Based On my experience:
F=earnings from free rolls.
D=total deposits minus total payouts.
C=earnings from referral commissions.
E=daily interests.
B=current balance.
X=something that has been changed recently.
C will be counted as D (not F).
E will be counted as D (as someone said that he saw captchas for some free rolls then saw no captchas and again captchas reappeared , the site paid daily interests so captchas removed for some rolls)
We must meet these conditions to remove captchas:
1. B must be at least X.
2. D(+C+E) must be more than F.
X was 30k before, but now I think it's 500k.
Spending some coins in multiply & lottery tickets will also remove captchas temporarily.
So if you deposit 500k , you'll see no more captchas until you reach 0.01 , it takes 7-8 months.
Interesting! Also, ivebeenpwnd2 below you seems to agree with the B ≥ 500k. (How di u find the '≥' symbol?)
BTW, since I already have no captcha the only reason I'm trying to figure this out is to see if it also applies to my freedoge account, where I still have captcha...
Let's see if this applies to me:
F = 0.00161312
BTCD = 1.33296526 - 0.00012567 = 1.33283959
BTCC = 0.00000000
BTCE = 0.00004770
BTCB = 0.00082345
BTCX = 0.00500000
BTCConditions test:
1. B >= X ---> 0.00082345 >= 0.00500000 ---> FALSE
2. [D + C + E] > F ---> [1.33283959 + 0 + 0.00004770] > 0.00161312 ---> 1.33288729 > 0.00161312 ---> TRUE
Did your hypothesis require both [1 AND 2] be TRUE,
or did it require either [1 OR 2] to be TRUE?
As you can see above, for me it works for [1 OR 2] only, if same for you, then we may have a solution.
However, if [1 AND 2] is required to remove your Captcha, then we need to do some more work...