One could guestimate the following based on known factors.
You could do but you would be making the schoolboy error of assuming that variance of luck doesn't exist. Some people just get very lucky and are able to gamble up a very small deposit to a very large balance.
I understand that winner may have started with a small amount and got very lucky and gambled a lot of money. But we are talking about a long standing amount of gambling, not like he gambled once and got lucky, we are talking about him gambling thousands every month, that is a lot of money.
This is why it is a shock to many people and most of us have hard time believing this dude started with a few bitcoins at best and managed to reach to 4000+ bitcoins wagered, that is still in the possibility of what could happen, but we are still talking about something that would require a few miracles in a row. Obviously you know what you are talking about and we do not, you can see what he deposited and we do not, which is why we can't say this happened or that happened because we all would be guessing it. However you should also realize how hard it is for us to understand something like a few bitcoins turning into few thousand bitcoin wagering.
The one thing they did to help keep the winning streak going for so long was to make very few rolls each day. Someone using auto-bet or a script would have made the same number of bets they did in 3 months in 1 day. The smaller the sample size the bigger the chance of variance occurring. That can obviously work against you as well.