There's a story about designing aircraft cockpits I like. The army designed a cockpit to fit an average pilot, based on 10 dimensions (e.g. arm length). But it turned out that no pilot fit the average on all 10 categories, and only 3.5% of pilots fit average on even three categories. There was no such thing as an "average" pilot.
Why does this matter? In a lot of discourse around splinterlands, there is a lot of talk about the average value of a pack, known as the expected value. What this means, is that, if I buy and open a lot of packs, on average, the packs will be worth that much. What it does not mean, is that every pack will have that exact value. Just as there are no average pilots, there are very few average packs. Most packs will be worth very little (see my one opened pack below) and a few packs will be worth a lot.
The strategy of buying packs for airdrop chances
In a recent video, @bulldog1205 advocated a strategy which I think will work for whales, but will not work for the average player, and it is because of the point above. The strategy, in short, is to take advantage of the high expected value of chaos legion packs relative to the total cost of a pack. So if a pack costs ~$6.6 to buy (~$2.6 for a voucher + $4 for the pack), but has an expected value of ~$5.93, you can open a pack and sell its contents for a net cost of $0.67 to get access to airdrop chances. And if airdrop cards are valuable (e.g. legendary summoners), you should make much more than $0.67 on average with the airdropped cards.
What's wrong with the strategy
If you're familiar with statistics or if you've been paying attention, you'll see the problem with the strategy above. It depends on the expected value of the pack, which only works out in the long run, over many packs. So yes, if you buy 100s or 1000s of packs, that math will work out, and you'll probably come out ahead (in his video, Bulldog says he's come out slightly ahead of EV on the packs he's bought, spending ~$0.2 per airdrop chance). I previously wrote a post showing that unless you open 1000 packs, you're putting yourself at the mercy of luck rather than a nice, smooth probability distribution.
But if you're an average player, this is not a good play. After seeing Bulldog's video, you might think it's a good strategy, go buy 10 packs, and open them up to find a total of $10 of value, instead of the $60 you'd expect on average. Because most packs will be worth less than average. So only follow this plan if you're going to buy A LOT of packs.
An additional minor, but still important error
In the same video and calculation, Bulldog determines that spending ~$50 doing this will net you a legendary summoner. While correct again in expectation, this is not likely going to work out if you buy only a few packs. If you buy 75 packs, and airdrop rates are similar to untamed, you will, on average, expect one legendary summoner. But your chance of getting 0 in this scenario is still 37%. This math only is certain once you buy enough packs for a guaranteed airdrop ~450, which will cost ~$315. At that price, you'd be guaranteed one of each legendary summoner (ish, depending on guarantee numbers). Again, assuming the expectation is the truth is likely to bite you in the ass unless you buy a lot of packs.
Conclusions
Bulldog's strategy is good for him, as he's buying 100s of packs, and the numbers average out nicely. But if you're only thinking of buying 10s of packs, I'd advise against it, as you are likely to lose more money than him on the deal. Instead, sell your vouchers or hold onto them and use them to get bonus packs in the general sale.
Hat tip to @jaelove for mentioning the video in relation to a previous post of mine regarding voucher strategies.
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