Cost of Saving: make informed decisions

Is it worth it?

Warranties, subscriptions, big purchases, pawn loans, a degree. Pick what you are deciding, start from a common example or your own numbers, and see the one figure that settles it.

What are you deciding?
What kind of deal?

The price for one go: one policy term, one ticket, one spin. "How many times" repeats it: 52 weekly tickets, 600 spins.

What could happen
Chance as 5%, 0.05 or 1 in 20. Payout as 250, $1,200, 2.5k or 100M. Add a row for each separate thing that could pay out.
This decides whether you need the protection at all.
Average payback vs what you pay, per go

Where each outcome sits

Across: the chance. Up: the payout. The black line joins every single outcome that would pay back exactly the price (chance × payout = price). A one-outcome deal above the line comes out ahead on average. With several outcomes, their payback adds up, which the bar above shows.

The two numbers behind every deal

chance × payout = average payback

Multiply to gather the deal into one number: what it returns on average each time. Several outcomes? Add their products.

price ÷ payout = break-even chance

Divide to split it back apart: how likely the outcome would have to be for the price to be fair.

times × (price − payback) = expected loss

Repeat a losing deal and the loss grows with every go. That is why an hour of slots costs far more than one spin.

A rule that holds up
  • If you could pay the loss yourself, skip protection that loses money on average. Keep the price instead.
  • If the loss would wreck you (a house, a big medical bill), paying a bit over the average can be the right call. The extra buys you out of a loss you could not absorb.
  • Bets that lose on average are entertainment. Set the budget as the ticket price and stop there.
What this cannot tell you
  • Your real chance. The answer is only as good as that number. Look for repair or claim rates for the exact product.
  • Fine print: claim denials, deductibles, and cover you may already have through a credit card or employer.
  • Taxes on prizes, and how much you enjoy playing.

Preset numbers are illustrative, not quotes, except the Powerball prize odds (the published odds for each tier; the jackpot varies) and the payday example, whose $15 per $100 fee is the typical figure the US Consumer Financial Protection Bureau cites. Real slot machines do not publish their odds; the slot presets use a typical 92% return. Nothing you type leaves this page; your own numbers are remembered in this browser only.