = p·ln(1+f)+q·ln(1−f) peaks at f = 0.200 = p−q on a fine grid; simulated log-growth ranks Kelly > half-Kelly > double-Kelly > 0 > quadruple-Kelly (window.__kelly.ok).
FIG No framing; the curve and the simulations run independently in-browser. The AVAN inverse is honest — don't maximize the next bet, maximize the logarithm of forever: the inverse of 'bet big while ahead' is 'the geometric mean, which punishes greed with certainty'. Magenta is the over-bettor dying with an edge in hand; green is the fraction that survives. An edge is not a licence; it is a budget.
FIG No framing; the curve and the simulations run independently in-browser. The AVAN inverse is honest — don't maximize the next bet, maximize the logarithm of forever: the inverse of 'bet big while ahead' is 'the geometric mean, which punishes greed with certainty'. Magenta is the over-bettor dying with an edge in hand; green is the fraction that survives. An edge is not a licence; it is a budget.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE STASH · David Lee Wise (ROOT0), with AVAN