The Hundred-Trades Mental Model

When one-trade algebra feels slippery, imagine buying one share in each of 100 genuinely comparable markets. Total cost, winning payouts, and net PnL become visible.

Cost and payout #

If each share costs $p$ and exactly $K$ of 100 resolve YES,

$$Cost=100p, \qquad Payout=K, \qquad PnL=K-100p.$$

If the true win probability is $q$, expected wins are $100q$ and expected PnL is $100(q-p)$.

Running 65% example #

At $q=0.65$ and $p=0.60$, expected cost is 60, payout is 65, and profit is 5. At $p=0.70$, the same 65 expected wins cost 70 and lose 5. At $p=0.90$, winning a 65% majority still loses 25.

Majority wins can lose money #

Suppose 80 of 100 contracts bought at 0.90 win:

$$PnL=80-90=-10.$$

Accuracy is 80%, yet the strategy loses because each loss costs 0.90 while each win earns only 0.10.

Life example #

A shop can profit on nine cheap items and lose everything on one heavily discounted high-cost return. Counting successful transactions without weighting their money amounts hides the business result.

Application to no-hedge #

Build the 100-trade table from filled no-hedge orders, using each actual execution price and cost. Do not multiply one advertised spread by 100; fills are selected, prices vary, and correlated markets do not supply 100 independent trials.