Devs have said that VIP Chests are 100x chance for Mythic. That means each VIP Chest has 10x the chance of a Gem Chest at only 5x the cost (45 gems vs 9 gems when buying in bulk). If the only thing you care about is getting a Mythic, you actually are better off spending your gems on VIP Chests.
From what we gather, the mythic drop rate should be around 1/100 for VIP Chests and 1/1000 for Gem Chests.
If that’s correct, here are some sobering statistics:
For 2250 gems, you can open 50 VIP Chests or 250 Gem Chests.
Chance of getting at least 1 mythic in 50 VIP Chests = 1 - .99^50 = 39.50%
Chance of getting at least 1 mythic in 250 Gem Chests = 1 - .999^250 = 22.13%
For 4500 gems, you can open 100 VIP Chests or 500 Gem Chests.
Chance of getting at least 1 mythic in 100 VIP Chests = 1 - .99^100 = 63.40%
Chance of getting at least 1 mythic in 500 Gem Chests = 1 - .999^500 = 39.36%
For 9000 gems, you can open 200 VIP Chests or 1000 Gem Chests.
Chance of getting at least 1 mythic in 200 VIP Chests = 1 - .99^200 = 86.60%
Chance of getting at least 1 mythic in 1000 Gem Chests = 1 - .999^1000 = 63.23%