Any hard proofs I can use to improve?

Arena Discussion
I'm working in a STEM field researching stuff. And the number one rule is that whatever claim you made you must provide a proof for it. Or if you don't have one at least cite a paper that provides it. So the claims can be verified.

The problem is that even after 3 months I'm not sure what I'm doing. My win rate is horribly bad around 30-40% in arena, which means 1-2 wins average, and have never went above 4 at all so far. It's seems 4 wins is like a concrete wall, there were many times I had 4-0, and then from that point I kept losing and losing until I dropped out (at least I broke even).

On the other hand everyone here bragging about their 4-5 win average and the how they manage to do 12 wins several times a month. It's obvious I'm doing something horribly wrong, but unable to realize what, and what should be done differently.

I followed Kripp's tips on draft: first 10 cards for value, second 10 for synergies, last 10 for curving out. I did that and he goes to 7 wins and I go to 2.

I started to realize that all these tips are vague and based on feelings of past experience and intuition and not hard science, and this bothers me. And probably the main cause of constant sense of uncertainty and not knowing what I'm doing.

For example what is the ideal mana curve in arena? A good mana curve can be defined as a card distribution that minimalizes the amount of wasted mana in the long run. To find one, one can run a computer simulation that simulates drawing and playing the cards from hand 1000 times and average the number of lost mana. Feed this into an evolutionary algorithms and see the deck evolve into a perfect mana curve. I did just that wrote a computer program that simulates playing cards from hand (only the cost is considered). This way one can get the best curve for 6, 8 and 10 turns. Having the hard numbers at hand I know what curve I should to aim for best result. I haven't played enough yet to find out if this really improves anything or not. But the last 3 runs seem to be promising.

The next thing I would like to know is how to read the board? In every chess program or whatever game where the AI already superseded human skills there is a heuristics that evaluates the current state of the game and assigns a score to it. Negative infinite score means the opponent has lethal and losing is imminent, negative score means the opponent has better board than you, 0 means balanced state, positive score means your board is better, positive infinite means you have lethal and victory is imminent. Is there a method that allows evaluating the state of the game this way? This would allow me to choose the best move by reevaluating the board using hard numbers instead of just feeling what would be the right move.

The next thing I would like to know is how to determine which card is the best draw while drafting? Heartharena comes with a tier list but it's not published what was the method they used to assign the numbers. Since there is no research and no merit behind these numbers, I cannot take it seriously.
Again is there any objective scoring system based on mathematics and statistics proofs that would allow me to pick the best card and I can be confident it's really the best I can pick?
Long post. I'll try to keep my answer from not being even longer.
(EDIT: And I failed)

First: Games are not STEM research fields. You are playing vs human players, so if you want to bring scientific methods and research into it, you should look at psychology as a major field of influence.

Second: The one bit of hard science you can do on Arerna is the likelihood of achieving 12 wins routinely. Most games pit you against an opponent at the same score - the only exception is when that pool is very small, which only happens at the extreme win rates (say 10+ wins). Each game has a winner and a loser (ties are effective discarded in Arena). So you can make a mattrix of you many wins you should get based on your average win rate. The table for all players (which is the same as the players with a 50% average win rate) is at https://hearthstone.gamepedia.com/Arena#Exact_sequence_of_matches - I am sure you can make your own for any give win rate. And I am sure you will find that to have several 12-win runs a month requires both an insanely high average win rate and a huge number of games playes --> huge time investment.
I tend to take some of the claims made here with a grain of salt. A 50% win rate is average. Your win rate is below average - but it is definitely not "horribly wrong".

There are a lot of suggestions on how to draft and how to play Arena. But the one thing they all fail to mention, in my opinion, is that you need to be flexible. There are no hard and fast rules. There are lots of guidelines but it is up to you to determine whether they apply in your situation.

Kripp himself does not follow his tips to the letter. If he sees insane synergy in the 7th pick, he'll take it. If he has a tough choice at pick 15, he'll look at synergy AND value AND curve. If he sees insane value at choice 28, he'll sacrifice curve.

Ideal mana curve? Depends on play style. Do you prefer to play an aggressive style? More control oriented? Or true late-game attrition? All these styles require a decent amount of early drops (cards playable on turns 2-4), because passing too often in the early game gives you a disadvantage that is hard to return from. But aggro requires way more early game; attrition requires more late game. Also, do not just look at the mana curve - I deliberately use the term "playable on turns 2-4" without specifying mana. Warpath is a 2 mana spell but you would never play it on turn 2!
But this is also where the flexibility comes in. I myself tend to play a very control-oriented style. But in Arena, I have to go with what the draft tells me. I used to lose very hard whenever I had a draft with lots and lots of early threats and no late game, until I learned to adapt to the draft and play more agressive when I have a draft that requires me to.

Reading and scoring the board - I am sure that algorithms for this already exist. The AI opponents that Blizzard provides in some solo modes probably use these (but given how they sometimes play, I am not convinced they are really very good yet). I have sometimes seen evidence of accounts using bots to play on ladder (even though this is a violation of the terms of service), and they usually do an even worse job.
You compare it to chess, but in chess all variables are known. In Hearthstone, there is the board, but also my hand, my opponent's hand, and the undrawn cards in our decks. Those all need to be taken into account.
For instance, do I cast my Flamestrike now? The board value will obviosuly improve if I do - but I might still decide to hold it and play something else if I expect my opponent to play even more low-health minions next turn. Do I now silence their taunt so I can attack some other minions or do I keep the silence in hand as a counter to evenbigger future threats? And also, do I play my biggest threat now, or do I play a slightly lesser threat to seduce my opponent to play their counter, and THEN slam my actual big threat? (This is where the psychology comes in).

Note that playing Arena takes skill and experience (just like playing Ranked, though the skill do not necessarily transfer). Even if Kripp would draft your deck for you, you would still not be able to get the same number of wins he does. He has many years of experience, playing Hearthstone for several hours per day. You do not. He is much more aware of what cards an opponent is likely to have. He will see smart combo's using his cards in creative ways faster than you do. Even at the mulligan stage, he will already make better decision than you.

On tier list and how they are assembled: There currently are three tier lists that I know of.
HearthArena (https://www.heartharena.com/) uses a panel of experts to assess cards (I believe the names are published), but they also use the statistics they get from people that track their runs on their website to adjust the scores if a card has a better win rate then expected. Their final tier list os not published though I guess one could recoonstruct it by watching the scores their drafting tool gives to cards (it shows both the unadjusted score and an adjustment based on how the card fits in the total draft).
Lightforge (http://thelightforge.com/TierList) is made by two players, ADWCTA and Merps. Their list is public. They use an algorithm to weigh cards based on stats and card text, and then manually adjust based on their own experience. I don't think their algorithm is pubished, but they have spoken about it at length in their videos.
Icy Veins has a public tier list (https://www.icy-veins.com/hearthstone/arena-tier-lists) that is maintained by individual players. They are less known and they do not disclose how they weigh cards. They do provide some additional feedback on many cards to help you understand their strengths and weaknesses. They also have a generic arena guide (https://www.icy-veins.com/hearthstone/arena-guide) that you might find useful. I do not know how actively that page is maintained though - and I do know that Arena itself changes over time.

The bottom line of your post appears to be: are there any algorithms out there that guarantee picking the bast cards, and playing the games the best possible way. My answer: I hope not. If there were, then what fun would there be? Anyone would run those algorithms; we can just let the computers play themselves. The fun of playing games is that we have to use our experience, our intuition, and our skill.
Leave the hard numbers and predictable algorithms at your job. Playing Hearthstone is for leisure. Don't make it a second job. ;)
Oh, one more thing I forgot to add: Whereas HearthArena do not make their tier list or their accumulated statistical data publicly available, another deck tracker does.

Look at hsreplay.net to see an impressive amount of statistics on cards used in Arena. Deep link: https://hsreplay.net/cards/#gameType=ARENA
I was in your position a few years ago but have worked up to a 5.5 average.

To directly answer one of your questions, obviously you could create something that analyzes board states and other known factors but I think that would be relatively pointless because of the range of unknowns. Those unknowns include what your opponent is holding (we can make some guesses but there is still a large pool of possibilities) and that many cards have random effects. So this phase of the game is best approached through gaining experience and knowing which 3-4 cards should reasonably be accounted for or played around.

My stock advice that I give for players in your position is this:
1) Do a post-mortem (win or lose) where you identify the turn where the game was won (i.e. had the biggest swing in "Game Score"). Being able to identify these turns will help you when you encounter them later and you may play differently based on experience.
2) Play lots and play every class. Knowing the ways how each class *typically* wins will make you better at drafting, playing and playing against them.
3) Track your average. It's a long curve but if you keep playing, you will see it curve upwards. Periodically assess some of the strategies you are using and always be aware of the meta and how it changes because your strategies should evolve with it.
You refine your own heuristics ofc...

You analyze the choices you made. Watch your replays of any game you suspect you could have played better, made a different decision to increase chance of winning, or drafted a different card in another card's place etc. Your replays and draft choices are historical data. Coupled with the choices you made in game, there's your training data.

Every time you're faced with a hard decision, remember it. The choice you made when faced with that situation will be rewarded or punished. After enough iterations your brain will naturally train itself and make higher ev choices, purely through proportion of rewards/punishes/nulls.

At first, when you know nothing about the game, you'll probably go through every possible choice during analysis, every permutation of outcomes. But this is extremely inefficient. Unlike Go or Chess, even though HS has greater number of perms, there are way less VIABLE perms. So the branching factor is actually very small. Go is like 250, chess is like 40, HS is like 10... It's not that hard, just keep at it and you'll be able to eliminate non-viable lines immediately and only analyze the 5 or so viable lines each fork.

Another problem with your mindset is HS is a game of information asymmetry, unlike chess and go. You will not have every opponent's deck list in your historical data. You have to infer occurrence probabilities empirically, then each probability of opponent having and choosing to play certain cards, an estimate with low confidence unless you play a shlt ton.

Ideal mana curve is subjective, because of the word ideal. For any optimization, YOU define the constraints. Ideal for you isn't ideal for someone else. My definition of ideal is minimize probability of missing mana per turn, maximize bucket value and sum of all mana cost in deck. with card draw effects adding rest of deck's mean mana cost * number of card drawn, same for card generators etc. Bucket value is marginal effect coefficient from all the HS replay card stats. Multiple regression, ind variables are each card exiting in deck from draft pool, and dep variable is number of resulting wins. Only the super commonly picked cards have statistically significant coefficients. I don't know which ones do, nor do I care.

But rilly doe, you're playing a game for fun. It's more fun if you don't formalize the process... you'll might as well be scripting to execute engine moves instead of playing. Fuk that
But rilly doe, you're playing a game for fun. It's more fun if you don't formalize the process... you'll might as well be scripting to execute engine moves instead of playing. Fuk that


The fun part is done when I do my daily quests (I try to experiment with stuff there) or the weekly tavern brawl, where I have nothing to lose, only to win.

However I consider Arena competitive, where I want to get more back than I put in for that extra 50 gold.

----

It seems the mana curves I worked out work quite well. 4 wins with mage, 5 win warrior (the first time).

I aimed for the "10 turn, replace above 4 curve" because I got quite a few high cost drops at the beginning. This was the curve I aimed for (that's what my simulations brought out as the best):
0 0 4 5 6 5 4 3 2 1. (for 0-9 costs). I didn't really got exactly this. But it was quite close. The interesting thing the with warrior I didn't even had the killer tools (warpath, super collider, etc), just lots of high value minions I can play on curve most of the time. Especially from the midgrame.

I also tried to make up a way of card valuation. When deciding which card to pick I ask myself "How much net damage can this card do, before it's removed from play (divided by the mana cost)?" The idea is if I can have more damage output for the same mana cost, then I can kill the enemy hero earlier than they do the same. Sometimes the valuation is easy, sometimes are hard. I have trouble with weapons especially. They can have a plenty of damage output in multiple turns, but if you consider the fact that your hero also takes damage when using it against minions, they become much less attractive. And the conventional wisdom is that you generally not using weapons on face (unless lethal is imminent). So I will need assistance for properly valuing weapons.

I also strating to understand the problem of overtrading. And against classes that don't have access to a lot buffs, it's better to go face, and let them trade instead. While against classes the buff their minions, it's better to trade everything to prevent them from using the buffs.

Join the Conversation

Return to Forum