Mana Maximization (Hearthstone) I recently started playing Hearthstone and a statistic / probability question came up my mind. Here's a quick breakdown:
The game is a turn-based card game which involves "points" that you can used called Mana. The amount of Mana each player gets start with 1 (in the 1st turn), 2 (in the 2nd turn) up to 10 (in the 10th turn), then 10 for any turn after that. Each card has a specific Mana costs (also range from 1 to 10) associates with it and each card deck has 30 cards total. Each player gets 3 card to start, with the person going 2nd (since it's a turn-based game) gaining an additional card and an additional freebie Mana that can only be used once. The players have special powers which costs 2 Mana regardless of the hero that they use, and the hero power can be used each turn.
Assuming an average game length of 15 to 25 turns, my question is, what combination of cards in terms of Mana cost would maximize expected Mana spendage (i.e. always spend all of your mana at the end of each turn)? Also, the cards you draw are at random (in case that was not clear).
I apologize if the explanation above is confusing or unclear; I've only started playing the game a few days ago.
I will check regularly to see if I can clarify any of the game mechanics to anyone.
 A: Unfortunatly it's a lot more complicated than it seems to be.
I know what you would like to know but it wouldn't be really useful in the reality (of the game). Actually it would be quite useful in arena mode.
Let's list a few facts or things you haven't said :


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*Each player have 30 health points (HP), the game finishes when a player reach 0.

*You (your hero) also have a special power that can be used every turn for 2 mana (so you can use that if you want to save you card or have nothing else to do) (however, in some situation or with some heroes you can't use your power all the time, if you are full life and have no injured creature, you can't use priest power that restore 2hp.

*Some cards are permanent and stay on the board (creature), some are semi-permanent (weapons) others are gone when played (spells). If you play a permanent and the enemy doesn't remove it, you could not play anything the next turn and still going forward. If you play a spell and you don't do anything, you won't go any further.

*Some cards can draw others cards.

*Sometimes you don't want to play any creature anymore during the turn (let's say it will be turn 6 next turn and the paladin in front of you will certainly equality+consecration and clean all your board) so you'll prefer to play a secret, a drawing spell or whatever.

*You recover all your mana at the beginning of each turn and you can't store mana not used in a previous turn
In constructed game mode, it's really difficult to make the perfect mana curve for the deck you're trying to build. What you ask is possible in the case of putting only creature (with no drawing power) in your deck.
Knowing all of that there is not one perfect mana curve. Depending on the deck type you want to create you'll have to find the right mana curve adapted to it.
For example, let's say you want to play a "Zoo" type deck which is a deck with only low mana creatures : you'll play 1 to 3 card per turn, which means that your hand will be empty after a few turns and if the enemy resist/ clear your board, you'll end up with 1 low mana card in your hand each turn and loads of mana unused, basically it's lost.
So what can you do ?


*

*Add more drawing cards spells/creatures or pick a warlock

*Add a few higher mana cards
Sorry I didn't answer your question but I just wanted to point a few things that might useful. If someone take the time to find an optimized mana curve at least taking into account only probability, mana cost and ressources, I would be interested in it though. 
I've read some maths as well about the value of the cards with a lot of parameter depending of the turn, etc. That may interest you as well. I can't remember where I read that but you should find that easily too :p
