The answer could well be Premium Bonds, because Ernie's growing legion of followers seems to believe that silence is golden - of the two dozen or so Pounds 1 million winners since the larger jackpot prize was introduced two years ago, none has gone public. Compare that with the lottery and its roll call of petty thieves and lager louts.
National Savings, which runs Ernie (Electronic Random Number Indicator Equipment) on behalf of the Government, cannot say how many teachers have been among the big winners - the only information it can legally reveal is the county in which the winner lives, the bond number and the size of the winning stake.
Of course, "stake" is a misnomer, because unlike the lottery there is nothing to lose. The money spent on bonds remains yours, so all that is lost is the notional interest you could have earned elsewhere. And with interest rates for savers being at record lows, that means not very much at all.
Although they could not name any teachers who had swapped the staffroom Nescafe for Pol Roger at the Savoy, the Blackpool headquarters of National Savings did have this to say: "Premium Bonds are the kind of product that appeals to professional people such as teachers. They are a serious investment which offers the exciting chance of winning a Pounds 1 million prize or one of the other 349,999 prizes Ernie pays out each month. Bonds are a safe bet because capital can be repaid in full at any time and any prizes won are completely free of income tax and capital gains tax."
Well, they would say that, wouldn't they?
So what are the odds of one Pounds 1 bond landing the Pounds 1 million jackpot available each month? Err . . . lengthy. That's lengthy as in 6.58 billion to one against. Compared to that, Camelot's oft-trumpeted odds of 14 million to one for a National Lottery jackpot looks as dead a cert as rain on a bank holiday weekend.
But if you have the maximum holding of Pounds 20,000, the big bond prize looks far more approachable, at roughly a one in 329,000 chance of winning, per Pounds 1 bond.
This month's Pounds 1 million winner, from suburban Hertfordshire, had a Pounds 20,000 holding, the winning bond coming from a stack of 5,000 bought simultaneously. But National Savings is keen to point out that Ernie millionaires have had as small a holding as Pounds 476. Three of the 27 millionaires have had the maximum allowed, however, and a fourth had Pounds 19,500. Ten had stakes of Pounds 2,000 or less.
Altogether, some 63,000 people have the Pounds 20,000 maximum holding, out of the 20 million people who own bonds, which nowadays must be bought as an initial purchase of Pounds 100, then in multiples of Pounds 10. They are available from post offices or direct from National Savings.
When the scheme was launched 40 years ago by the then Chancellor, Harold Macmillan, in his April Budget speech, bonds could be bought singly for Pounds 1. In June 1957 Ernie was switched on by the then Postmaster General, Ernest Marples, and the first prize draw took place.
Since then, Premium Bonds have paid out Pounds 3.15 billion in prize money, and a grand total of 52.72 million prizes. The 350,000 prizes drawn last month were worth Pounds 25.42 million.
Last month was also notable for a change in the prize structure which improved the chances of winning prizes between Pounds 100 and Pounds 100,000 - although the number of Pounds 50 prizes was cut. Rising sales slightly worsened the already astronomical odds against winning the jackpot.
But National Savings says that even assuming Ernie only ever gives you the lower value prizes - Pounds 50 and Pounds 100 - average return on capital could be 3.5 per cent a year. Given that this is tax-free, it still beats many building society accounts, none of which offers the chance of winning Pounds 1 million.
You might win nothing, but the odds of a Pounds 20,000 bondholder winning no prizes for a year are claimed to be more than seven million to one against. Each Pounds 1 bond has an equal chance of winning a prize, no matter where it was purchased or how long ago. The list of Pounds 1-million winners certainly seems to favour the South, but National Savings says this simply reflects the fact that more bonds are held by those who live there.
As with the lottery, prizes can go unclaimed. But Ernie puts no time limit on claims, and National Savings says it has paid out prizes to more than 99 per cent of all winners. This still leaves 242,000 prizes, totalling more than Pounds 13 million, with no homes to go to.
This is usually because bondholders fail to notify National Savings of changes of address. If you want to check whether those bonds bought in 1977 and forgotten about for four house moves are winners, send National Savings your present address and the one current when the bonds were bought. Giving the holder number as well as the bond numbers will speed the search.
Contact: Premium Bonds, National Savings, Blackpool FY3 9YP.