Okay, so this started as a napkin thought. How do you rinse prop firms? And the honest answer is that it's a simple equation. Time to pass, probability of passing, cost of evals. That's it. Three variables. But when you actually sit down and formalize those three variables, a whole system falls out of it, and that system is worth walking through properly. So that's what this post is. THE FORMULA Per attempt, the expected value of an eval is simple arithmetic: EV per attempt = p x payout, minus cost p is your probability of passing. payout is what the funded account is actually worth to you, and note that this is not one payout, it's the expected cumulative payouts before you eventually breach the account. cost is the eval fee. But per attempt is the wrong lens. The number that actually matters is: EV per day = (p x payout, minus cost) divided by T where T is the time it takes to resolve an attempt. Pass or fail. And this one division changes everything about how you should think about evals, because your eval fee is small. Your time is the expensive input. The bottleneck on rinsing is not capital, it's throughput. WHY SPEED WINS Here's where almost everyone gets it wrong. The retail instinct is to maximize p. Highest win rate, safest pass, tiptoe to the target. Feels responsible, right? But a pass rate means nothing on its own. What matters is what that pass rate earns you per day it takes to get there. A 70 percent probability that takes 40 days loses to a 45 percent probability that takes 12. Run the division yourself, it's not close. The riskier setting wins even though it fails more often, because it resolves three times faster and lets you go again. Think of it like a card counter at a casino table. The counter doesn't optimize for winning every single hand, that's impossible anyway. The counter optimizes hourly rate. Hands per hour times edge per hand. The eval fee is your table buy-in, and EV per day is your hourly rate. Speed is not recklessness here. Speed is literally what the formula tells you to chase.

This is a long one. The a complete review with the citations and the appendix at the bottom so you can check everything yourself. Grab a coffee. 1. INTRODUCTION AND METHOD Okay, so this whole review exists to answer one question: which model of bitcoin actually survives contact with the 2025 to 2026 data? The period under review runs from the all time high on October 6, 2025, around 126,100, through August 2026 where we sit around 63,000. That is minus 49 percent, ten months into a bear market. And I want you to understand why this window is a gift for anyone who thinks in systems: it contains out of sample tests for basically every major claim from both the bull side and the bear side. The 2020 to 2024 period could not give us that, because it was one long adoption impulse in one direction. You cannot test a claim in a regime that only ever confirms it. This one tests everything. Before the analysis, the method, because the method is the whole point. I graded every source by quality tier and I weighted accordingly. Top tier: peer reviewed finance papers and primary legal documents. That means Griffin and Shams (2020, Journal of Finance), Lyons and Viswanath-Natraj (2023, Journal of International Money and Finance), Wei (2018, Economics Letters), Kristoufek (2021, Finance Research Letters), Liu and Tsyvinski (2021, Review of Financial Studies), Makarov and Schoar (2020 in the Journal of Financial Economics, and their 2021 NBER blockchain paper), Baur, Hong and Lee (2018). And the legal record: the CFTC order against Tether from October 2021, the New York Attorney General settlement from February 2021, Strategy's 8-K filing from July 6, 2026, the Federal Reserve statement from July 29, 2026, and the IMF Article IV review of El Salvador from July 2025. Second tier: institutional research. Fidelity Digital Assets, Galaxy Research, ARK, CF Benchmarks, and sell side notes from Citi and Standard Chartered. Third tier: on-chain analytics, Glassnode, CryptoQuant, Arkham. Important, this is probabilistic entity clustering, not audited holdings. Fourth tier: journalism. Bottom tier: the advocacy content, bear polemics like the King article and bull narrative work like stock to flow and hyperbitcoinization essays.

So I've been building out this dataset the past few days — long-run S&P (Shiller's data, goes back to 1871) and Nikkei 225, and stripping both down to the ugliest, most honest version I could make them. No dividends reinvested. Deflated for inflation. Just the raw price, doing what the raw price actually did. Here's why that matters. Every "stocks always go up" chart you've ever seen is wearing two coats of paint. Coat one: dividends reinvested, which most retail investors don't actually do with precision, and which flatters the buy-and-hold case by a lot over long horizons. Coat two: nominal terms, meaning it's not adjusted for the fact that a dollar in 1990 bought more than a dollar today. Strip both coats off, sand it back to bare wood, and you see what the asset actually did to your purchasing power, full stop. Then I ran a stupid-simple trend filter on top of the bare wood version — 200-day MA for Nikkei, Faber's classic 10-month SMA for the S&P. Same treatment both sides, right? No dividends for either line, same deflator for either line. Not comparing a flattered buy-and-hold against a bare-bones timing strategy, that would be cheating. The timed version won. Not by a little. Nikkei especially real, price-only, buy-and-hold spent DECADES underwater after 1990, and the 200-day version was compounding the whole time. The S&P version is less dramatic but the same shape, going back a hundred and fifty years. Now — before anyone screenshots this and goes "Rick says index funds are a scam," slow down, that's not what I'm saying, and here's the honesty part that actually matters more than the flex: Q: Does this hold up if you'd stopped the chart in a different year? A: Not perfectly. Look at Nikkei mid-2010s, buy-and-hold actually claws back a chunk of the gap during that bull run. A cumulative curve ending today is vulnerable to "well you just got lucky with the endpoint." I'd want rolling 10-year windows before I'd put real money conviction behind the headline number, not just one long path that happens to end well.

Below, is the PDF in attached files. Please consider joining this (free) skool as a member so that I can send you an email whenever I release something new. Suggest some new topics in the comments. If you want 1-on-1 guidance, don't hesitate to message me on here and/or consider joining my paid school, where I have full sample models, tutorials, AI-coding guides, etc. https://www.skool.com/quant-rick/about Anyway, enjoy the article. Feel free to comment, give me suggestions, and/or let me know what you would like to see next. Enjoy!

Paper and notebook in attachments.