Reading the numbers

A calculator can be exactly right and still be read wrong. These are the figures this site publishes, the readings they invite, and where each one stops being able to answer the question.

Every entry names a calculation that runs on this site and cites the version it describes. Nothing is explained here that no tool on the site actually produces.

  1. Expected balance is a lower bound, not a floor

    The expected balance after wagering, from the expected balance calculator.

    Read as
    The expected balance is the amount a session will end with, and results should land near it.
    Actually
    It is the average over very many repetitions of the same wagering, computed as though the entire requirement gets staked — which is usually more staking than actually happens, so the figure typically sits below the true expectation.

    expected-balance v1.0.0

  2. The multiple is not the cost

    The playthrough multiple — the “10x” in a promotion’s headline.

    Read as
    A 10x requirement means playing through a balance ten times, so it costs roughly a tenth of it.
    Actually
    The multiple sets how much must be staked, not what that staking costs; the cost is the multiple multiplied by the house edge and divided by the contribution rate, which can exceed the balance entirely.

    playthrough v1.0.0

  3. An average is not a typical session

    The mean outcome reported by the variance explorer.

    Read as
    The average result describes what usually happens, so a session should look roughly like it.
    Actually
    The mean is pulled upward by rare large wins, so in a high-volatility game most sessions finish below the average and the median is the better description of a typical one.

    variance-simulation v1.0.0

  4. Cost per coin is not cost per redeemable coin

    Coins per dollar, and cost per coin, from the package value calculator.

    Read as
    The package offering more coins per dollar is the better value.
    Actually
    Coins per dollar prices the coins as received; what determines value is the price divided by the balance expected to survive the wagering attached to them, which two packages with identical headline ratios can differ on sharply.

    package-value v1.0.0

  5. The cheapest scenario is not the safest one

    The ranking produced by the scenario comparison tool.

    Read as
    The scenario ranked first is the best choice, and the ones missing from the ranking are the worst.
    Actually
    The ranking orders scenarios by expected cost per redeemable coin and by nothing else; it does not account for how widely results scatter, and scenarios absent from it were excluded as unmeasurable on that scale rather than ranked last.

    scenario-comparison v1.0.1

  6. There is no completion probability here

    The figure this site does not publish: the chance of clearing a requirement.

    Read as
    A calculator that knows the requirement, the balance and the RTP can work out the odds of clearing it.
    Actually
    Computing that probability requires the game’s full payout distribution and the bet size, neither of which is an input to any tool here or published for real games, so the site reports no completion probability at all.

    expected-balance v1.0.0

  7. A box's average is not what a box usually returns

    The expected value of a randomised purchase, from the box and pack calculator.

    Read as
    An expected value close to the price means the purchase is roughly break-even, so most purchases come back worth about what they cost.
    Actually
    The average is carried by the rarest outcomes. A box whose average sits near its price can still return a fraction of that price on nine purchases in ten, because one outcome in a hundred holds most of the mean.

    box-economics v1.0.0

  8. A seller's stated value is not what the item is worth

    The expected value at the seller's stated values, from the box and pack calculator.

    Read as
    A box advertising $180 of average value against a $100 price is offering more than it charges.
    Actually
    That figure is computed from values the seller chose. The number that matters is computed from prices recorded somewhere the seller does not control, and then reduced again by what the seller's own terms charge to turn an item back into money.

    box-economics v1.0.0

  9. Odds that add up to 96% do not give an answer that is 96% right

    The disclosed probability mass, published beside every odds table.

    Read as
    If a seller publishes probabilities covering most of the outcomes, an expected value over those is approximately correct and can be published with a caveat.
    Actually
    The missing mass is not a small error term. An expected value over part of a distribution is an exact answer to a question about a different product, and the undisclosed part is where the largest outcomes usually sit.

    box-economics v1.0.0