# Only buy packs from Splinterlands if you get enough for a guaranteed airdrop. Otherwise, buy from the P2P marketplace. (math inside)

Well, today is the day where a lot of people are waking up and finding only coal in their stocking. I'm talking about airdrops from Phase 2. Yes, the posts you'll see here will largely be the people who got lucky and got more than they expected, but the silent majority will be people who got less than they were hoping for.

#### What does buying 300 vs. 299 packs get you?

The drop chance per card per pack was 0.3%, with a guaranteed at 300 packs. I previously posted that people should only buy packs using vouchers during phase 2 if they were going to buy at least 300, as the probability shifts so much when you shift that threshold. I used the below graph to illustrate, where the 300th pack give you a free 20% probability in getting an airdrop.

What this graph didn't get across is just how huge a difference it makes. By getting enough packs for a guaranteed airdrop, you completely eliminate the chance of getting 0, which shifts the entire probability distribution up.

Here is the probability distribution if you buy 299 packs. You can see the most likely outcome is 0 legendaries at ~40%. The expected value of this distribution is 1; you expect an average of one airdrop. The median is also 1, so 50% of the time you'd expect at least one airdrop.

Now let's see what happens if we buy 300 packs. We have 0% of getting none, so we have no feelsbad moments. All that probability has been shifted to 1 airdrop, meaning we now have ~70% at one legendary. The median is still 1, but the mean is 1.3; by getting the guarantee, we've increased our expectation by ~0.3 airdrops.

#### Conclusions

If you're buying less than the number of packs needed for a guaranteed airdrop, you should buy them from the P2P marketplace. Full stop. The market prices things accordingly (I think even overvalues the potential of airdrops), and so you're paying for those airdrop chances even if you don't get it. During Phase 2, vouchers cost ~\$2, and got you (1/300)(30)(2) = \$0.20 in value of expected airdrops. Crazy! And even crazier if you didn't get enough to get a guarantee.

#### What's next?

General Sale. And between my previous article and this, I've got some surprising conclusions about whether to buy packs from splinterlands or from the P2P marketplace. If you want more of this content, pay attention as that post with less intuitive conclusions will be dropping tomorrow!

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Wow, I knew that the guaranteed airdrops would increase EV, but did not expect it to be by a whooping 30%! Thanks for doing the math :D

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(Edited)

1 - (1 - 0.003) ^ 299 = 59.3%
300th pack gives you 40.7% extra

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I think my math is right. I said

You can see the most likely outcome is 0 legendaries at ~40%.

Which aligns with your number (I rounded the 0.7%).

Where there might be a miscommunication is me saying

by getting the guarantee, we've increased our expectation by ~0.3 airdrops.

This is about a different metric. Instead of what is the probability of getting none, I'm now asking what is the expected value? The expected value of 299 is just under 1. The expected value of 300 is now ~1.3, a difference of 0.3. (expected value being the summation of the probability times the value across all possible values).

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