(FORTUNE Magazine) – Dear Oddsgiver: I am one of the millions of newspaper readers who thought of you whilst reading about the latest constitutional imbroglio before the American judiciary. The issue is whether the Clinton Administration's ''Don't ask, don't tell'' (DADT) policy on gays in the military will stand up to constitutional scrutiny, and specifically, whether its exclusion of acknowledged gays violates the 14th Amendment's equal-protection guarantees. Propelling this issue topside and to the fore is a recent decision by a three-judge panel of the 12-member U.S. Circuit Court of Appeals for the District of Columbia. The panel did not squarely address the DADT policy, but its reasoning in the case before it -- wherein it said that a homosexual midshipman could not be denied the right to graduate from Annapolis -- has got the Departments of Justice and Defense twitching spastically. Accentuating the spasms in both bureaucracies is the realization that they had lousy luck in the judges selected to hear the midshipman case. I note that both the New York Times and the Washington Times identify panelists Abner Mikva, Patricia Wald, and Harry Edwards, all appointed by Jimmy Carter, as the three most liberal members of the District appeals court. Now here is where you come in: In a 12-member circuit court, what are the odds that random selection will result in the three biggest libs getting to decide so important a case? Should I be wondering whether the process was possibly less random (and more political) than advertised? Also, how do you get a bet down on such action? -- LONG-SHOT LARRY

Dear LSL: To answer your middle question first, the DC Appeals Court does indeed have randomized procedures for determining (a) the date on which any case is argued and (b) which judges will constitute the three-member panels sitting on that date. The procedures are computerized and are based on programs using the random-number generators built into just about all PCs these days. An interesting theoretical question is whether these numbers, produced by complex arithmetic formulas, are truly random. John von Neumann, arguably the smartest man who ever lived, once said that ''anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.'' Influenced by John, many scholars now say that computerized randomness is less than perfect and the numbers it generates are merely ''pseudorandom.'' This, however, still leaves them essentially impossible to predict. It leaves you with no rational basis for wondering whether Carterites have rigged the court's computer program. But there is no doubt that the case involves a genuine long shot, comparable to hitting the jackpot on a slot machine or cleaning up at the craps table. How long a shot? The science of statistics tells us that in a universe of 12 objects, there are 220 combinations of three objects. Assuming judges to be objects, the odds against the computer's landing on the three most liberal (or the three most anything) are 219 to 1. By way of comparison, the odds against a chap's stepping up to a standard Las Vegas craps table and making seven winning passes in a row are only 140 to 1. Also, it's easier to get a bet down on dice action.