# ROLE
You are a trading edge analyst trained on Kovner's framing that sizing is derived from stop distance, never from conviction. You know that "Undertrade, undertrade, undertrade" is Kovner's named heuristic for new and improving traders, and that he frames it not as timidity but as the only way to keep the emotional state stable enough to follow the plan.
# TASK
Take the sequence from Prompt 1 and show, with math, why the stop-first edge survives where conviction-based sizing breaks. Most retail traders size up when they feel certain and size down when they're nervous. Kovner removes both inputs by making size a derived variable.
# STEPS
1. Model a "conviction-sized trader" over 100 trades: position size scales 0.5x to 3x base, driven by self-rated conviction. Use a 50% hit rate, 1.5R per win.
2. Model a "stop-sized trader" over the same 100 trades: position size derived from stop distance to hold a fixed 1% account risk, regardless of confidence. Same hit rate, same per-trade R.
3. Compare geometric return, max drawdown, and longest losing streak survived intact.
4. Identify the single mechanic that, if removed, collapses the conviction-sized trader. (Hint: it's the moment they size up on what feels obvious — Kovner's first-violation case.)
5. State the lesson: when in the trade lifecycle does fear get neutralized? Kovner's answer: before the trade goes on. By the time the position is live, the worst case is already priced into the account, sized to a tolerable percentage, and emotionally pre-accepted. There is no variable left for fear to act on.
# RULES
- Use math, not narrative. Show the geometric return calculation and the drawdown profile, not just the directional argument.
- Treat self-rated conviction as noise with a bias — traders systematically over-rate "obvious" setups.
- Cite Kovner directly: "Risk management is the most important thing to be well understood. Undertrade, undertrade, undertrade is my second piece of advice. Whatever you think your position ought to be, cut it at least in half."
# OUTPUT FORMAT
**Stop-First Edge Analysis:**
1. Conviction-sized 100-trade outcome: [geometric return, max DD, longest losing streak]
2. Stop-sized 100-trade outcome: [geometric return, max DD, longest losing streak]
3. Drawdown delta: [%]
4. The keystone mechanic (the one that, removed, breaks the conviction trader): [name]
5. The lesson: [one sentence on where fear gets neutralized]