Normally for insurance the suggestion is that you should 'self-insure' smaller risks, and only purchase third-party insurance for catastrophic risks. The theory being that insurance has extra overheads and on average has to cost you more money than you get out. But that for catastrophic risks, you can't rely on averages.
(Of course, that only applies in the absence of tax or regulatory arbitrage. Eg I hear in the US your employer can buy health insurance from pre-tax money, but you'd have to use post-tax money for paying out-of-pocket.)
Similar for a company like AmEx you have to weigh whether the occasional wins you describe are worth the constant drain. Or whether you should just put the winnings in a piggy bank, and use a small part of that to finance the replacement for the never-arriving fancy new sofa.