# Rationale: the alternatives considered and rejected

Tags are the same as in decision.md:
- **[P]** paper;
- **[BM]** broker_map.json;
- **[NB23]** notebook section 23;
- **[R]** rules.json;
- **[V]** vault;
- **[C]** exact chains computed by me from `modules/prime.py`, γ = 2.87%, target clipped, stop at the floor;
- **[W]** `prime.wallet_mc`, $1,000 on the $3,000 tier, 500 trades, 6,000 paths, seed 5;
- **[A]** arithmetic.

## How I read the operator

The operator gave five wishes:
- "Not a lot of drawdown."
- "A high payout rate per account."
- "Not flagged for gambling."
- "Wallet $1,000 max."
- "I need money."

The first four point one way: a low funded risk, a record with more trades per pass, and no reliance on readings of the rules that might not hold. The fifth points the other way, toward speed and larger tiers.

The evidence says the fifth cannot be met by this play on a $1,000 wallet. Even with every payout honoured:
- one account slot earns about +$134 a year [A on C];
- a single $3,000 account's median wallet goes from $1,000 to about $1,269 over about 1,000 days [W].

So I weighted the first four. I treat the play as a small positive bet that answers the one question only the firm can: does it pay? I say this plainly in decision.md rather than dress up a growth figure.

## Assessment risk

**4% at RR 1, the current cell ([NB23] verdict, the map's "today"). Rejected, for now.** It passes 46.24% against 45.38% at 3%, and in 12 days against 21 [C, BM]. It grows the wallet +0.203 against +0.167 [W]. That is the whole case for it, and it is real.

Against it are two rule readings the grounding leaves open.

- **The 35% distribution cap in the assessment.** Its application there is on rules.json's unverified list. One full win at 4% is 3.89% of the bankroll, above 0.35 × 9% = 3.15% [A]. So under that reading essentially every 4% pass contains a non-compliant day.
- **The daily loss rule.** It is "5% of the previous day's equity" and "equity based, so unrealised counts" [R]. The paper's Proposition 18 checks one trade's loss from entry. But a trade held across the firm's day boundary while in profit resets the reference upward. At 4% the room left is only 0.11–0.23 of the stop distance [A]. The broker cannot see this: its balance is realised-only and the floor is checked at completed trades [V; brief]. Trades last about 2 calendar days at RR 1 [BM pace], and 33–48% of London-open entries are still open at the 21:00 UTC rollover [V, entry-hour entry]. So day-boundary crossings are common, not rare.

The price of insurance against both is 0.86 points of pass rate and 9 days. The downside of 4% under the strict 35% reading is losing nearly every pass. So 3% is the better bet unless the probability of that reading is below about 2%. Nothing in the grounding supports so low a figure.

The decision says what moves it back: the firm confirming the cap is funded-only, plus the declared test showing the daily rule does not separate 4% from 3%.

**3.5%. Rejected.** It passes 45.95% [C]. But one win is 3.40% > 3.15%, so it breaks the strict 35% reading as surely as 4% does, for most of 4%'s cost.

**2% and 2.5% for account A. Rejected.** They pass 43.37% and 44.59%, over 44 and 28 days [C, BM]. Both are safer under the strict daily reading. But A enters at the London open, and most of its trades close the same day [V]. The extra safety buys little, and it costs 0.8–2.0 points and one to three weeks per pass.

B is different. It enters at 16:00–19:00 UTC and almost always holds overnight (0–12% close before rollover [V]). So B takes 2.5%, the highest risk at which the strict reading cannot fire while equity is at or above the start (g/ℓ ≤ 1.02 [A]).

**RR 3 at 3.5%, the map's best pass rate, 48.4% [P T27]. Rejected.**
- One win is 10.5% of the bankroll: more than the whole target, and far beyond any 35% reading.
- A pass takes a median of 3 trades [P T27], which is the "gambling" record the operator wants to avoid.
- Through the broker, plain RR 3 brackets reach the target 1.4 standard errors below fair [P T28].
- The pass-rate gain over RR 1 comes from a larger up-step. With the up-step capped near 3%, RR 1 through RR 2 pass within 0.4 points of each other [P Fig. 4: RR 1 at 3% 45.4, RR 1.5 at 2% 45.5, RR 2 at 1.5% 45.6]. That is Proposition 14.

**Leaving the target unclipped, which is what the live runner does today. Rejected.** At 3% this is the lattice trap: three wins net of cost fall short of 9%, and the pass rate drops to 40.19% against 45.38% clipped [C]. The clip is a take-profit at the target, fair by Proposition 21, and already built in `set_account` [strategy docstring]. It is required, not optional.

## Funded risk

**4% (the paper's published cell). Rejected.** The chance of any payout is 29.4% against 52.4% at 1.5% [P §14.9]. The operator asked for payout rate per account. Under the tick floor, gross withdrawn is nearly flat in risk (7.2% against 6.7% [P §14.9]), so the high risk buys almost nothing.

**2%. Rejected, but it is the "I need money" alternative.**
- Chance of any payout 46.31%, payouts per account 0.86 [C].
- Wallet growth +0.248 against +0.167 [W], because a funded account turns over faster (life 36 trades against 54 [C]).

It loses 6 points of payout rate per account, the operator's stated objective. The rule's tie band is 1 point, so it is excluded.

**1% and 1.25%. Rejected.** They pay at least once 52.21% and 52.14% of the time, a tie with 1.5% [C]. But gross withdrawn is lower (5.95% and 6.36% against 6.66%), and the first payout comes later: 78 days against 46 at 1% [BM Fig. 8]. At 1% the $143 minimum binds, so a lower risk only lengthens the climb [P §14.4].

1.5% sits just under r* = 0.35 × 4.76% = 1.67%, where the 35% rule starts setting the hurdle [P §14.4]. Floored lots only ever lower the effective risk, so flooring never pushes it over r*.

**Other ratios in the funded stage, the map's best: RR 3 at 0.5% at 55.7%, and RR 1.25–1.5 at 1% at about 53.5% [P T27, Fig. 5]. Rejected.**
- The gains are 1–3 points.
- Every one of these cells is unresolvable through the broker. RR 3 at 0.5% reads 9.7% on 1 block [BM].
- Off RR 1, the per-trade fairness through the broker drops by up to a point (RR 1.5 at −3.3 standard errors) [P T28].
- At RR 1 the random side makes every trade an exact coin whatever the price did [P §14.10]. That is the only reason a chain-only funded choice is defensible at all.
- RR 3 also takes 37 trades to the first payout, at 3.5 days a trade [P T27, T29].

## Tier and number of accounts

**$10,000 tier. Rejected at this wallet.** At 1% funded risk, the $10,000 tier's minimum request is only 2.86%. So it pays at least once 61.7% of the time, with 1.61 payouts per account [C]. That is a better per-account payout rate than anything at $3,000. But one $10,000 account on $1,000 carries:
- 8.2% ruin (12.1% at 1.5% funded);
- a $552 median drawdown;
- less growth (+0.099) than $3,000 [W].

The fee is 9.9% of the wallet, past the 6% rule [P Cor 8]. It becomes the choice once the wallet reaches about $1,650 with payouts honoured.

**The 90% add-on. Rejected.** Proposition 11 [P §6]. At this cell expected value breaks even at P(paid) = 62.5% against 60% without it [A on C].

**One account only. Rejected as the default, kept as the fallback.**
- The number of purchases before the first cash is geometric whatever the parallelism. So a second account adds almost no fee exposure before the first payout request [P Prop 12–13].
- It halves the wait for the first evidence on P(paid) and doubles the income.
- The ruin bound at q = 0.762 is 0.762^26 ≈ 0.09% with 26 fees in the wallet [A on C], so ruin is not what limits the count.

The paper's pooled ladder at $1,000 prefers 2 × $3,000 staggered over one account (ruin 2.7%, growth +1.21 against +0.79) [P T20]. That was at the paper's original cell (4% in both stages, floor overshoot allowed), so it gives the direction, not the size.

**Five independent accounts, or three or more staggered [P T20]. Rejected.**
- Beyond two, the correlation between entry hours is unmeasured, and hours closer together correlate more [P §11.6, §16].
- Every later window holds overnight, which is exactly where the strict daily reading bites.
- Each extra account is one more thing a risk team may read as stacking.

**A second account in the same 07:00–10:00 window. Rejected.** Its correlation with the first is near 1. That is one larger account at a higher fee, which the paper shows loses to the larger tier [P T19, ρ = 1 column].

**The second account at 12:00 UTC. Rejected.** The measured outcome correlation with 07:00 is 0.45, against 0.26 for 16:00, at a 30-pip stop [P §11.6]. That gives n_eff about 1.2 against about 1.4 [A], and 13:00–15:00 entries also hold overnight [V].

## The instrument, the side, the stop, the news rule

**Other instruments (NDX100, USDCHF and others that rank cheaper [P §9]). Rejected.** None has a real-path control or a broker replay. The paper itself says its ranking "is a statement about cost, not a recommendation to switch".

**Random side, or long. Rejected.** Long pays a swap debit ($6.24 a lot a night [P T6]), and the random side averages it in. The short side is the one the broker validated: 50.0% ± 6.6 [P T31]. The credit is about $0.44 a night at 0.25 lots [A], too small to read as swap abuse [V].

**A fixed 60-pip stop, or other multiples of σ. Rejected.** 0.75 σ, floored at 30 pips, won the walk-forward on both halves and both direction policies [P T23]. GARCH did not beat it [P App. A].

**Going dark for news. Rejected.** It lost 26.2% of accounts to the daily rule against 0.2% stepping aside [P T24].

**A day-boundary flatten or time exit. Rejected as untested.** It is fair in mean by Proposition 20. But it breaks the ±ℓ trade law the chains rest on, and it adds round trips. The boundary stop-tightening named in the test is the fallback if S(A3) ≥ 3%.

**Mirroring against Maven. Rejected.** Both rulebooks prohibit it [V, §14 entry].

## Objectives considered for the rule

**Expected value per purchase. Rejected.** It always buys the largest tier and ignores ruin [P §7, T17].

**Unconstrained log growth. Rejected.** At $1,000 it chooses the $25,000 tier at 31% ruin [P T18].

**Growth under a 5% ruin cap alone, the paper's rule. Rejected as the primary objective.** On its own it chooses the highest funded risk tested (4%/4% grows +0.577 against +0.311 at 4%/1.5% in [NB23]; 3%/2% +0.248 against 3%/1.5% +0.167 [W]), trading payout rate for pace. That contradicts "high payout rate per account". I keep the ruin cap as a constraint and put the operator's payout rate first.

**First cash within 120 days, then the most payouts ([NB23] rule). Mostly kept.**
- The funded choice is the same (1.5%).
- NB23 used the 60-pip cost share, 1.67%, not the deployed 2.87%. At the right cost its payout chance reads 52.4%, not 55.0% [P §14.9].
- NB23 had no compliance filter. That filter is what separates my assessment choice from its choice.

## How cells the broker cannot resolve were treated, and one trap

The funded 1.5% cell has 4 calendar blocks. The broker reads 50.0% against 52.7% under its protocol, z −1.0 [BM]. The seed-mean reading is 52.5% ± 3.3 [BM "today"].

I rank it on the chain because of three things together:
- it sits at RR 1, where per-trade fairness through the broker is +0.4 standard errors [P T28];
- the resolvable RR 1 cells agree with the chains;
- nothing in the broker contradicts it by more than 2 standard errors.

**The trap.** The lifecycle grid's z-scores [BM grids.LZ] at funded 1.5% swing from −3.3 (assessment 3%) to +0.9 (assessment 4%). In the model, assessment risk cannot change what a funded account does. So the swing across the row is history noise that the between-seed standard error understates, as the paper warns [P §14.10]. It is not evidence against 3%.

I also opened the cached lifecycle replays on branch prime-academy to confirm this. They show the same swing in the funded payout chance across assessment risks. I cite none of their numbers, because they are outside the grounding folder.

## Readings I assumed, and what the other reading would do

These are listed in decision.md §1 and §3:
- **The floor** is on the tick (the operator's position). On review, 4% gains 5.1 points and becomes the assessment choice if the cap allows.
- **The 35% cap** is assumed to apply in the assessment. If it is funded-only, the test decides between 3% and 4%.
- **The daily rule:** loss from entry, as in the paper, is the base reading. The stricter reading drives B's 2.5% and the test.
- **The 14-day clock** is read in calendar days. 1.5% is best at every clock length tried [C].
- **The live spread** is assumed at 0.5 pip (the operator's position). At 0.0 pip the rule moves funded risk to 1.0% (57.0% against 55.4% for 1.5%); at 0.25 pip and above 1.5% stays [C].
- **The Expert Advisor (EA) ban** [V]: the API runner is used only after the firm confirms it in writing; until then orders are placed by hand, and without the runner B is dropped.
- **Recurring funded charges** are unknown. They would push the funded risk up.