Engine: tiny legal loan rates (2^-62) make amortPayment divide by zero, +Inf books #95

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opened 2026-09-30 02:10:13 +00:00 by Winnie · 0 comments

Winnie commented

2026-09-30 02:10:13 +00:00

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Engine: a legal tiny loan rate can push +Inf through the books (found during the #80 round evaluation re-bench).

Repro: duel preset (players 3, survivors 1, d15, loans 5/turn), seed 87113, roster super/empire/mill. Empire is the sole bidder on loans 35 and 36 and bids exactly 4.3368086899420177e-19 (= 2^-62, the float64 epsilon signature of its clearing-spread arithmetic). That rate is legal: it lands inside the [0, loan-rate-cap] clamp.

Blowup: amortPayment(P, r, n) uses P*r / (1 - (1+r)^-n). At r = 2^-62, (1+r) rounds to exactly 1.0 in float64, the denominator becomes 0, and every payment on those loans becomes +Inf. Trace from the game (turn 8):

· NON-FINITE EQUITY Bank 2 turn 8: equity +Inf
  ACCT DIVERGENCE Bank 2 turn 8: dEq +Inf netInc -958 diff +Inf cash +Inf deps 76179 loans 53183
  CF DIVERGENCE Bank 2 turn 8: cf 15396 actual +Inf

Cascade: the poisoned books flow into AI inputs. Turn 9: empire's bond-offer size goes non-finite (the #91 guard fails it), mill's bankruptcy-bid goes non-finite from the +Inf market-acquisition-net (guard fails it too), and the auction winner (super) books +Inf bargain gain. One 2^-62 bid takes down the whole game.

Secondary bug: iterations.json marshaling fails on +Inf (iterlog: json: unsupported value: +Inf), so the iteration record is silently dropped for any run containing a blowup.

Scope: 1 of 30 duel seeds (87113) on current master 8ec3eca. The old engine (pre-#91, cda484d) runs the same seed clean. Fix is in the amortization formula, not the rate (the rate is legal).

Engine: a legal tiny loan rate can push +Inf through the books (found during the #80 round evaluation re-bench). **Repro**: duel preset (players 3, survivors 1, d15, loans 5/turn), seed 87113, roster super/empire/mill. Empire is the sole bidder on loans 35 and 36 and bids exactly 4.3368086899420177e-19 (= 2^-62, the float64 epsilon signature of its clearing-spread arithmetic). That rate is legal: it lands inside the [0, loan-rate-cap] clamp. **Blowup**: `amortPayment(P, r, n)` uses `P*r / (1 - (1+r)^-n)`. At r = 2^-62, `(1+r)` rounds to exactly 1.0 in float64, the denominator becomes 0, and every payment on those loans becomes +Inf. Trace from the game (turn 8): ``` · NON-FINITE EQUITY Bank 2 turn 8: equity +Inf ACCT DIVERGENCE Bank 2 turn 8: dEq +Inf netInc -958 diff +Inf cash +Inf deps 76179 loans 53183 CF DIVERGENCE Bank 2 turn 8: cf 15396 actual +Inf ``` **Cascade**: the poisoned books flow into AI inputs. Turn 9: empire's bond-offer size goes non-finite (the #91 guard fails it), mill's bankruptcy-bid goes non-finite from the +Inf market-acquisition-net (guard fails it too), and the auction winner (super) books +Inf bargain gain. One 2^-62 bid takes down the whole game. **Secondary bug**: iterations.json marshaling fails on +Inf (`iterlog: json: unsupported value: +Inf`), so the iteration record is silently dropped for any run containing a blowup. **Scope**: 1 of 30 duel seeds (87113) on current master 8ec3eca. The old engine (pre-#91, cda484d) runs the same seed clean. Fix is in the amortization formula, not the rate (the rate is legal).

Winnie referenced this issue from a commit

2026-09-30 02:10:20 +00:00

[#95] Stable amortization for tiny loan rates: expm1/log1p form, +Inf books impossible (Closes #95)

Winnie referenced this issue from a pull request that will close it,

2026-09-30 02:11:31 +00:00

[#95] Stable amortization for tiny loan rates: expm1/log1p, +Inf books impossible #96

Winnie referenced this issue

2026-09-30 02:11:50 +00:00

v0.5.0: the super AI — state machine, 85%+ wins in all scenarios, validated #80