RESEARCH ANALYSIS & GAME MATH
The research and assumptions behind the choices.
A 38.3% higher purchase rate with a cart reminder. About 20% more opens with a name in the subject. This is myuser.ai’s analysis of the external experiments by Li and colleagues and by Sahni, Wheeler and Chintagunta: the comparisons behind those figures, and why Inbox Arena shows only the first, beside its cart-timing choice. The guide also shows the separate assumptions that produce the game’s simulated buyers and dollars, and how a score is compared with the best possible result. Links lead to the original research.
In this guide
Follow the money, from assumptions to result
| Round | Assumed rate | Buyers | After item costs |
|---|---|---|---|
| Cart reminder | 5% | 50 | $1,500 |
| Free guide | 2.6% | 26 | $780 |
| Refill | 4.6% | 46 | $1,380 |
| Small bottle | 4% | 40 | $600 |
| Return code | 4.4% | 44 | $1,003.20 |
| All five rounds | 206 | $5,263.20 |
Each round has 1,000 sample shoppers and eight preset conversion rates: one for each combination of three choices. Buyers equal the shopper count multiplied by the selected rate, rounded to a whole person. Each buyer purchases one item, and orders are counted for 30 days after the email.
Money made after item costs equals buyers × (price after discount − item cost). For example, 50 × ($48 − $18) = $1,500. The 50 buyers come from an assumed 5% rate, not an observed campaign. In the small-bottle round the chosen bottle sets the price: the 200 ml bottle keeps $30 a sale after item costs and the 60 ml bottle keeps $15.
Your score is compared with the best possible result: the highest-scoring combination under the same preset rates. The game shows your money, the best money and your share of it for each round and in total. There is no opponent. The best combination is a property of the preset table; it does not show that any person or AI would find it in a real store.
The preset rates follow stated rules. Each round has one best combination. In every combination, swapping a pick that differs from the best one for the best one makes more money. The decision each round’s lesson is about moves the money most. Shoppers who left a checkout buy more often than past buyers who asked for a code, and both buy more often than new sign-ups.
The totals exclude plan fees, sending fees, shipping, payment fees, taxes, returns and other costs. They also do not subtract purchases that would have happened without the email.

A discount has a calculable hurdle
In the $48 face-wash example, the item costs $18. A full-price sale makes $30 after that cost. With 10% off, the customer pays $43.20 and the same item makes $25.20.
Matching the full-price total requires $30 ÷ $25.20 = about 1.1905 times as many buyers: about 19.05% more. With 15% off, $40.80 − $18 leaves $22.80, requiring about 31.58% more buyers. These percentages are arithmetic, not predictions that a discount will attract those buyers.
Whole orders matter. To match 50 full-price buyers ($1,500), the 10%-off offer needs at least 60 buyers: 60 × $25.20 = $1,512. This comparison holds the item cost fixed and excludes other costs.
The game’s buyer responses are assumptions. In the cart round, the 10% code is assumed to bring about 8% more buyers, short of the 19% it needs. In the return-code round, where shoppers asked for the 15% code, it is assumed to bring about 70% more, past the 32% it needs.
What supports the choices?
Some choices follow explicit facts in the scenario: a pop-up promised a guide “now”, a bottle lasts about 30 days and delivery takes five, or a code expires on Sunday. A 30-day supply minus five days of shipping gives a day-25 reminder, counting from delivery when this shopper starts using it. That assumes a prompt reorder; it does not prove how quickly an individual shopper uses the product.
The game labels each explanation. “Game assumption” marks reasoning whose size in dollars comes from the preset rates, not a measurement. “Calculated tradeoff” marks arithmetic, such as a discount’s break-even or the 60 ml bottle’s $15 a sale against the 200 ml bottle’s $30. “Copy tip” marks W3C guidance that a link’s purpose should be understandable from its wording or context, as in “Reorder Daily Cleanser”. That supports understandable links, not a particular conversion rate.
Picks can interact. Telling shoppers “You’re out” is wrong for most of them on day 25 and for fewer on day 35, so the game charges it more on day 25. A recent product view is a useful clue, but it does not prove that a product-specific email always beats a broader message. The game’s preferred choices and sales differences teach the scenario’s logic; they are not independent experimental findings.
A replenishment example is one possible reason for customer win-back outreach. The buying cycle is a planning clue, not proof that every customer needs a reminder on the same day.
Source: W3C WAI — Understanding WCAG 2.4.4: Link Purpose (In Context)
38.3% higher purchase rate with a 24-hour cart reminder
The finding: at a Japanese fashion retailer, 8.3% of shoppers bought after a reminder sent at 24 hours, compared with 6.0% in the corresponding no-email control. Li, Luo, Lu and Moriguchi measured purchases over the following month. Their email experiment included 33,234 shoppers across all timing groups.
That is +2.3 percentage points (p < .01). myuser.ai’s relative-lift calculation is (8.3 ÷ 6.0 − 1) × 100 = 38.3%. The reminder repeated information about the abandoned product; it did not offer a discount. See Figure 2A and page 8 of the author copy.
Timing mattered in both directions: at one hour, 13.4% bought with a reminder versus 16.7% without. Each timing group has its own no-email control, so those rates are not a direct comparison of sending at one hour versus 24 hours.
Our application: the game illustrates waiting a day because this study gives a concrete reason to test reminder timing, and shows the study only beside that timing choice. It does not establish tomorrow as the best choice for every store. The external 38.3% result supplies none of the game’s preset conversion rates or simulated dollar advantage.
The cart-recovery guide explains how to review timing and message choices for your store. Use the study as a reason to test, rather than a promised result from myuser.ai.
Sources: Li et al. — The Double-Edged Effects of E-Commerce Cart Retargeting (Journal of Marketing)Li et al. — Author-uploaded article (PDF), Figure 2A and page 8The authors’ free explanation — American Marketing Association
How to measure a real improvement
Randomly assign comparable eligible shoppers to versions of the same message. Change the feature you want to test, such as the destination or send time. Keep the other conditions comparable. Count recipients and purchases over the same period for each group.
To estimate additional sales caused by sending, include an appropriate group that does not receive that message. An order attributed to an email may still have happened without it. Include discounts, item costs and the other costs relevant to your store.
Report the sample size, absolute rates, time window and uncertainty with any percentage increase. A game result or a published result from another retailer does not substitute for that measurement.
Recordings can help choose what to test after a message click. For example, several available visits may reveal that the promised product option is difficult to find on the landing page. Confirm the issue directly and define one change. Measure its effect with the relevant orders, costs and comparison described above; neither one compelling replay nor the number of replays proves an improvement.
The Shopify session recording guide connects an observed issue to a checkable change.
A name in the subject: about 20% more opens
The finding: Sahni, Wheeler and Chintagunta (Marketing Science, 2018) added the recipient’s name to an email subject and compared it with a subject without the name. In their main randomized experiment, the open rate rose from 9.05% to 10.80%. The authors report an approximately 20% relative increase; the displayed, rounded rates give 19.3%. The absolute difference is 1.75 percentage points.
Why Inbox Arena does not show it: none of the game’s choices adds or removes a name, and the game scores orders after item costs, not opens. The free-guide round uses Maya’s name in both subject lines, so this experiment cannot pick a winner there.
The reported lift concerns opens, not 20% more purchases. It does not establish a general benefit from AI writing or every personalized message, and it does not supply the game’s conversion rates. This is myuser.ai’s analysis of the external finding, not another experiment.
Sources: Sahni, Wheeler & Chintagunta (2018) — Personalization in Email Marketing, Stanford research recordPersonalization in Email Marketing — published paper, Marketing Science
