Reward value

https://hearthstone.gamepedia.com/Arena

We first convert all card packs to gold, and all cards to their dust value. The final result is a tuple of (gold, dust).

For reward pools, we take all possible rewards, normalize their ranges to the mean average, divide each possible reward by the total amount of possible rewards (assuming even distribution of all rewards and ranges) and multiply that final amount by the number of picks.

In order to convert random "golden or regular" card to its dust value, we also assume an even distribution between golden and regular, and assign it the mean of the dust value of both the golden and regular versions. (Those are noted as grcard)

All values here are approximation because we do not know the exact probabilities of each reward pool

Arena

0 wins

• 1 pack = 100 gold
• 1 of 25-40 gold, 25-40 dust, 1 common card
• = 1 of 32.5 gold, 32.5 dust, 5 dust

• = 10.83 gold + 10.83 dust + 1.7 dust

Total value: 110.83 gold, 12.53 dust

1 win

• 1 pack = 100 gold
• 1 of 30-50 gold, 25-50 dust, 1 common card, 1 card pack
• = 1 of 40 gold, 37.5 dust, 5 dust, 100 gold

• = 10 gold + 9.375 dust + 1.25 dust + 25 gold

Total value: 135 gold, 10.625 dust

2 wins

• 1 pack = 100 gold
• 1 of 40-60 gold, 40-50 dust, 1 common card, 1 rare card, 1 card pack
• = 1 of 50 gold, 45 dust, 5 dust, 20 dust, 100 gold

• = 10 gold + 9 dust + 1 dust + 4 dust + 20 gold

Total value: 130 gold, 14 dust

3 wins

• 1 pack = 100 gold
• 25-35 gold = 30 gold
• 1 of 20-25 gold, 20-25 dust, 1 common card, 1 rare card, 1 card pack
• = 1 of 22.5 gold, 22.5 dust, 5 dust, 20 dust, 100 gold

• = 4.5 gold, 4.5 dust, 1 dust, 4 dust, 20 gold

Total value: 154.5 gold, 9.5 dust

4 wins

• 1 pack = 100 gold
• 40-60 gold = 50 gold
• 1 of 20-30 gold, 20-25 dust, 1 common card, 1 rare card, 1 card pack
• = 1 of 25 gold, 22.5 dust, 5 dust, 20 dust, 100 gold

• = 5 gold, 4.5 dust, 1 dust, 4 dust, 20 gold

Total value: 175 gold, 9.5 dust

5 wins

• 1 pack = 100 gold
• 45-60 gold = 52.5 gold
• 1 of 45-60 gold, 45-60 dust, 1 common card, 1 rare card, 1 card pack
• = 1 of 52.5 gold, 52.5 dust, 5 dust, 20 dust, 100 gold

• = 10.5 gold, 10.5 dust, 1 dust, 4 dust, 20 gold

Total value: 183 gold, 15.5 dust

6 wins

• 1 pack = 100 gold
• 75-85 gold = 80 gold
• 1 of 45-60 gold, 45-60 dust, 1 common card, 1 rare card, 1 card pack
• = 1 of 52.5 gold, 52.5 dust, 5 dust, 20 dust, 100 gold

• = 10.5 gold, 10.5 dust, 1 dust, 4 dust, 20 gold

Total value: 210.5 gold, 15.5 dust

7 wins

• 1 pack = 100 gold
• 150-160 gold = 155 gold
• 1 of 20-30 gold, 20-25 dust, 1 common card, 1 rare card, 1 card pack
• = 1 of 25 gold, 22.5 dust, 5 dust, 20 dust, 100 gold

• = 5 gold, 4.5 dust, 1 dust, 4 dust, 20 gold

Total value: 280 gold, 9.5 dust

8 wins

• 1 pack = 100 gold
• 150-160 gold = 155 gold
• 2 of 20-45 gold, 20-25 dust, 1 common grcard, 1 rare grcard, 1 epic grcard, 1 legendary grcard, 1 card pack
• = 2 of 32.5 gold, 22.5 dust, 27.5 dust, 60 dust, 250 dust, 1000 dust

• = 2x(5.42 gold, 3.75 dust, 4.58 dust, 10 dust, 41.7 dust, 166.7 dust)
• = 10.84 gold, 453.46 dust

Total value: 265 gold, 453.46 dust

9 wins

• 1 pack = 100 gold
• 150 - 165 gold = 157.5 gold
• 2 of 20-120 gold, 20-50 dust, 1 common grcard, 1 rare grcard, 1 epic grcard, 1 legendary grcard, 1 card pack
• = 2 of 70 gold, 35 dust, 27.5 dust, 60 dust, 250 dust, 1000 dust

• = 2x(11.67 gold, 5.83 dust, 4.58 dust, 10 dust, 41.7 dust, 166.7 dust)
• = 23.34 gold, 457.62 dust

Total value: 280.84 gold, 457.62 dust

10 wins

• 1 pack = 100 gold
• 150-185 gold = 167.5 gold
• 2 of 65-125 gold, 65-95 dust, 1 common golden, 1 rare grcard, 1 epic grcard, 1 legendary grcard, 1 card pack

11 wins

• 1 pack = 100 gold
• 195-210 gold = 202.5 gold
• 2 of 70-180 gold, 60-95 dust, 1 common golden, 1 rare grcard, 1 epic grcard, 1 legendary grcard, 1 card pack

12 wins

• 1 pack = 100 gold
• 215-235 gold = 225 gold
• 3 of 25-185 gold, 1 common golden, 1 rare golden, 1 epic grcard, 1 legendary grcard, 1 card pack