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Break-even move at +4 on a 6 pip stop and 9 pip target: what a no-edge market does to it

Plan: stop 6 pips, target 9 pips. Variation: once price is 4 pips in profit, move the stop to the entry. Does the variation change the odds in a market that goes nowhere on average?

For a driftless random walk, the chance of reaching +9 before -6 is 6 / 15 = 40%. So the plain version wins 40% and loses 60%: expectancy 0.40 x 9 minus 0.60 x 6 = 0, before costs.

With the break-even move, work through the branches. The chance price gets to +4 before -6 is 6 / 10 = 60%. The other 40% are full losses of 6 pips. From +4, the chance of reaching +9 before returning to the entry is 4 / 9 = 44.4%. So 0.60 x 0.444 = 26.7% win 9 pips, and 0.60 x 0.556 = 33.3% are scratched at zero, and 40% lose 6. Expectancy is 0.267 x 9 minus 0.40 x 6 = 2.4 minus 2.4 = 0 again.

So in a market with no edge, the move doesn't change the average at all. It changes the shape: win rate falls from 40% to 27%, a third of trades become scratches, and the losers shrink from 60% to 40% of trades. If each trade also costs 1 pip, both versions lose 1 pip per trade on average, since the scratches still pay the spread.

So the move is not an edge by itself. It helps in a market that tends to fall back through the entry after reaching +4, and it hurts in one that shakes you out at the entry and then carries on to the target.

Real charts differ from the continuous model in one important way. Price moves in discrete ticks, and a wick can touch the entry price while the bar closes in profit. So scratches in practice are more frequent than 33%, since a trade that reaches +4, pulls back 4 pips, and then runs to +9 gets stopped out in the break-even version and would have been a 9 pip winner in the plain version. This is the cost people feel after moving a stop. It's less obvious that the same pullback, sometimes, is the one that continues down to -6, which the move saves.

To test the move on your own trades you need two numbers per trade: the furthest the price went in your favour (MFE) and what it did afterwards. Count trades in three groups. Those that reached +4 and then your target without touching the entry: these are the winners the move would have kept. Those that reached +4, came back to the entry, and later hit the target anyway: these are the ones it would have scratched. Those that reached +4 and then hit the stop: these are the ones it would have saved. The move earns its place only when 9 pips times the number of scratched winners is smaller than 6 pips times the number of saved losers.

In pips per 100 trades, the numbers work like this under the random walk: 100 plain trades produce 40 x 9 minus 60 x 6 = 0 pips. The break-even version produces 26.7 x 9 minus 40 x 6 = 0. Add a 0.8 pip cost per trade and both lose 80 pips in 100 trades. Nothing is lost by the move itself in this model, but nothing is gained either. If you're holding a stop at entry because it feels calmer, that's a fair reason, as long as you record it as a comfort choice and don't expect it to add to the results.

Where the break-even trigger sits matters. With a trigger of +2 instead of +4, the chance of reaching it is 6 / 8 = 75%, and from +2 the chance of reaching +9 before the entry is 2 / 9 = 22.2%, so 16.7% win, 58.3% scratched, 25% lose 6. Expectancy remains 0. With a trigger at +8, the chance of getting there is 6 / 14 = 42.9%, and then 8 / 9 = 88.9% go on to +9, so 38.1% win, 4.8% scratch, 57.1% lose. As the trigger moves out, the numbers move back toward the plain trade. Every trigger lands on the same zero, which tells you that the choice is about behaviour and not about edge.