Fortune draw win rate stats

Lore trivia: The beauty you see in the cover image is Nahla Oshannus, aka one of the new reward cards (Surgeblade) and also aka Djinn Oshannus's daughter! The image was created using Midjourney.

In this post I take a look at some high level calculations to help folks understand the chances of winning a card in the reward card fortune draws, as I've seen some comments floating around asking about this.

First off, let me explain how to calculate the odds here. If you have X draws, there are Y total draws, and Z prizes available, then the formula to estimate you probability of winning a draw is equal to the following:

Chance of winning: 1 - [(1 - X/(Y))^Z]

In a nutshell, you take your odds of losing (1-(X/Y)), then assume you lose every time (^78), and then you take the inverse of that (if you don't lose every time, it means you win at least once). Now in our case, you can only win ONCE, not more than once, but that doesn't affect this calculation. That's because the odds of winning more than once would only "compete" with the odds of winning once (and not with the odds of losing). Since you can only win once in this mechanic, it doesn't apply. If that doesn't make sense, let me know in the comments and I can try to further elaborate.

One other caveat before getting into the data: in the fortune draw mechanic since each winner can win only once, their draws are removed from the pool (i.e. the denominator) when they win. I did not include this in my calculation because it makes it a bit more complicated without adding much value. Assume for example we have 4000 players eligible to win prizes - you could then take the average number of draws by dividing the total draws by the number of players and remove that from the denominator after each "miss". However that would only reduce your denominator by 30 each time, which wouldn't meaningfully affect the result. However, you can look at the percentages below as a lower bound (i.e. actual win rates will be a fraction of a % higher than what's in the tables below due to the reduction in the denominator as eligible winners get removed).

Ok so here's the data for THIS draw (in a few hours). Here I used 125k as the total number of draws, which is what it is currently for the first draw:

You can see that if you only have 1 draw, you have 0.06% chance of winning a prize, while if you have 800 draws you have 39.4% chance of winning a prize. If that seems higher than you expected, remember the formula above - in order to NOT win any prize, you need to not win 78 times in a row. Trust the math!

Now I want to project this out to next week's draw and simulate the win % based on what people can reasonably expect if they max out their draws at each different SPS tier. The tables below show your yield based on maximizing your draws per batch in 1 league (i.e. Modern OR Wild) and, in the second table, in both leagues. It then shows the win rate based on the number of total draws. I used three different numbers for the total draws by extrapolating from the current total number of draws from 4 days of activity. If the extrapolation continues we'd be around 220-225k total draws, but of course it could be lower (less chests, less activity) or higher (more players, more SPS renting) so I wanted to show a few different scenarios.