The Art of War for Trading — Chapter 1: Initial Estimations & Probabilistic Edge

"The art of war is of vital importance to the State. It is a matter of life and death, a road either to safety or to ruin." — Sun Tzu

Strategic & Financial Context

The first chapter of The Art of War, Initial Estimations, focuses on "temple calculations": analyzing every strategic variable prior to engaging the enemy.

In markets, failure stems from opening trades impulsively and hoping for profit. Professional traders operate like seasoned commanders, establishing a statistical edge before committing capital.

How this chapter differs from Chapter 1 of our Sun Tzu and the US Stock Market series: that one reads the temple calculation as strategic judgment — how the Five Factors decide whether to engage at all. This one covers the arithmetic itself: how expectancy is computed, how large a sample must be before it means anything, and why most expectancy figures traders quote are fictional. Sun Tzu said "many calculations bring victory." He did not say how to calculate.

Wall Street Application

1. The Five Trading Factors

• The Moral Law (Philosophy Alignment): Is your trading system tailored to your risk tolerance?
• Heaven (Macro Regimes): Are central banks easing or tightening? Market trend dictates 80% of individual stock moves.
• Earth (Market Geometry): Are prices sitting on major support? Is the risk-to-reward ratio better than 1:3?
• The Commander (Execution Discipline): Can you cut losses without emotional hesitation?
• Method & Discipline (Capital Rules): Are position sizing and max drawdown limits strictly enforced?

2. Probabilistic Calculations (Expected Value)

3. The Actual Arithmetic

Expectancy = (Win% × Average Win) − (Loss% × Average Loss)

A system winning 40% of the time, averaging 3R wins against 1R losses (R = the capital risked per trade):

EV = 0.4 × 3R − 0.6 × 1R = +0.6R per trade

Six of every ten trades lose money. A 40% hit rate feels terrible — and most retail traders abandon a system like this around the eighth trade.

Invert it. A system that wins 90% of the time, averaging 0.5R wins against 5R losses (the signature of never cutting a loser):

EV = 0.9 × 0.5R − 0.1 × 5R = −0.05R per trade

Nine trades in ten are profitable and the account still goes to zero. This is precisely why Sun Tzu opens with calculation: without it, you see the 90% and miss the minus sign.

4. Three Ways the Number Lies

Costs are missing. The formula above contains no commission, spread, or slippage. A system with +0.1R expectancy whose round-trip friction costs 0.15R is a losing system. Subtract friction from the average win before you believe the result — the subject of Chapter 2.

The sample is too small. Twenty trades tell you nothing. A system whose true win rate is 40% will produce twelve winners in twenty (60%) purely by chance often enough that you cannot distinguish it from skill. Stabilizing a win-rate estimate to within ±5% takes hundreds of trades.

Average loss is the one term you control, and most people don't. The formula assumes every loss exits at the predetermined stop. Move the stop once — "this time is different" — and that trade loses 5R. A single 5R loss erases eight +0.6R winners. Systems are rarely destroyed by the market; they are destroyed at the point of execution.

Execution Rules

1. No calculation, no position: never open a trade before the stop and target are defined.
2. Demand asymmetry: trade only structures offering better than 1:3 reward-to-risk.
3. Stay systematic: apply the five-factor screen every time; never trade on feel.
4. Keep records in R, not dollars: dollar figures shift with account size; R is comparable across time.
5. Put costs inside the expectancy: deduct round-trip friction from the average win; it must still be positive.
6. Don't judge a system before 100 trades: and don't abandon it after five losses — at a 40% win rate, five consecutive losses occur roughly every thirteen cycles.

Relevance to a Retirement Portfolio

The goal of retirement investing is not to beat the market but to preserve principal and secure cash flow. Initial Estimations insists that you calculate maximum drawdown under the most extreme conditions — a 2008-style liquidity crisis — before allocating.

The limits of expectancy thinking matter here. This arithmetic applies to tactical satellite positions. It does not apply to the core of a retirement portfolio, and the reason is sample size: a system needs hundreds of trades to confirm positive expectancy, while your retirement capital gets one run. You will not live long enough for the law of large numbers to average out your luck.

The long-run positive expectancy of a low-cost broad index comes from a structural source — corporate earnings growth — and requires you to get no individual trade right. Tactical expectancy requires you to calculate correctly and execute without deviation hundreds of times. The first is the foundation; the second is, at most, a thin layer above it. Become unbeatable first; discuss expectancy second.