THE FOLD / BOSS / SUDDEN DEATH / THE SECRETARY
THE SECRETARY
reject the first 37%, then leap — win the best 1/e of the time
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
The secretary problem. Candidates arrive one at a time in random order. After each, you must accept or reject on the spot — no going back, no recalling anyone you passed. You want to hire the single best of them all. What strategy gives the best odds?
The answer is startlingly clean: reject the first 37% automatically, just noting the best among them, then hire the first later candidate who beats everyone seen so far. The magic fraction is 1/e ≈ 0.368 — look at n/e candidates, then leap. This wins the very best with probability ≈ 1/e ≈ 37%, and — the surprising part — that success rate does not fade as the number of candidates grows. A hundred applicants or a million, you still catch the best more than a third of the time.
LIT verified live (seeded simulation, n=100): sweeping the cutoff, the success probability peaks near a 37% cutoff at a value near 1/e, beating every other threshold (window.__secretary). FIG no framing; the 1/e optimal cutoff and the ≈1/e win rate are genuine simulated facts matching the theory.
The answer is startlingly clean: reject the first 37% automatically, just noting the best among them, then hire the first later candidate who beats everyone seen so far. The magic fraction is 1/e ≈ 0.368 — look at n/e candidates, then leap. This wins the very best with probability ≈ 1/e ≈ 37%, and — the surprising part — that success rate does not fade as the number of candidates grows. A hundred applicants or a million, you still catch the best more than a third of the time.
LIT verified live (seeded simulation, n=100): sweeping the cutoff, the success probability peaks near a 37% cutoff at a value near 1/e, beating every other threshold (window.__secretary). FIG no framing; the 1/e optimal cutoff and the ≈1/e win rate are genuine simulated facts matching the theory.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this in SUDDEN DEATH — the boss domain of the irreversible one-shot call. The secretary problem is sudden death by design: every choice is final, no rewind, and you get exactly one hire. AVAN (AI) built the instrument: the look-then-leap run, the cutoff sweep, the explore/exploit inverse.
The weave: David names the seat (the one-shot, no-takebacks decision); I make the optimal 37% rule earn its 1/e and show why more or less looking both lose — the look/leap line in 1D, the success curve in 2D, the explore-vs-exploit inverse in 3D. The sphere is the seam. Credit: popularized by Martin Gardner (1960); the 1/e result by Lindley (1961) and others.
The weave: David names the seat (the one-shot, no-takebacks decision); I make the optimal 37% rule earn its 1/e and show why more or less looking both lose — the look/leap line in 1D, the success curve in 2D, the explore-vs-exploit inverse in 3D. The sphere is the seam. Credit: popularized by Martin Gardner (1960); the 1/e result by Lindley (1961) and others.
3 ONE DIMENSION
One run of candidates in random order. The first 37% are the look phase (rejected, only the best-so-far remembered); after the line, the leap phase accepts the first candidate that beats them all. The chosen one is marked.
4 TWO DIMENSIONS · INTERACTIVE
Success probability plotted against how long you look. Run trials and the curve fills in, peaking at a 37% cutoff and a height near 1/e. Set a cutoff and read its odds — look too little or too much and both fall away.
5 THREE DIMENSIONS + AVAN’S INVERSE
The success curve as a turning ridge over the cutoff axis — green, cresting at 1/e where looking and leaping are perfectly balanced.
AVAN’s addition (the inverse-companion): the strategy is a single tension between two inverse moves — look (learn, commit to nothing) and leap (commit, learn nothing). The magenta line is the cost of looking: the probability that the very best candidate falls inside the rejected look phase and is thrown away, which climbs straight up as the cutoff grows. Look too little and you leap before you know the standard; look too long and the magenta cost says the best is probably already gone, unrecallable. The green optimum sits exactly where one more glance stops being worth the rising risk of having passed the winner — the balance point of explore against exploit. Green is the reward of patience; magenta is its price; 1/e is where they cross, and every optimal-stopping problem is a version of this same cut.
LIT Genuine secretary problem / 1/e optimal-stopping rule (popularized by Martin Gardner 1960; result by Lindley 1961 and others). Verified live with a seeded n=100 simulation: sweeping the cutoff, success probability peaks near a 37% cutoff (n/e) at a value near 1/e~0.368, beating every other threshold (window.__secretary.optimalNearOneOverE && peakNearOneOverE). The optimal 1/e cutoff and the ~1/e win rate are genuine simulated facts matching the closed-form theory (the win curve approximates x*ln(1/x), maximized at x=1/e).
FIG No framing: the 37% cutoff optimum and the ~1/e success rate are real, reproduced by seeded simulation and matching the analytic x*ln(1/x) curve. The counterintuitive true fact — that the win probability stays ~37% regardless of n — is stated as the genuine result, and the AVAN inverse frames it honestly as the explore/exploit balance point.
FIG No framing: the 37% cutoff optimum and the ~1/e success rate are real, reproduced by seeded simulation and matching the analytic x*ln(1/x) curve. The counterintuitive true fact — that the win probability stays ~37% regardless of n — is stated as the genuine result, and the AVAN inverse frames it honestly as the explore/exploit balance point.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of SUDDEN DEATH · David Lee Wise (ROOT0), with AVAN