Ergodicity Wealth Growth Laboratory Ole Peters Model

"You've been computing expected return with a formula borrowed from statistical physics. It averages over a billion parallel copies of you that don't exist. You are one trajectory, played once, in sequence." — Ole Peters
📊 Parallel Multiverse vs Time Trajectory
Sequential Step Scrubber: 100 / 100 Step 100
⚙️ Strategy & Game Parameters
Wager Fraction (Kelly Leverage): 100%
*100% wager causes full trajectory decay (-5.27%). Adjust to optimal Kelly fraction (~25%) to achieve positive time growth (+1.02%).
Heads Win Multiplier (+50% = 1.5x): 1.50x
Tails Loss Multiplier (-40% = 0.60x): 0.60x
Simulation Steps (T): 100
Parallel Universes (N): 1000
Ensemble Expected Wealth
$131,501.26
Average across 1,000 parallel universes
Median Single Trajectory
$5.15
50th percentile individual traveler outcome
Time Growth Rate (gtime)
-5.27%
Single trajectory geometric growth per step
Ensemble Growth Rate (gens)
+5.00%
Theoretical expected value rate per step
Optimal Kelly Allocation
25.0%
Maximizes long-term geometric rate
[PROOF] Target: ergodic-wealth-growth-14 | Ensemble Expected Wealth: $131,501.26 | Median Wealth: $5.15 | Time Rate: -5.27% | Ensemble Rate: +4.88%

🧠 Why Standard Financial Expectation Fails You

In classical economic theory, decision makers evaluate coin tosses by calculating expected value across parallel states. When tossing a fair coin with a +50% win and a -40% loss, expected return is:

E[W] = 0.5 × (+50%) + 0.5 × (-40%) = +5% per step

However, as physicist Ole Peters demonstrated, wealth accumulation is non-ergodic. Because you play sequentially over time rather than simultaneously across 1,000 parallel copies of yourself, your wealth multiplies:

gtime = 0.5 × ln(1.5) + 0.5 × ln(0.6) = -0.05268 → -5.27% per step

While the average wealth across all parallel universes grows exponentially to over $131,500, almost every individual traveler's sequence decays exponentially toward bankruptcy ($5.15 after 100 steps). By scaling your bet fraction down to the Kelly Criterion fraction (25%), you align ensemble expectations with single-trajectory survival!

💾 Export complete Monte Carlo path telemetry (CSV or JSON)