What 1,000 simulated lifetimes reveal that one projection hides

A retirement calculator that prints one number is not lying about arithmetic. It is lying about the object. The object is a life, and a life is a sequence. 1,000 simulated lifetimes are 1,000 sequences the model believes in. A single projection is the sequence the model would write if every year were the same year. Those are different sentences. This page is the picture of that difference on one frozen specimen.

The specimen is already retired, age 65, $1,000,000, 80/15/5, spending a rigid 4% of the starting pot, 30-year horizon, seed 20260622, 1,000 paired paths from the regime-switching engine. The treatment is not a policy. The treatment is the reporting device: a constant 7% path versus the percentile cone of the same cashflows. Worlds are identical except for the return draws. That is the control.

What 1,000 simulated lifetimes reveal

They reveal a band. At year 10 the real p10 on this freeze is $420,744 and the p90 is $2,305,367. The median is $1,005,962, still near the starting million. A person who was handed only the median would not know that the lower tenth of lives had already lost more than half the real pot, and would not know that the upper tenth had more than doubled it. 1,000 simulated lifetimes put those three facts on one chart. One projection puts none of them.

They also reveal a ruin mass. 10.4% of the 1,000 paths hit zero before year 30. That is not a rounding error. It is 104 lives in this sample. A single 7% path cannot print those 104 lives because it never visits a clustered crash. It compounds. Compounding is what a spreadsheet is for. Sequence is what a lifetime is for.

The title asks what 1,000 simulated lifetimes reveal that one projection hides. On this freeze the honest list is short: a left tail that reaches $0 at year 30, a right tail at $5,692,838, a median at $1,083,603, and a success rate of 89.6% that the projection never states because the projection cannot fail.

The projection is not the median

People sometimes defend the 7% line by saying it is "about the average." On this freeze it is not about the median. The dashed path ends at $1,727,805. The simulated p50 ends at $1,083,603. The p75 ends at $2,672,674. The advertised 7% path, once deflated by the engine's median inflation factor, sits above the simulated median of $1,083,603 and below p75 of $2,672,674. That is not a small miss. It is a different story about whether the million lasted.

Why? Because 7% every year is not the mean of a fat-tailed, regime-switching process with spending. Spending turns a return distribution into a hitting-time problem. A year of −30% with a 4% withdrawal is not cancelled by a later year of +30%. The projection never has the −30% year. The 1,000 lives do, in the share the generator assigns to crisis and recession. The gap between $1,727,805 and $1,083,603 is that mechanism, not a plotting choice.

Read the chart from year 0 to year 30. The median line barely climbs. Real wealth after inflation and a $40,000 starting withdrawal is not a rocket. The dashed 7% line is a rocket. If you only saw the rocket you would think a 4% rule on a million was a wealth-building program. The 1,000 lives say it is, for this specimen, a program that usually keeps the lights on and sometimes does not.

What a single "you will have $X" hides

It hides the width. Two households can share a median and not share a night's sleep. The p10/p90 gap at year 30 on this freeze is $5,692,838 minus $0. That width is the plan. The point is a summary of the plan. Summaries are allowed. They are not allowed to pose as the plan.

It hides the mechanism of ruin. Zero on the p10 line at year 30 means at least a tenth of worlds have already failed, and the plotted p10 is then pinned at the floor. A projection that stays positive has no place to put that floor. Users of deterministic tools often read a positive ending as "it worked." On this engine, 89.6% of worlds work under that same rule. The other 10.4% do not. Both facts are true of the same household. Only one of them is true of the 7% path.

It hides sampling error too, unless you print it. 1,000 paths give a success-rate standard error of about 1.1 percentage points on an 85% rate. This freeze printed 89.6%. That is precise enough to see that the plan is not a coin flip and not a certainty. It is not precise enough to rank two policies that differ by half a point. The sample-size piece is the other half of that sentence.

Experimental control, and what this page is not

The domain is a teaching identity. No policy is ranked. The roster is a rigid 4% guardrail (band 0, adjust 0) plus a buy-and-hold anchor. Information set: the agent sees the observation before this step's return. It does not see the latent regime. The deterministic path uses the advertised 7% from the specimen card, not the realized mean of the 1,000 lives. Using the realized mean would have been look-ahead dressed as fairness.

Q1 is the 1,000 orderings. Q2 is not run: we did not shave the equity premium on this cone. Q3 is not run: this is not a historical claim. Q4 is not a 0-versus-5-bps stress. The vector engine used 5 bps. Tax is off. Nominal engine, real fan for the chart. If a lower equity premium pulled the median onto the 7% line, or if 1966 on the tape sat next to the dashed path, this picture would move. We did not run those tests here. The takeaway is scoped to this generator and this specimen.

A later page in this batch asks why deterministic retirement calculators quietly mislead you. This page is the cone those calculators flatten. The two articles share the freeze. They do not share a ranking.

A cone of outcomes is the honest picture of 1,000 lives

Call the chart a cone of outcomes if that helps. The upper edge is not a promise and the lower edge is not a curse assigned to you at birth. They are percentiles across lives. At year 5 the real p10 is $580,547 and the p90 is $1,639,125. At year 15 they are $276,442 and $2,913,701. The band opens as time passes because sequence has more room to work. A single projection cannot open. It has only one weather.

The product default of 1,000 paths is the same integer as this freeze. That is deliberate. A research table that needs to rank close policies uses 5,000. This page is not ranking close policies. It is showing that a point and a range are different objects. 1,000 is enough for that. The standard error on 89.6% is about a point. It is not enough to pretend the 7% ending of $1,727,805 is a rounding error away from the median of $1,083,603.

Readers who want a more careful walkthrough of p10, p50 and p90 should read the cone article in this batch. This page is the comparison to the projection. That page is the legend. They share the CSV. They do not share a heading, so search can tell them apart.

See a range instead of a point

The matching tool is the Monte Carlo retirement calculator, which prints a success rate and a band on a household you type, not a single ending. The no-signup demo runs the same seeded engine the product uses. If the band is wide, that is the finding. If you only wanted $X, you already had a spreadsheet.

Replication, in sentences instead of a table

Anyone can replay this page from the CSV. Start with $1,000,000. Retire immediately. Hold 80% stocks, 15% bonds, 5% cash. Spend $40,000 a year with no guardrail band and no annual raise or cut. Run the regime-switching generator from seed 20260622 for 1,000 paired episodes of 360 months. Deflate the fan to today's dollars. Read p10, p50 and p90 at each year. Separately, compound 7% a year on the same spend with no noise. If the 7% ending is not $1,727,805 and the median is not $1,083,603, the freeze moved and this article is stale. Do not type a kinder median into the prose to match a screenshot.

The buy-and-hold anchor is in the roster because the engine injects it. It is not the reporting device. The reporting device is rigid 4% versus the 7% identity. Costs are 5 bps on the vector path. Tax is off. Inflation is in the engine; the chart is real. If you rebuild in nominal dollars the cone will sit higher and the 7% path will look closer to the median, which would be a display trick, not a better experiment.

Year 0 on every series is $1,000,000 by construction. Year 2 p10 is $736,943; year 2 p50 is $1,003,692; year 2 deterministic is $1,009,039. The split starts immediately. That is the last thing a 30-year sheet hides: the lie is not only at the horizon.

Notes on the figures. Household B4_RETIREE: age 65, already retired, $1,000,000, 80/15/5, rigid 4% of start ($40,000/year), 30-year horizon, income $0. Seed 20260622. 1,000 paths. Generator: regime_switching, default calibration. Pairing: shared EnvStep[] (Mode A). tradingCostBps 5 (vector default). Tax off. Real fan (today's dollars) for p10/p50/p90. Deterministic comparator: 7% annual, same spend, no path noise, then divided by the engine's median cumulative inflation factor (inflationFactorBands.p50) so both series are real. Primary metric: year-30 real percentiles versus the real 7% terminal. Q1 run. Q2 not run (inside this calibration). Q3 not run (not a historical claim). Q4 not run as a 0-versus-5 stress. CSV: /data/studies/1000-simulated-lifetimes.csv. Study card dated 2026-08-28, before the runner. This article is educational analysis, not investment advice, and does not recommend any security or strategy.