This is a long reply and I don't want to come off offensive in any way. This is just my way of talking numbers
Price per limited booster seems a little backwards as it doesn't account for rares passed by the bots. EV calculation seems more straightforward. I'm not sure if there's a better source for average number of rares seen per draft so I'll use mine (76 rares over 20 drafts) for a rate of 3.75 taken per draft. I'll use Frank's numbers for a 50% win rate and value rares at 200 gems.
I think the price of a limited booster is the only value we can determine without subjective assumptions. Let's say this value is x. Both FK's and your calculations are based on defining x as a numerical value first. All the results are then based on this subjective value.
FK has rares at 412 gold (=82.40 gems) which I could get behind, you say 200 gems which I can't - see next.
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Packs: 5000 gold = 5 packs = 5 rares = 1000 gems EV
Bo1 gold draft: 5000 gold = 3.75 rares (750 gems EV) + 347 avg gem return + 1.33 avg reward packs (266 gem EV) = 1363 gems EV
This of course doesn't account for the wildcard track yet. As you noted, it's up to the individual to determine how valuable those wildcards are personally; given that I aim for (near) rare completion of each set and duplicate protection largely ensures I get the all the important rares from the set anyway, I value them only as much as a normal rare. At that rate, each tick of track progress to me is worth 33.3 gems. Updating the numbers:
Packs: 5000 gold = 5 packs = 5 rares (1000 gems EV) + 5 ticks (166.5 gems EV) = 1166.5 gems EV
Bo1 gold draft: 5000 gold = 3.75 rares (750 gems EV) + 347 avg gem return + 1.33 avg reward packs (266 gem EV) + 1.33 ticks (44.3 gems EV) = 1407.3 gems EV
The bolded part is the issue here. Let me try to reverse-engineer where you want to go with evaluations: For you, a rare wc is = 1 rare (FK has it at 6:1 and my calculations avoid this definition)
We can agree to treat everything below rare as zero for simplification purposes. So with your values, a booster contains 7/6 of a rare, ergo the actual rare is worth 171.43 gems and the 1/6 of a wc 28.57 gems.
As long as you stick to this personal evaluation of a wildcard, every event at 50% win-rate has a positive EV because the most expensive format (bo1 gold draft) costs you 129 gems. And you are right that a draft booster has the chance to contain more than 1 rare. So -with your numbers for #of rares- for 129 gems you get 1.25 rares, which are worth (1.25 x 171.43) 214.29 gems to you. So you win.
If we take FK's value of 82.40 gems, you get (1.25 x 82,40) 103 gems for an investment of 129 gems - ergo you lose. Now before someone else does it, this isn't entirely fair for FK did attribute some value to commons and uncommons and therefore got to this very low value. If we remove values for those cards and stick to his initial assessment of 1 wc = 6 rares, we'd get close to 50:50 in a booster, so the actual rare is at 500 (100 gems) and the wc progress has the same value.
With that number it's pretty close: 1,25 x 100 = 125, so you only lose 4 gems - it still is a negative EV.
You see, all these EV-based calcs are completely based on that personal evaluation of how much a rare is worth.
My approach removes that subjective step: I know that I want the 212 rares and I want them as cheap as possible. I don't need a random number how much those rares are worth, I just look at how much I pay for 1 rare in the various formats. And the answers are:
45,67 gems for 1.25 rares through gem draft -> 36.54 per rare
is better than
66,33 gems for 1.00 rares through sealed
is better than
buying a booster with FK's streamlined values: 100 gems for 1.00 rares (plus benefit of dupe protection)
is better than
129 gems for 1.25 rares through gold draft -> 103,20 gems per
is better than
buying a booster with your values: 171 gems for 1.00 rares
So what does this give? Bo1 gem draft is far and away the most efficient way to get rares being almost half the price of sealed which is next. If Bo1 gold draft is worth it, is quite subjective and requires that you put a very low value on wildcards. Ironically the target audience of gold draft are f2p players for which wildcards have much more value than they have to us who pay.
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Another thing you also have to consider is that limited lets you reinvest your winnings and play more events
I could but I think this is only relevant when you try to go infinite as a f2p. I don't worry about acquiring gems but only about spending them (and my gold) in the most efficient way.
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Sealed: Each earns an avg of 1002 gems, allowing 5 sealed runs before finishing with ~1000 gems. 30 rares + 15 reward packs.
Let me ignore that you start with a given amount of gems. This endeavour has cost 5x 998, so 4,990 gems. Subtracting the reward boosters at 3k gems, you've paid 1,990 gems for the 30 rares, which is 66.33 - see above, exactly what I claimed before
So you do pay a premium in sealed (never forget that this depens on win-rate and we assume 50% here) for the benefit of early access.
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Draft: 90k gold on 18 drafts comes to ~67 (18 * 3.75) drafted rares and ~24 (18 * 1.33) reward packs. 6240 gems (18 * 347 avg) are saved for following set release.
Spent: 90k gold ~ 18k gems
return before rares: 6,240 gems and 24 boosters -> ~11k gems
rare acquisition: 67 rares for 7k gems -> 104 gems per rare -> again see above (difference of 1 gem due to rounding)
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Sitting on 97 rares after that. 39 reward packs plus an avg mastery track of 39 packs plus assumed earn of ~12 packs total from rank rewards is 90 8-card packs; good for about 15 rare WC (12 from track, 3 in-pack) and 6 mythic WC (3 from track, 3 in-pack). That means 84 in-pack rares for a total of 181 rares, 15 rare WC, and 6 mythic WC.
If I spent that 90k gold on packs instead (those 6240 gems wouldn't exist in this scenario, but keeping mastery and rank packs the same) I'm looking at: 90 packs + 39 mastery track packs + 12 rank packs = 141 8-card packs. That's good for almost five trips 'round the WC track (19 rare WC and 5 mythic WC), along with about 6 rare and 6 mythic in-pack WC for about 25 rare WC and 11 mythic WC total. You're looking at 129 in-pack rares as well.
We can significantly shorten this by removing all the parts that are equal in both scenarios.
Let's look at the 90 drafts again where you simply trade (the gold equivalent of) 11k gems into 24 boosters and gems at no cost/gain.
Then remain 7k gems that you spend on 67 rares. The alternative to that is buying 35 boosters. Of course you can't get 67 rares out of those, so as long as you value wcs so little, you'll stay correct drafting even with gold. However I value wildcards higher (mostly mythics) so with the same numbers we get different results on what we should do.
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Any form of limited is my favorite way to play though, so I'm staying the course either way.
Then you can safely ignore any EV calculations
I do like limited, too and therefore I felt bad during my f2p time for spending gold on drafts when the lame alternative of buying boosters had more value - remeber that as a fp2 wildcards have tremendous value.