EASTERBROOK, Circuit Judge.

For many years Archer Daniels Midland (adm) bought $50 million of business-interruption coverage from Employers’ Insurance of Wausau. But when Wausau quoted a price increase of roughly $19,000 (from $43,750 to $62,500) for adm’s 1993 fiscal year, adm deemed the premium excessive and went shopping for a bargain. This attempt to save $19,000 has cost adm $50 million, for the replacement insurance did not cover the losses adm sustained as a result of the flood in the upper Mississippi River basin during 1993, the greatest in the nation’s history. In this litigation under the diversity jurisdiction, adm asked the court to “reform” the policy it purchased from Hartford Fire Insurance Company so that it would cover adm’s loss.

The flood inundated about eight million acres of farmland and disrupted transportation on the Mississippi and Missouri Rivers and their tributaries. Much of adm’s business depends on corn, which increased *371 in price by about 15<t per bushel after at least 5% of expected 1993 u.s. production was lost and healthy crops could not be moved to market. Disruption not only of water transport but also of railroads with tracks near or crossing the rivers made it more costly for adm to ship its own products. adm sought to insure against such events. Regular business-interruption insurance replaces profits lost as a result of physical damage to the insured’s plant or other equipment; contingent business-interruption coverage goes further, protecting the insured against the consequences of suppliers’ problems. Regular business-interruption coverage did adm little good in 1993, for the flood largely spared its plants, but contingent business-interruption coverage was just the ticket, adm’s plan called for $100 million of coverage for both its own and its suppliers’ business interruptions. Until fiscal 1993 Wausau furnished the layer between $50 and $100 million, excess to four other layers of coverage. Because Wausau effectively had a $50 million deductible (though it had some drop-down obligations in the event lower-tier insurers failed to indemnify for a loss), its band of coverage cost adm less than 1$ for every $11 of insurance, reflecting a judgment that the covered loss had a less than 1 in 1,000 chance of occurrence. But, as adm grew, Wausau’s exposure grew too; equipment failure is more likely as a firm has more machines, and the probability that the loss would exceed $50 million also climbed. Wausau quoted a higher price for 1993, and adm directed Rollins Hudig Hall of Minnesota, Inc., to replace the coverage. (This broker has become part of Aon Risk Services, but we follow the parties’ convention and use the rhh acronym.)

adm expected rhh to ensure that insurance in the $50 to $100 million layer followed form — that is, covered the same risks as the carriers in the lower bands. adm and rhh had developed a detailed form on which they took bids from insurers; adm is large enough that the costs of calculating risks on an unusual form are acceptable to its carriers. But something went wrong. Hartford Fire Insurance, which agreed to insure the $50 to $100 million band (for an annual premium a little less than Wausau had charged in 1992), issued its policy on its own standard business-interruption form, which covered the profits lost because of failures in adm’s equipment but not losses caused by problems afflicting adm’s suppliers, adm concedes that the policy Hartford issued does not cover the loss it sustained, and it blames rhh for failing to secure from Hartford a follow-form policy. To justify reformation of Hartford’s policy, it had to persuade the district court that rhh acted as Hartford’s agent for the purpose of binding coverage. Like all demands for reformation of a contract, that contention posed equitable issues, triable to the court rather than a jury, and at a bench trial adm failed to persuade the district judge that rhh was Hartford’s agent for the purpose of making underwriting decisions. Judgment therefore was entered in Hartford’s favor.

Hartford and adm agree that rhh butchered the job. That’s easy for them to say. rhh is not a party, and an empty chair can’t defend itself. About two years after filing this suit against Hartford in the Southern District of Illinois, adm sued rhh in the District of Minnesota. See Archer Daniels Midland Co. v. Aon Risk Services, Inc., 187 F.R.D. 578 (D.Minn.1999). In Minnesota adm contends that rhh is hable for negligent execution of its duties as adm’s agent; in Illinois adm contends that Hartford is liable because rhh erred in its role as Hartford’s agent. (These positions are not inconsistent; adm believes that rhh acted as both parties’ agent.) One complex commercial dispute thus has been broken into two, not only wasting judicial (and the litigants’) resources, for discovery and trial must be duplicated, but also potentially precluding either district court from finding out what happened. In Duluth there is a different empty chair: Hartford’s. Sundering the dispute carries with it the risk of inconsistent outcomes, *372 which cannot be rectified on appeal because the districts are in different circuits — though, if that occurs, adm will bear both the responsibility and the consequences, for it can lose in both forums but not win in both, and it may not prevail in either. Still, because rhh is not a party to this case, everything we say about it reflects only the mutual strategy to cast Rhh as the villain; facts developed in Minnesota may put rhh’s acts in a better light, and neither our narrative nor the district court’s findings have any effect adverse to rhh in the Minnesota case.

Here is a sketch of events according to adm. For many years rhh had been adm’s insurance broker, administering an elaborate set of policies. After Thomas Duf-field, adm’s Vice President of Insurance and Risk Management, decided to reject Wausau’s bid, he told rhh to find replacement coverage on the same terms and conditions as Wausau’s policy, but costing less. Hartford agreed to insure the $50 to $100 million layer and sent Rhh a binder of coverage. The binder promised regular but not contingent business-interruption coverage; it also reserved Hartford’s right to examine the underlying policies and use its own form. Hartford likely bound only regular coverage because Rhh’s solicitation did not request contingent business-interruption coverage, did not include copies of the Wausau policies or adm’s form, and did not ask Hartford to follow form to the underlying policies, rhh told adm that it had replaced the Wausau policy, which adm then canceled, but did not send it a copy of Hartford’s binder, which would have revealed the differences between Wausau’s policy and Hartford’s commitment; instead rhh falsely told Duffield that Hartford had agreed to follow form to the underlying policies.

By now it was the middle of November 1992. Hartford wanted to see the underlying policies, but rhh tarried. It sent adm’s form to Hartford at the end of January 1993; this caused Hartford to ask for engineering data so that it could assess the risk of contingent business-interruption coverage. It took some two months for rhh to comply, and with the data in hand Hartford decided to use its own form rather than adopt adm’s. By now it was mid-April 1993, but still before the flood; adm might have had time to secure contingent business-interruption coverage had rhh alerted Duffield, but it did not send him the Hartford policy until September 27, 1993, after the flood had abated (and only three days before the end of the policy year). On September 30, the policy’s final day, rhh sent Hartford a fax stating: “Expiring [Hartford] form does not meet specs in several areas and may provide coverage not needed.” Nonetheless, rhh renewed Hartford’s coverage for the next year and once again erroneously informed adm that Hartford had provided “Contingent Business Interruption ... per Brokers manuscript policy on file with companies.” No, it hadn’t — not for 1993, and not for 1994, as adm later learned.

rhh acted throughout as adm’s agent. Nonetheless, adm contends, rhh also acted' as Hartford’s agent, with at least apparent authority to bind Hartford to the adm form. The district court found otherwise, concluding not only that Hartford had done nothing to imbue rhh with apparent authority to act on its behalf but also that adm did not think of rhh as anyone else’s agent in this transaction. On appeal, adm contends that the district court committed a legal error, which we may review de novo. That error, according to adm, was a belief that it is impossible for an insurance broker to serve two masters. True enough, Illinois permits dual agency. See State Security Insurance Co. v. Burgos, 145 Ill.2d 423, 164 Ill.Dec. 631, 583 N.E.2d 547 (1991). (The parties agree that Illinois law supplies the rule of decision.) But we cannot find any part of the district court’s opinion that says otherwise, or even a passage that could be taken from context and misunderstood to deny the possibility. If the district judge thought it conclusive that *373 Rhh was adm s agent, there would have been no need for a trial. Yet the judge took evidence and asked whether the record supported a finding that Rhh also was Hartford’s agent. The judge found the evidence wanting, and that finding, on which appellate review is deferential, see American Insurance Corp. v. Sederes, 807 F.2d 1402, 1406 (7th Cir.1986), is not clearly erroneous. The district court wrote that it was granting “judgment as a matter of law” to Hartford, a formulation, borrowed from Fed.R.Civ.P. 50, implying plenary appellate review: it is the phrase used to describe the act of taking a case away from a jury. But here the district court was sitting in equity and conducted a bench trial, after which it made findings of fact and conclusions of law. See Fed. R.Civ.P. 52. The reference to “judgment as a matter of law” was a misdescription of the procedure. Appellate review of fact-specific decisions after a bench trial is deferential, see Anderson v. Bessemer City, 470 U.S. 564, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985), and review of decisions to grant or withhold equitable relief, or to characterize the parties’ relations, likewise is deferential. Cf. Icicle Seafoods, Inc. v. Worthington, 475 U.S. 709, 106 S.Ct. 1527, 89 L.Ed.2d 739 (1986).

One of adm’s theories at trial was that rhh acted as Hartford’s agent because Hartford had signed an agreement naming rhh as its agent. That would create actual authority — if the agreement covered policies such as this one. The district court found, however, that this agreement covered only other types of policies and “had nothing to do with the excess policy that adm was seeking here.” adm no longer argues that Rhh had actual authority to bind Hartford and concentrates on apparent authority. But its only evidence of apparent authority is that rhh received the policy from Hartford and sent it on (eventually) to adm, signing it in the process, and received the premium from adm and deducted a commission before sending the remainder to Hartford. These events show that rhh was a go-between, but why does this status imply that it was Hartford’s agent? Did rhh behave any differently in the hundreds of other transactions in which it was solely adm’s agent? It did what adm had hired it to do, and as in other cases it was compensated for these services by a percentage of the premium.

Conducting a brokerage business in the normal way does not demonstrate apparent authority to make underwriting decisions for an insurer — for recall that adm must establish not simply that rhh had authority to receive money and shuffle (or even sign) papers on its behalf but also that it was Hartford’s agent for the purpose of deciding what risks to accept, and at what price. If adm really thought that rhh had that authority, then adm must have believed that the world was its oyster. Why should rhh bother soliciting bids? It could just write insurance, on behalf of Hartford or any other convenient company, for whatever coverage adm wanted at bargain-basement prices. Neither rhh nor adm behaved in that manner, however, which supports the district court’s conclusion. Dual agency is most likely in thin markets; if there is only one insurance broker in town, both the driver and the auto insurer may need to use that person’s services. But adm was shopping in an international market, and it hired rhh to be its long-term champion. Only an exceedingly foolish insurer would have deemed rhh its agent in the same transactions, and adm was too sophisticated to believe that for a big-stakes transaction an insurer would appoint as its agent a firm that had already promised to put adm’s interests first.

What the district court concluded is not that it was legally impossible for rhh to be a dual agent, but that rhh did not have apparent authority to act on Hartford’s behalf in the only way that matters — in promising to cover a particular risk for a particular price. The district judge added an independent ground of decision: that an insurer “is not responsible *374 for the broker’s representations of which it is unaware and which it did not ratify.” That proposition is true even if the insurer holds the broker out as its agent. There are contrary suggestions in some state cases, but we have concluded that the Supreme Court of Illinois, when it resolves the conflict among the intermediate appellate courts, will hold that brokers’ unauthorized conduct does not create authority from thin air. See Anetsberger v. Metropolitan Life Insurance Co., 14 F.3d 1226 (7th Cir.1994); Lazzara v. Howard A. Esser, Inc., 802 F.2d 260 (7th Cir.1986). Nothing Hartford did created whatever authority adm perceived, and impressions conveyed by rhh without Hartford’s consent are inadequate under Illinois law. So the district court’s ultimate conclusion is sound; Hartford’s policy cannot be reformed to cover what rhh unilaterally said it would cover.

More than two years into the suit, and shortly before the bench trial, adm tried to amend its complaint to add multiple additional claims. The proposed amended complaint — at 45 pages and 204 paragraphs a rollicking transgression against the spirit of Fed.R.Civ.P. 8(a) (a complaint must be “a short and plain statement of the claim showing that the pleader is entitled to relief’) — would have added six new claims to the demand for reformation. Much of the new complaint is just the same claim multiplied, the sort of redundancy (four reformation theories rather than one) that does little beyond running up lawyers’ bills. Complaints need not plead law, so why four claims that differ only in the legal foundation for a single grievance? See Bartholet v. Reishauer A.G. (Zurich), 953 F.2d 1073 (7th Cir.1992). Still other claims in the proposed amended complaint just made official strains of argument (such as ratification and estoppel) that adm had espoused without need for statement in a complaint. Its original complaint specified that it wanted Hartford held to the coverage rhh told adm it had obtained. Multiple “counts” recapitulating that demand were so much dross, except that the proposed amendment tried to avoid the impending bench trial by stating legal rather than equitable theories. Only one aspect of the revised complaint was a genuine novelty— a claim that Hartford itself defrauded adm. Fraud, which must be pleaded with particularity, see Fed.R.Civ.P. 9(b), could enter the case only via an amendment. But the district court declined to allow adm to file its amended complaint, and again appellate review is deferential. See Foman v. Davis, 371 U.S. 178, 182, 83 S.Ct. 227, 9 L.Ed.2d 222 (1962); Perrian v. O’Grady, 958 F.2d 192, 194 (7th Cir.1992); Bohen v. East Chicago, 799 F.2d 1180 (7th Cir.1986).

Once again we perceive no abuse of discretion. The suit was two years old and on the eve of trial. It had been four years since the underlying events. (A penchant for delay is manifest, adm appealed early in 1998 but did not file its opening brief until September 2000.) adm wanted not only to expand the suit by adding a fraud claim but also to switch the locus of decision from a judge to a jury. Trying to change the rules when the game seems to be going badly is not a tactic that district judges are obliged to facilitate. If the district court had allowed the amendment, it would have been necessary to reopen discovery and take new depositions, of persons who had been through that unpleasant process already, to explore topics that had been irrelevant to the original claim for reformation. It might have been possible to litigate about estoppel, ratification, and waiver without new discovery, but the district judge accurately observed that these amendments likely would have been futile given the limits of the evidence revealed at the bench trial. adm treats this comment as a violation of the principle that, when some elements of a case are triable to a judge and others to a jury, the jury’s findings control on the common issues. See Beacon Theatres, Inc. v. Westover, 359 U.S. 500, 511, 79 *375 S.Ct. 948, 3 L.Ed.2d 988 (1959); Dairy Queen, Inc. v. Wood, 369 U.S. 469, 472-73, 82 S.Ct. 894, 8 L.Ed.2d 44 (1962). But the judge was not saying that his findings would preclude a jury from reaching different conclusions; he was saying instead that the evidence revealed the unlikelihood that a jury would do this, making it wasteful to allow the amendment in the first place, adm could amend its complaint only with the judge’s leave, and it was sensible for the judge to take into account the improbability that Hartford would prevail on the revised claims — for if the destination is fated, it is best to avoid the travail of the journey.

Affirmed.