Draft Winrate Needed for F2P to Collect All Rares From The Current Set (tl;dr It's 45-54%)

**Tl;dr** Including the other free packs you earn, you can get all the rares in a set by using all your gold to do Ranked Draft if you have a 53-54% winrate and 4 wins per day without spending any rare wildcards. If you do 15 wins per day, you only need about a 49% winrate, again without spending any rare wildcards. If you spend your WCs to complete your set, then it's 51% for 4 wins/day and 45-46% for 15 wins/day.

**Intro**

I wanted to analyze if it was possible to obtain a complete set of rares without spending money, and if so what winrate do you need to accomplish this.

**Assumptions**

4 wins per day (550 gold)

Complete quests daily (750 gold quest once per week)

3 free packs from “PlayRavnica” type code

3 free packs per week

2 total packs and 1000 gold per month from Ranked Constructed and/or Ranked Limited: Should be easily doable to reach Gold on 1 ladder. If you can reach Gold on both you would get 4 packs and 2000 gold per month

13 weeks per set (4 sets per year)

212 Rares per set (53 x 4)

Draft 2.7 rares per draft : this comes from my personal experience drafting RNA with some selective rare drafting

You wait to open your packs until you are done drafting to get maximum duplicate protection.

You don’t get any 5th rares while drafting (though you will probably end up with a couple, which makes real numbers slightly worse than I am reporting).

You spend all your gold on Ranked Draft and nothing else.

You are only spending gold (and then the earned gems from draft). If you are spending money and using those gems to draft, the numbers are better than stated compared to buying packs.

**Winrates to Complete Rare Playsets**

Ranked Draft winrates required to obtain 100% of the rares in the current set. “Spend WCs” column means whether or not you spend the WCs you earn to complete your set. If you spend them you complete your set faster of course.

|Wins/Day|Spend WCs?|Winrate Required|Rare WCs Left| --:|:--|:--|--:| |4|No|53-54%|19| |4|Yes|51%|0| |15|No|49%|19| |15|Yes|45-46%|0|

**Set Completion with Opening Packs Only**

|Wins/Day|Spend WCs?|Rares Earned|% Rares Complete|Rare WCs| --:|:--|--:|--:|--:| |4|No|133|63%|27| |15|No|150|70%|30|

By drafting at the winrates noted in the previous chart (not spending WCs), you are giving up 8-11 Rare WCs in exchange for the extra 60-80 rares you need to complete your set.

Also note that if your winrate is 62%, then drafting is strictly better than buying packs valuewise (Ignoring the time it takes to draft), since you get the same number of prize packs that you would have gotten in the store, and you get all the drafted cards for free.

**Full Chart of Winrate vs Rare Set Completion**

(Edit for more explanation: Total Drafts refers to how many drafts you should be able to complete with the allotted gold and also any gems you win from draft. Total Rares refers to how many rares you drafted + how many rares you open in the packs you receive, both the draft prize packs and the packs from other sources. Rare WC earned is how many Rare WCs you will have after you open all your packs. % rares earned (inc WC) is % rares you will have if you spend all your rare WCs filling in the missing rares in your set rather than keeping them to craft other stuff)

4 Wins per day (101800 gold per set)

|Winrate|Total Drafts|Total Rares|% rares earned|Rare WC earned|% rares earned (inc WC)| --:|--:|--:|--:|--:|--:| |Packs Only|0.00|133.70|63.07%|26.81|75.71%| |40%|29.48|156.77|73.95%|15.47|81.25%| |42%|30.66|161.53|76.19%|15.79|83.64%| |44%|32.05|167.12|78.83%|16.16|86.45%| |46%|33.67|173.72|81.95%|16.60|89.78%| |48%|35.60|181.59|85.66%|17.13|93.74%| |50%|37.92|191.04|90.11%|17.78|98.50%| |52%|40.71|202.51|95.52%|18.56|104.28%| |53%|42.33|209.19|98.67%|19.02|107.65%| |54%|44.14|216.62|102.18%|19.54|111.40%| |55%|46.15|224.92|106.09%|20.11|115.58%| |56%|48.40|234.24|110.49%|20.76|120.28%| |58%|53.81|256.66|121.07%|22.33|131.60%| |60%|60.84|285.90|134.86%|24.39|146.36%| |62%|70.28|325.24|153.42%|27.16|166.23%|

15 Wins per day (120,000 gold per set)

|Winrate|Total Drafts|Total Rares|% rares earned|Rare WC earned|% rares earned (inc WC)| --:|--:|--:|--:|--:|--:| |Packs Only|0.00|149.63|70.58%|30.00|84.73%| |40%|34.75|176.82|83.41%|16.64|91.26%| |42%|36.14|182.43|86.05%|17.01|94.08%| |44%|37.77|189.02|89.16%|17.45|97.39%| |46%|39.69|196.80|92.83%|17.97|101.31%| |48%|41.97|206.08|97.21%|18.60|105.98%| |50%|44.69|217.21|102.46%|19.36|111.59%| |52%|47.99|230.74|108.84%|20.28|118.41%| |53%|49.90|238.61|112.55%|20.83|122.38%| |54%|52.03|247.37|116.68%|21.43|126.79%| |55%|54.40|257.15|121.30%|22.11|131.73%| |56%|57.05|268.13|126.48%|22.88|137.27%| |58%|63.43|294.57|138.95%|24.72|150.61%| |60%|71.72|329.04|155.21%|27.15|168.01%| |62%|82.85|375.41|177.08%|30.42|191.43%|

**Optional Boring Math Stuff**

How “Total Drafts” was calculated - When you use gold to draft, you get some gems back which you can then use to draft more, which gives you more gems and so on. You can calculate how many drafts you can expect to play per 5000 gold based on the ratio of the gems you earn/gem entry fee using the infinite geometric series sum equation.

number of drafts per 5000 gold = 1/(1- (gems earned/entry fee))

For example, at 52% winrate, you earn about 375 gems back for each draft (1/2 your gems). If you play a draft, you get 1/2 draft worth of gems back, then you use those gems to draft and get back 1/4 draft worth of gems and then 1/8 draft worth of gems and so on. Using the equation above, 1/(1- (375/750)) = 1/(1-½) = 2. Therefore, for each 5000 gold you earn, you expect to get about 2 drafts in. 4 wins per day gets you 101,800 gold. Divide by 5000 then x 2 = 40.72 drafts.

If you get 2.7 rares per draft, then you get 40.72 x 2.7 = 109.9 rares from the draft and 54.8 packs via prizes. You also get 51 packs for free from the various sources I mentioned previously, so 105.8 packs total. If you open the packs, ⅞ of them will contain a rare or 92.6 rares (you actually get slightly fewer than this due to losing a rare occasionally from a wildcard drop). Adding the 109.9 rare from the draft then 92.6 rares from the packs gives you 202.5 total rares, which is about 95% of the rares (since there are 212 total).