Arcade: Effective Price Per Credit With Bonus Play

Excel Formulas › Arcade & Family Entertainment

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Bonus credits are the whole pricing engine of a game card, and almost nobody works out what they actually give away. A $100 card with 40% bonus is not a 40% discount — it is a 28.6% discount, because the bonus is added to the credits rather than taken off the price. That gap is worth knowing before you print the sign.


Quick formula: Total credits first, then price over credits:
=ROUND(B2/(C2*(1+D2)),3)

A $50 card with 250 base credits and 20% bonus is 300 credits at 16.7 cents each — a 16.7% discount off the entry tier, not 20%.

Functions used (tap for the full reference guide):

The example

A three-tier card menu, with the entry tier as the reference price.

ABCDEFG
1CardPriceBase creditsBonusTotal credits$/creditDiscount vs base
2$20 card$201000%100$0.2000.0%
3$50 card$5025020%300$0.16716.7%
4$100 card$10050040%700$0.14328.6%

The formula

Two columns, and the second one is the one that changes how tiers get designed:

=ROUND(C2*(1+D2),0) then =ROUND(B2/E2,3) then =ROUND(1-(B2/E2)/($B$2/$E$2),3) // total credits, price per credit, and the discount against the entry tier

How it works

Follow the money and then follow the credits:

  1. C2*(1+D2) is what the customer actually receives. A 40% bonus on 500 base credits is 700 credits, not 540 — the bonus multiplies the base, it does not add to the price.
  2. B2/E2 is the effective price of one play. This is the only number that compares tiers honestly, because base credits differ between them.
  3. 1-(B2/E2)/($B$2/$E$2) compares each tier back to the entry price per credit. Lock the reference row with dollar signs so it stays pointed at the base tier as you copy down.
  4. Note the asymmetry: a 40% bonus yields a 28.6% discount, because 1-1/1.4 is 0.286. Bonus percentages always look bigger than the discount they represent, which is exactly why they are the industry's preferred way to say it.

Compare the per-credit price against your revenue per play on the floor. A tier that sells credits below the average cost of a play is a promotion, not a price — which is fine, as long as it is deliberate.

Try it: interactive demo

Interactive

Enter a card price, its base credits and the bonus percentage.

Variations

Bonus needed for a target discount

Rearrange when you know the discount you are willing to give. A 25% discount needs a 33.3% bonus, because the relationship is not symmetric.

=1/(1-TargetDiscount)-1

Revenue per credit sold

Sum the tier prices over the total credits issued to get the blended rate across the whole card menu, weighted by what actually sells.

=SUM(B2:B4)/SUM(E2:E4)

Pitfalls & errors

Unredeemed credits are a liability, not profit. A card sold today with credits left on it is deferred revenue in most accounting treatments, and breakage assumptions are the fastest way to overstate a good month.

Design tiers on the per-credit column, not on the bonus percentage. Two tiers with different bonuses can land at the same effective price, which means one of them is doing nothing for you.

Do not describe a 40% bonus as “40% off” in marketing copy. It is 28.6% off, and the difference is the kind of thing that draws attention from people whose job is to notice it.

Practice workbook

📊
Download the free Arcade: Effective Price Per Credit With Bonus Play practice workbook
Edit the yellow price, base-credit and bonus cells; total credits, price per credit and discount recalculate.

Frequently asked questions

Why is a 40% bonus only a 28.6% discount?
Because the bonus grows the denominator while the price stays fixed. Paying $100 for 140% of the credits means each credit costs 1/1.4 of the base rate, which is 71.4% — a 28.6% reduction. The general rule is that a bonus of B gives a discount of B/(1+B).
Should every tier have a bonus?
Not the entry tier, because it is the reference price everything else is measured against. Once the base tier carries a bonus you have effectively lowered your list price and the higher tiers stop looking like a deal, which is the opposite of what a tiered card menu is for.

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Function references: ROUNDPRODUCTSUM