EPTBut I have fun doing calculations. I learned how to apply time values to money in my economics class this year. The math is dumb but I thought I could apply basic math to hearthstone.
Time value of cards
Obviously having more cards at all times gives you better options. But when is it better to have 5 cards? Turn 10? or turn 1?
What do all these cards have in common?
![[image loading]](http://i.imgur.com/xXfmwfs.png)
![[image loading]](http://i.imgur.com/vVCgg7O.png)
![[image loading]](http://i.imgur.com/8xb6UuN.png)
![[image loading]](http://i.imgur.com/ci0cKwc.png)
![[image loading]](http://i.imgur.com/R3NiVt0.png)
![[image loading]](http://i.imgur.com/eyPldsm.png)
They all give you cards. Novice engineer gives you one card but only after she is played. If we assume that getting that card only after spending 2 mana doesn't matter, then novice engineer is 1 card and 2 mana for 1 card returned and 1/2 stats. Another way of saying this is that 2 mana is worth 1/2 stats in the early game. Another card that gives 1/2 stats is the goldshire footman. If you added 1/1 to the stats of novice engineer you'd have 2/3, the stats of a regular 2 drop like river crocilisk.
Novice engineer's big sister, gnomish inventor gives you 1 card on turn 4, and also gives 2/4 stats. 2/4... that's like so much worse than chillwood yeti. Does this mean that gnomish inventor is a shit card?
I'd rather have more cards late game where mana is less of a hindrance and I can play 2,3, even 4 cards in 1 turn than early game where I'm limited to 1/2 cards. Most decks are centered around the 3/4 drop so if you're top decking 3/4 mana cards on turn 10 then that's like 6-7 mana wasted (don't tell me your hero power is worth 2 mana late game. It's not). A card on turn 4 is worth 4/5 (yeti) - 2/4 (gnomish inventor) = 2/1 in stats lost. 3 stats is worth 1.5 mana since minions grow in strength by 1/1 per mana in general. So it's now become more expensive to cycle through cards.
Now let's look at Arcane intellect. Arcane intellect trades 1 card and 3 mana for 2 cards. That means that 1 card is worth 3 mana later on in the game! It does help you to cycle through your deck and there are some decks that work off of cycling through decks because they want some great synergy like equality consecration/wild pyro/lots of 1/1 summonables or want to burn through their opponent's life with the right cards.
Sprint trades 7 mana and a card for 4 cards. That means that if you play a 7 drop card and have no mana left to do anything else in the turn, then 3 cards are worth 2.5 mana.
Druid of lore trades 2/3 in stats (war golem is a 7 drop with 7/7 stats and druid of lore is a 7 drop with 5/5 in stats) for 1 extra card. For him that means he's trading 2 mana(7-5) per card but he's a class specific card so he's allowed to be more efficient. Since he has a choose one mechanic he's supposed to be less efficient though than most class specifics though.
Nourish grants 2 extra card for 5 mana.
TL DR: Cards tends to have a fairly steady cost. When put on minions it tends to be cheaper than when put on spells. That's all I can see. This is Blizzard's perspective.
I have to disagree. I think extra cards are more valuable later on in the game and find topdecking against a warlock that's also topdecking impossible.
Time value of mana
![[image loading]](http://i.imgur.com/CPEZ4Bw.png)
Innervate grants you 2 mana regardless of what turn it is used. But if you can innervate on turn 1 and you go second, you can summon a yeti on turn 1 with innervate and coin. How broke is that? Many people can't deal with a yeti on turn 2 and have to lose lots of health or make inefficient trades which can set them behind and cost the game.
But if you use it on turn 10, it rarely does anything for you. Whoop dee doo, now you have 12 mana instead of 10. There are valid reasons to use innervate like on turn 6 to get an ironbark protector that can protect you enough to draw to late game.
![[image loading]](http://i.imgur.com/hxuNjSf.png)
Wild growth on the other hand, if used on turn 2 (no coin), gives you an extra mana crystal on turns 3,4,5,6,7,8 and 9. That's 8 extra mana, at the cost of 1 card and 2 mana. We said earlier that a card was worth anywhere between 1 and 3 mana. That's a net gain of between (8-3, 8-1) 5 and 7 mana!
But using wild growth on turn 2 causes you to lose board control. Because it gives you nothing else on turn 2. This means that you'll have to make some inefficient trades in the early game to make up that board control loss. You'll lose cards and mana compared to your opponent.
Mana is worth more earlier than later because having mana early on lets you gain board control and you are more gated by mana early on.
Nourish, shown again for reference grants 2 full mana crystals on turn 5. That means it'll be useful again on turn 6 (8 mana), turn 7 (9 mana), and turn 8(10 mana) for 6 mana gained. And it only costs you 3 mana (5 mana used, 2 mana returned). Using nourish at turn 5 is much safer than wild growth at turn 2 since nourish does not relinquish map control in the early game and lets you get your 7 drops much sooner.
I'll leave time value analysis on health as an exercise to the reader.
![[image loading]](http://i.imgur.com/if4VZgR.png)
