Splinterlands DEC values of potions

So with some help from @aggroed and @cryptoeater tonight I refined my model for valuing the DEC values of using the Legendary and Gold potions on Splinterlands/Steem Monsters. There are three different places the potions take effect: on beta packs, on orbs, and on reward card issuance. It gets more fun because the value is calculated differently for each. Legendary potions cost 20,000 DEC and Gold potions cost 25,000 DEC so it's good to know how much they'll return. (I've used the 100% potions for this analysis but the ev of the others is the same, just reduced at par with their price.)

We'll start with Rewards, because they're the easiest - every card's rarity is an independent chance based on the basic rarity table:

As you can see, none of the potion combinations are profitable on a pure DEC basis for reward cards, although the gold potion by itself comes pretty close. That's not to say you definitely shouldn't use potions - just that the extra value from them has to come from cards which are worth more than the DEC floor market price. However, there aren't a whole lot of those in Rewards - and importantly almost no golds - so it's probably not a great idea to use potions on your Reward cards.

Betas and orbs distribute a little differently because of the requirement for one rare+ card per pack, and here I'm thankful to @cryptoeater's analysis of pack distribution. This makes a 3-5% difference in the card distribution and changes the numbers a bit for Betas:

Interestingly the change in the numbers makes the legendary potion a little bit worse, because while both normal pack value and those with the potion increased, the normal pack value increased more. While again none of these options are immediately profitable by DEC, you should almost certainly use potions when opening beta packs because Beta packs, unlike Rewards, are full of cards whose market value is higher than their DEC value. Almost all Beta commons carry a significant premium, as do all summoners, especially the Legendary summoners. This is difficult to model without using live market prices, but as long as commons are trading well above DEC value it's a no-brainer.

Orbs, on the other hand, are super-easy. They trade for DEC like Alphas, at a 2x premium, which makes the decison very simple:

You should always use potions while opening orbs. Every potion option is immediately profitable by pure DEC value, and using both potions yields a remarkable 84% profit.

Additionally, the potion benefit from opening orbs is so high that you should take it even if you end up spending a significant fraction of the potion charges on Rewards. Even if 8/9 of the cards you open are Rewards, if the ninth one is from an orb you'll still come out ahead. So if you're someone who's mixing what cards you acquire, the potions still end up a pretty good deal as long as they're from orbs sometimes. It's still better to time your potions so that they're applied to orbs and betas, but if you're opening some orbs it's better to have them than not.

The basic upshot here: potions are essential when opening purchased cards, so we can expect demand for them to remain high. At 45k DEC per 100 packs, using them on all the remaining beta packs and orbs would cost nearly 250 million DEC. (Not to mention 466 million to buy the orbs.)

So, um, Buy DEC. That's a pretty amazing amount of demand.