i am a legend: hacking hearthstone with machine learning - defcon 22 talk slides
TRANSCRIPT
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Digital Collectible Card Game
Released by Blizzard in 2014
Based of World of Warcraft universe
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Sometimes too interesting leads to un-intended consequences
Painting by http://www.jason-w.com/blog/the-fall-of-lordaeron
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Game complexity generates exploitable biases
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Outline
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Outline
1. Finding undervalued cards
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Outline
1. Finding undervalued cards
2. Predicting opponent deck
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Outline
1. Finding undervalued cards
2. Predicting opponent deck
3. Predicting the game outcome
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Outline
1. Finding undervalued cards
2. Predicting opponent deck
3. Predicting the game outcome
4. Incoming alien invasion (or not)
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
You hero
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
You hero
Opponent hero
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Hero health
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Deck
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
hand
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
hand
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
mana pool
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Weapon
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Minions
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
video of a turn
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
video of a turn
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Mana
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Mana
Attack
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Mana
Attack Health
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Card special abilities is what makes the game complex and interesting
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Card special abilities is what makes the game complex and interesting
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Finding undervalued cards
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Model assumptions
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
1. Mana cost is proportional to card power
Model assumptions
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
1. Mana cost is proportional to card power
2. The power of cards roughly increase linearly
Model assumptions
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
1. Mana cost is proportional to card power
2. The power of cards roughly increase linearly
3. Card effects have constant price
Model assumptions
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
1. Mana cost is proportional to card power
2. The power of cards roughly increase linearly
3. Card effects have constant price
4. A card have an intrinsic value
Model assumptions
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
1. Mana cost is proportional to card power
2. The power of cards roughly increase linearly
3. Card effects have constant price
4. A card have an intrinsic value
5. The value of the card is the sum of its attribute
Model assumptions
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
= +mana attack +health intrinsic value
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
= +mana attack +health intrinsic value4 4a + i= + 5h
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
6 = 6a + 7h + i
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
6 = 6a + 7h + i
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
6 = 6a + 7h + i 4 = 4a + 5h + i
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
6 = 6a + 7h + i 4 = 4a + 5h + i/6
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
6 = 6a + 7h + i
1 = 1a + 1.16h + i
4 = 4a + 5h + i/6
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
6 = 6a + 7h + i
1 = 1a + 1.16h + i
4 = 4a + 5h + i/6 /4
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
6 = 6a + 7h + i
1 = 1a + 1.16h + i
4 = 4a + 5h + i
1 = 1a + 1.25h + i
/6 /4
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
4 = 6d
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
4 = 6d 1 mana = 1.5 dmg
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
4 = 6d 1 mana = 1.5 dmg
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
4 = 6d
10 = 10d
1 mana = 1.5 dmg
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
4 = 6d
10 = 10d 1 mana = 1 dmg
1 mana = 1.5 dmg
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
4 = 6d
10 = 10d 1 mana = 1 dmg
Pre nerf (8 mana)
1 mana = 1.5 dmg
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
4 = 6d
10 = 10d 1 mana = 1 dmg
8 = 10dPre nerf (8 mana)
1 mana = 1.5 dmg
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
4 = 6d
10 = 10d 1 mana = 1 dmg
8 = 10d 1 mana = 1.25 dmgPre nerf (8 mana)
1 mana = 1.5 dmg
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
10 damages 4 damagesimply
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
15 damages 6 damages
10 damages 4 damagesimply
imply
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Hunting for under-valued cards
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
How to find undervalued cards?
Model cards
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
How to find undervalued cards?
Model cards
Reverse coefficients
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
How to find undervalued cards?
Model cards
Compute cards real value
Reverse coefficients
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
How to find undervalued cards?
Model cards
Compute cards real value
Reverse coefficients
Profit :)
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Simple 5 cards example
Use simpler coefficientsApproach illustrated
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Charge
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Charge Divine shield
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
4 = 4a + 3h + c + i
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
4 = 4a + 3h + c + i
6 = 5a + 2h + c + i
6 = 4a + 2h + c + d + i
3 = 3a + 1h + d + i
1 = 1a + 1h + d + i
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Reversing attribute cost
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Reversing attribute cost
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Reversing attribute cost
mana Atk Health Charge Divine Intrinsic
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Reversing attribute cost
mana Atk Health Charge Divine Intrinsic
4 4 3 1 0 1
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Reversing attribute cost
mana Atk Health Charge Divine Intrinsic
4 4 3 1 0 1
6 5 2 1 0 1
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Reversing attribute cost
mana Atk Health Charge Divine Intrinsic
4 4 3 1 0 1
6 5 2 1 0 1
6 4 2 1 1 1
![Page 75: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/75.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Reversing attribute cost
mana Atk Health Charge Divine Intrinsic
4 4 3 1 0 1
6 5 2 1 0 1
6 4 2 1 1 1
3 3 1 0 1 1
![Page 76: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/76.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Reversing attribute cost
mana Atk Health Charge Divine Intrinsic
4 4 3 1 0 1
6 5 2 1 0 1
6 4 2 1 1 1
3 3 1 0 1 1
1 1 1 0 1 1
![Page 77: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/77.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Reversing attribute cost
mana Atk Health Charge Divine Intrinsic
4 4 3 1 0 1
6 5 2 1 0 1
6 4 2 1 1 1
3 3 1 0 1 1
1 1 1 0 1 1
Least square
![Page 78: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/78.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Reversing attribute cost
mana Atk Health Charge Divine Intrinsic
4 4 3 1 0 1
6 5 2 1 0 1
6 4 2 1 1 1
3 3 1 0 1 1
1 1 1 0 1 1
Atk
Health
Charge
Divine
Intrinsic
=====
1
-1
2
1
1
Least square
![Page 79: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/79.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Reversing attribute cost
mana Atk Health Charge Divine Intrinsic
4 4 3 1 0 1
6 5 2 1 0 1
6 4 2 1 1 1
3 3 1 0 1 1
1 1 1 0 1 1
Atk
Health
Charge
Divine
Intrinsic
=====
1
-1
2
1
1
Warning these example attribute costs are bogus as we didn’t use enough cards
Least square
![Page 80: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/80.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Finding card real price using reversed coefficients
Atk = 1 Health = -1Charge = 2 Divine = 1 Intrinsic = 1Coeffs:
![Page 81: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/81.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Finding card real price using reversed coefficients
4a + 2h + c + d + i
Atk = 1 Health = -1Charge = 2 Divine = 1 Intrinsic = 1Coeffs:
![Page 82: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/82.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Finding card real price using reversed coefficients
4a + 2h + c + d + i4*1 + 2*-1 + 2 + 1 + 1 = 6
Atk = 1 Health = -1Charge = 2 Divine = 1 Intrinsic = 1Coeffs:
![Page 83: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/83.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Finding card real price using reversed coefficients
4a + 2h + c + d + i4*1 + 2*-1 + 2 + 1 + 1 = 6
Atk = 1 Health = -1Charge = 2 Divine = 1 Intrinsic = 1Coeffs:
![Page 84: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/84.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Finding card real price using reversed coefficients
4a + 2h + c + d + i4*1 + 2*-1 + 2 + 1 + 1 = 6
1a + 1h + d + i
Atk = 1 Health = -1Charge = 2 Divine = 1 Intrinsic = 1Coeffs:
![Page 85: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/85.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Finding card real price using reversed coefficients
4a + 2h + c + d + i4*1 + 2*-1 + 2 + 1 + 1 = 6
1a + 1h + d + i1*1 + 1*-1 + 1 + 1 = 2
Atk = 1 Health = -1Charge = 2 Divine = 1 Intrinsic = 1Coeffs:
![Page 86: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/86.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Finding card real price using reversed coefficients
4a + 2h + c + d + i4*1 + 2*-1 + 2 + 1 + 1 = 6
1a + 1h + d + i1*1 + 1*-1 + 1 + 1 = 2
Atk = 1 Health = -1Charge = 2 Divine = 1 Intrinsic = 1Coeffs:
Under-valued card!
![Page 87: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/87.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Redit story Thanks you for the feedback!
https://www.elie.net/hs
![Page 88: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/88.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Modeling dependance between characteristics
Thanks to Niels for the idea
![Page 89: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/89.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Charge = Atk * charge coeff
Windfury = Atk * windfury coeff
Divine = ? (health related?)
!
Modeling dependance between characteristics
Thanks to Niels for the idea
![Page 90: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/90.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Charge = Atk * charge coeff
Windfury = Atk * windfury coeff
Divine = ? (health related?)
!
Modeling dependance between characteristics
Thanks to Niels for the idea
Model also use a card budget: 2*mana + 1
![Page 91: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/91.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
oi
Et voila!
![Page 92: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/92.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Reversed budget coefficientsEffect cost per pointDestroy minion 10.63Board damage 3.69Draw card 3.68Divine Shield 2.74Freeze 2.04Silence 1.66Damage 1.64Durability 1.22Stealth 1.21Attack 1.14Taunt 1.02WindFury 0.96SpellPower 0.93Health 0.81Battlecry heal 0.69Battlecry self hero heal 0.68Charge 0.65Intrinsic value 0.32
![Page 93: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/93.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Reversed budget coefficientsEffect cost per pointDestroy minion 10.63Board damage 3.69Draw card 3.68Divine Shield 2.74Freeze 2.04Silence 1.66Damage 1.64Durability 1.22Stealth 1.21Attack 1.14Taunt 1.02WindFury 0.96SpellPower 0.93Health 0.81Battlecry heal 0.69Battlecry self hero heal 0.68Charge 0.65Intrinsic value 0.32
2 coeff point ~ 1 mana point
![Page 94: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/94.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Reversed budget coefficientsEffect cost per pointDestroy minion 10.63Board damage 3.69Draw card 3.68Divine Shield 2.74Freeze 2.04Silence 1.66Damage 1.64Durability 1.22Stealth 1.21Attack 1.14Taunt 1.02WindFury 0.96SpellPower 0.93Health 0.81Battlecry heal 0.69Battlecry self hero heal 0.68Charge 0.65Intrinsic value 0.32
Effect Cost per pointOpponent draw card -3.97Discard cards -2.67Overload -1.68Self hero damage -0.54
2 coeff point ~ 1 mana point
![Page 95: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/95.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Reversed budget coefficientsEffect cost per pointDestroy minion 10.63Board damage 3.69Draw card 3.68Divine Shield 2.74Freeze 2.04Silence 1.66Damage 1.64Durability 1.22Stealth 1.21Attack 1.14Taunt 1.02WindFury 0.96SpellPower 0.93Health 0.81Battlecry heal 0.69Battlecry self hero heal 0.68Charge 0.65Intrinsic value 0.32
Effect Cost per pointOpponent draw card -3.97Discard cards -2.67Overload -1.68Self hero damage -0.54
2 coeff point ~ 1 mana point
![Page 96: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/96.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Cos
t est
imat
ed b
y th
e al
gorit
hm (i
n m
ana)
0
1
2
3
4
5
6
7
8
9
10
Cost assigned by Blizzard (in mana)0 1 2 3 4 5 6 7 8 9 10
![Page 97: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/97.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Cos
t est
imat
ed b
y th
e al
gorit
hm (i
n m
ana)
0
1
2
3
4
5
6
7
8
9
10
Cost assigned by Blizzard (in mana)0 1 2 3 4 5 6 7 8 9 10
undervalued cards
![Page 98: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/98.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Cos
t est
imat
ed b
y th
e al
gorit
hm (i
n m
ana)
0
1
2
3
4
5
6
7
8
9
10
Cost assigned by Blizzard (in mana)0 1 2 3 4 5 6 7 8 9 10
undervalued cards
overpriced cards
![Page 99: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/99.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Model found a couple of clearly undervalued cards :)
Cos
t est
imat
ed b
y th
e al
gorit
hm (i
n m
ana)
0
1
2
3
4
5
6
7
8
9
10
Cost assigned by Blizzard (in mana)0 1 2 3 4 5 6 7 8 9 10
undervalued cards
overpriced cards
![Page 100: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/100.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Most under-valued cards (~130 cards)
Full data https://www.elie.net/tools/hearthstone/cards_value
![Page 101: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/101.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Taking it to the next level
![Page 102: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/102.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
• 100 000 games from May to June
• Thanks to … for it :)
• Need a longer term solution
Game replays
![Page 103: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/103.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Pricing cards with unique effects
![Page 106: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/106.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Cards in hand
![Page 107: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/107.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Health Real Value
1 1.3
2 1.9
3 2.5
4 3
5 3.6
6 4.1
7 4.7
8 5.3
9 5.9
Cards in hand
![Page 108: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/108.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
1.31.9
2.5
3.0
3.6
4.2
4.7
5.35.9
OverpricedFairUndervalued
Num
of T
wilig
ht D
rake
s m
ade
0
500
1000
1500
2000
2500
Drake Health1 2 3 4 5 6 7 8 9
Average real value 3.7
![Page 109: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/109.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Twilight drake price is fair
1.31.9
2.5
3.0
3.6
4.2
4.7
5.35.9
OverpricedFairUndervalued
Num
of T
wilig
ht D
rake
s m
ade
0
500
1000
1500
2000
2500
Drake Health1 2 3 4 5 6 7 8 9
Average real value 3.7
![Page 112: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/112.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Cards played
this turn
![Page 113: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/113.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Edwin size Real value2/2 1.094/4 3.046/6 4.988/8 6.9210/10 8.8712/12 10.5114/14 12.7516/16 14.7018/18 16.6420/20 18.5822/22 20.53
Cards played
this turn
![Page 114: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/114.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
1.1
3.0
Over-pricedFairUndervalued
5.06.9
8.9
10.8
12.8
14.7
16.6 18.620.5 22.5 24.4 26.4
Num
of V
anCl
eef m
ade
0
100
200
300
400
500
600
700
800
VanCleef size (atk/hp)2/2 4/4 6/6 8/8 10/10 12/12 14/14 16/16 18/18 20/20 22/22 24/24 26/26 28/28
![Page 115: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/115.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
1.1
3.0
Over-pricedFairUndervalued
5.06.9
8.9
10.8
12.8
14.7
16.6 18.620.5 22.5 24.4 26.4
Num
of V
anCl
eef m
ade
0
100
200
300
400
500
600
700
800
VanCleef size (atk/hp)2/2 4/4 6/6 8/8 10/10 12/12 14/14 16/16 18/18 20/20 22/22 24/24 26/26 28/28
Average real value 8.1
![Page 116: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/116.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
VanCleef is undervalued, a fair price is probably between 5 and 7 mana
1.1
3.0
Over-pricedFairUndervalued
5.06.9
8.9
10.8
12.8
14.7
16.6 18.620.5 22.5 24.4 26.4
Num
of V
anCl
eef m
ade
0
100
200
300
400
500
600
700
800
VanCleef size (atk/hp)2/2 4/4 6/6 8/8 10/10 12/12 14/14 16/16 18/18 20/20 22/22 24/24 26/26 28/28
Average real value 8.1
![Page 119: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/119.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Num Minions
![Page 120: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/120.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Num Minions
Damage Value
4 6.5
8 13.9
12 21.3
16 28.6
20 36.0
24 43.4
28 50.7
Board damage coeff
![Page 121: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/121.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Num Minions
![Page 122: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/122.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Num Minions
Normal damage coeff
Damage Real Value
4 2.43835
8 5.71835
12 8.99835
16 12.27835
20 15.55835
24 18.83835
28 22.11835
![Page 123: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/123.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Flamestrike price is fair Don’t split board damage and single damage coeff
2.4
5.7
9.0
12.3
15.6
18.822.1
Over-pricedUndervalued
Num
of F
lam
estik
e ca
sted
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
Potential damage4 8 12 16 20 24 28
![Page 124: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/124.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Predicting cards
Predicting opponent deck
![Page 125: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/125.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Celine
![Page 126: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/126.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Celine
Our tool :)
![Page 127: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/127.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
My deck with card tracking
Game metrics
Opponent cards played so far
Opponent next cards prediction
Real time dashboard
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Game metrics
MeOpponent
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
My deck
T = TotalP = PlayedD = Dead
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
My opponent
T = TotalP = PlayedD = Dead
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Predictions
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Game data from
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Sniff packets
Game data from
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Sniff packets
OCRGame data from
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Sniff packets
OCR
Debug log
Game data from
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Sniff packets
OCR
Debug log
Game data from
Real logs from Blizzard like in WoW ?
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Demo video
https://www.youtube.com/watch?v=--byrlBQLCY
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Demo video
https://www.youtube.com/watch?v=--byrlBQLCY
![Page 139: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/139.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Turn by Turn History
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Available on Github LightWind/hearthstone-dashboard
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Naxx new cards made the meta to unstable to be predicted accurately for now
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Anatomy of our prediction system
Model card affinities
![Page 143: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/143.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Anatomy of our prediction system
Model card affinities
Evaluate affinities
![Page 144: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/144.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Anatomy of our prediction system
Model card affinities
Learn from replays
Evaluate affinities
![Page 145: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/145.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Anatomy of our prediction system
Model card affinities
Learn from replays
Evaluate affinities
Profit :)
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Modeling cards affinities
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Cards bigrams
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Cards bigrams
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Cards bigrams
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Cards un-ordered bigrams
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Evaluate cards affinities
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Played
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Played
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Played Bi-grams
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Played
500
Bi-grams
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Played
500
350
Bi-grams
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Played
500
400
350
Bi-grams
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Played
400
500
400
350
Bi-grams
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Played
400
500
400
350
Bi-grams Ranked Predictions
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Played
400
500
400
350
Bi-grams
750
Ranked Predictions
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Played
400
500
400
350
Bi-grams
500
750
Ranked Predictions
![Page 162: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/162.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Played
400
500
400
350
Bi-grams
500
750
400
Ranked Predictions
![Page 163: I am a legend: Hacking Hearthstone with machine learning - Defcon 22 talk slides](https://reader035.vdocuments.us/reader035/viewer/2022062902/58f9a99e760da3da068b709e/html5/thumbnails/163.jpg)
Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Training: 45000 replays
Testing : 5000 replays
1 model per class
Training and evaluation
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Suspense is killing me
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
97% success rate for best prediction by turn 3
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Best predictionAverage10th prediction
Prob
abilit
y pr
edic
tions
will
be p
laye
d
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Turn2 3 4 5 6 7 8 9 10
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Best predictionAverage10th prediction
Prob
abilit
y pr
edic
tions
will
be p
laye
d
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Turn2 3 4 5 6 7 8 9 10
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Predicting game outcome
How to optimize deck for mana-throughput
Hero powers comparison
Comparing decks typesWhat’s next?
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Celine & Elie Bursztein I am a legend - Defcon 2014 https://www.elie.net/hs
Thank you! https://www.elie.net/hs & @elie/@cealtea on Twitter
http://swiatgry.pl/tapety/pc/5488,hearthstone_heroes_of_warcraft