tl;dr - Purples are never worth your time.
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We will assume that one always succeeds when upgrading maps, a best case scenario. We will also assume that one fights with a party of 4 to maximize bonuses. Assume that the player only spends wine to upgrade.
Knowing this, we can answer the question if it is better to spend 2 wines on 2 blue maps, or 2 wines on one purple:
But what about if we have 3 wines? We can now potentially upgrade to an orange, which increases rewards by 33% for the opener. This allows for the following combinations:
Okay, easy enough. Orange looks great if you never fail. So what if we fail on one upgrade? That will alter the shards-per-wine ratio. Again, assuming no failures:
Blue = (56 - 36) * 3 = 60 shards/wine
Purple = (72 - 36) shards * 3 / 2 wine = 54 shards/wine
Orange = ((108 * 1.33) - 36) shards * 3 / 3 wine = 107.64 = 108 shards/wine
Orange looks pretty nice, doesn't it? Here's what happens if there is a failure upgrading from blue to purple:
Blue = 60 shards/wine
Purple = (72 - 36) shards * 3 / 3 wine = 36 shards/wine
Orange = ((108 * 1.33) - 36) shards * 3 / 4 wine = 80.73 = 81 shards/wine
Orange still looks pretty good. Let's look to see what happens if purple fails once to upgrade to orange:
Orange = ((108 * 1.33) - 36) shards * 3 / 5 wine = 64.58 = 65 shards/wine
Even after two failures, orange outperforms blue. After a third failure, blue wins out. The arithmetic is left as an exercise for the reader.
"So what if I want to spend 8 wines to guarantee an orange map?"
Don't. Spending 6 wines on an orange map is a losing proposition. Spending 8 will only make it worse. I learned this the hard way.
*****
By chance, does anybody have figures on the probability of failure to upgrade? This could help my modeling out a bit more.
*****
We will assume that one always succeeds when upgrading maps, a best case scenario. We will also assume that one fights with a party of 4 to maximize bonuses. Assume that the player only spends wine to upgrade.
Knowing this, we can answer the question if it is better to spend 2 wines on 2 blue maps, or 2 wines on one purple:
- 1 purple + 4 green = 1 * (72 * 3) + 4 * (36 * 3) = 648
- 2 blue + 3 green = 2 * (56 * 3) + 3 * (36 * 3) = 660
But what about if we have 3 wines? We can now potentially upgrade to an orange, which increases rewards by 33% for the opener. This allows for the following combinations:
- 1 orange + 4 green = 1 * (108 * 3 * 1.33) + 4 * (36 * 3) = 862.92 = 863
- 1 purple + 1 blue + 3 green = 1 * (72 * 3) + 1 * (56 * 3) + 3 * (36 * 3) = 708
- 3 blue + 2 green = 3 * (56 * 3) + 2 * (36 * 3) = 720
Okay, easy enough. Orange looks great if you never fail. So what if we fail on one upgrade? That will alter the shards-per-wine ratio. Again, assuming no failures:
Blue = (56 - 36) * 3 = 60 shards/wine
Purple = (72 - 36) shards * 3 / 2 wine = 54 shards/wine
Orange = ((108 * 1.33) - 36) shards * 3 / 3 wine = 107.64 = 108 shards/wine
Orange looks pretty nice, doesn't it? Here's what happens if there is a failure upgrading from blue to purple:
Blue = 60 shards/wine
Purple = (72 - 36) shards * 3 / 3 wine = 36 shards/wine
Orange = ((108 * 1.33) - 36) shards * 3 / 4 wine = 80.73 = 81 shards/wine
Orange still looks pretty good. Let's look to see what happens if purple fails once to upgrade to orange:
Orange = ((108 * 1.33) - 36) shards * 3 / 5 wine = 64.58 = 65 shards/wine
Even after two failures, orange outperforms blue. After a third failure, blue wins out. The arithmetic is left as an exercise for the reader.
"So what if I want to spend 8 wines to guarantee an orange map?"
Don't. Spending 6 wines on an orange map is a losing proposition. Spending 8 will only make it worse. I learned this the hard way.
*****
By chance, does anybody have figures on the probability of failure to upgrade? This could help my modeling out a bit more.
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