Mathematically, you should always gamble for 500k jades, and here's why.

First, let me introduce you to a simple but fun math: Expected Value = (Probability of reaching a scenario x what you get from that scenario) summed over all possible scenarios stemming from your choice. Essentially, it is the weighted average of all possible outcomes.

Now, let's look at what can happen in one phase of the event i.e. a single day of choosing what to do. We have:

Option 1: 100% chance of getting 100 jades, so EV = 100

Option 2 has 3 cases:

  • 90% chance of getting 50 jades: EV = 0.9 x 50 = 45
  • 10% chance of getting 600 jade: EV = 0.1 x 600 = 60
  • very low chance of getting 500,000 jades. Assuming everyone (about 19m players according to activeplayer.io) chooses this option, then EV is 1/19m x 500,000 which turns out to be about 0.025 So the total EV for Option 2 is (at least) 105.025

The EV for option 2 is ALREADY slightly higher even without the jackpot and I’m 100% sure it’s intentional by hoyo lol.

Now, let's consider the long run. Logically, what should we do over the 7 days of this event?

  • If you choose 100 jades every day, you are guaranteed to get 700 jades, simple.
  • Gamble every day, lose every day, and get 350 jades. Bruh.
  • However, notice that if you gamble every day and get 50 jades 6 times and 600 jades just once, you will have 900 jades in total, and that's the second-to-worst case, which is already better than not gambling!

Now, what are the chances of winning 600 jades at least once in 7 days? It's 100%-(the chance of not winning 7 times in a row) which is 90% x 90% x ... 7 times. So the chances are 1-(0.9)^7 which is around 52%. It's actually better than the chance of winning the actual gacha in this game!

(An aside: By the binomial distribution, the chance of winning 600 jades *exactly* once in 7 days is about 37.2%, twice is about 12%, and the chance decreases rapidly; for example, you have only 2.3% to get 600 jades 3 times etc. But the sum of these chances from winning 1 time to 7 times equals 52% as shown above)

But wait, can we do better? What would happen if we try to strategize a bit and choose to gamble only n out of 7 days? Let's math it out as well:

  • for each of the 7-n days we do not gamble, we automatically get 100 jades
  • for each of the n days we do gamble, we have the EV of 105.025 from above which will decrease to 105 in case you win 500k since you can't win more than once, so let's just say 105 for convenience.

Thus, the total jade you get is J = 105n + 100(7-n) = 700 + 5n. Notice that J increases with n, which means the more days you choose to gamble, the more expected jades you get over this event. This is without even considering the chance of winning 500k jades.

In conclusion: yes, the more “logical” option is to be a true gacha player and gamble. However, keep in mind that this is just simple math without any of the mental side (for example, if you are a risk-averse and just want some nice, guaranteed 700 jades or a risk-loving person who thinks 'even if I lost all of them I can just get 350 jades in less than a week'). Also, this result DOES NOT GUARANTEE that you’re always going to be better off with gambling. But hey, it's not like we'll lose anything: just win some or win more!