Objective The purpose of this post is to have a look into the RNG surrounding card re-rolling and suggesting corrective measures.

Assumptions We assume that the probability of rolling each bonus stat is the same.

Formulating the problem Consider a regular card Marvel123, with 2 fixed stats and 4 bonus stats. Suppose the 4 bonus slots are A,B,C and D respectively. Each bonus slot has 5 stats to roll for, let's name them A1,A2,A3,A4 and A5 for A, B1-B5 for B and so on. Consider that the card is at 2 stars, ready to be rolled for the first bonus stat. Suppose, our end goal is to roll the card to 4,5,6 or 7 quality with stats A2, B4, C1 and D4.

Analyzing chances

• Upgrade 1 – the probability of rolling A2 is 1/5
• Upgrade 2 – here's where the fun begins, since on the second upgrade, the first bonus stat is also liable to change, the probability of rolling A2 and B4 becomes 1/25 (you're working with ordered pairs now)
• Upgrade 3 – Now we're working with triplets, the probability of rolling A2, B4 and C1 is 1/125
• Upgrade 4 – We are dealing with quintuples now, and the probability of roliing A2, B4, C1, and D4 becomes 1/625
• Quality – Since we are rolling for 4,5,6 or 7 quality, assuming equally likely rolls, the chances of desired outcome is 4/7
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Net probability – Since upgrade 4 and quality are mutually independent), the probability of them occurring simultaneously is `1/625 * 4/7 = 4/4375` or approximately 0.09%.

Material Cost Each rolling consumes 1 mythic card. 1 mythic card = 5 legendary cards = 25 heroic cards = 125 rare cards = 625 advanced cards = 3125 normal cards.

Suggestions for improvement Off the top of my head, I could think of 2 ways to improve card rolling. Please feel free to add more in comments.

• Options to lock stats – For a mythic card, every 5 rolls should give you the option to lock a stat for 100 crystals (or 500,000 gold) each. So on the 10th roll, you could lock 2 stats for 200 crystals (or 1,00,000 gold), and so on. The option should be available at 5th, 10th, 15th and 20th rolls, but it's not necessary for the user to apply them outright – you could lock a stat on the 7th roll, if you wanted.
• Less cost to re-roll – Each roll could consume 1 mythical card, 2 legendary cards or 3 heroic cards.
• Seasons – Implementing the above suggestions would imply everyone acquiring perfect card stats in a few months, which is not very lucrative from a marketing point of view. Instead they could start a season with 50 base cards, and introduce cards with every update. Each T3/awakening could come with a premium card, and each uniform with a normal card. The normal cards get added to the dimension chests after the update, and the premium cards go into the store chests. All cards and effects reset after a year. This would ensure a fresh look to card collections and avoid a "meta". It would also give NM the freedom to push certain uniforms by attaching good cards with them.

TLDR Current system outdated, some stats given as to why, improvement suggestions.

Source: reddit.com

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