Magic the Gathering: Arena is an online client for playing the collectable card game Magic the Gathering (MTG). One of the most popular MTG formats is Booster Draft - players open booster packs, build their decks, and play until reaching either 7 wins or 3 losses. Depending on your record at the end of the event, you receive rewards. MTG:A Premier drafts have the following payout structure:
| Wins | Gems | Packs |
|---|---|---|
| 7 | 2200 | 6 |
| 6 | 1800 | 5 |
| 5 | 1600 | 4 |
| 4 | 1400 | 3 |
| 3 | 1000 | 2 |
| 2 | 250 | 2 |
| 1 | 100 | 1 |
| 0 | 50 | 1 |
However, you can’t just use your win rate to calculate expected value from this event. That’s because the “first to 7 wins or 3 losses” format results in lower-than-expected event win rates for a given game win-rate. Consider the following sequence of games:
| Game 1 | Game 2 | Game 3 | Game 4 | Game 5 |
|---|---|---|---|---|
| W | W | L | L | L |
| W | L | L | L | W |
While both sequences end up with 2 wins and 3 losses, the second sequence’s final win wouldn’t be counted, as you’d be eliminated after the 3rd loss, and you’d only get 100 gems (compared to 250 gems in the first sequence). Let’s simulate this event structure at different win rates to see what the payouts are like. We’ll simulate 3000 events (sequences ending at 7 wins or 3 losses) for various winrates. Then we’ll calculate the expected gem payout, considering a premier draft costs 1500 gems to enter.
From this, you can see you need a single-game win percentage of over 65% before you can expect to break even on premier drafts in MTG: Arena. Here’s a table with the expected outcomes for gems and packs for different winrates:
| Single-game Win% | Average Net Gems | Average Packs |
|---|---|---|
| 0.30 | -1217.89 | 1.4380 |
| 0.35 | -1094.41 | 1.6656 |
| 0.40 | -989.63 | 1.8668 |
| 0.45 | -845.99 | 2.1464 |
| 0.50 | -664.64 | 2.5292 |
| 0.55 | -499.89 | 2.9018 |
| 0.60 | -308.27 | 3.3344 |
| 0.65 | -121.53 | 3.7904 |
| 0.70 | 87.78 | 4.3234 |