Each bet is not independent of each other. Each bet is determined by a algorithm where a nonce is incremented each bet. Which means each bet is dependent on all previous bets, since the bet with nonce=10 would never exist without the previous 9 nonces.
The algorithms that determine the outcome are pseudo random and not truly random.
The result is independent.
If I give you 10 rolls, can you predict the next? No. That is referred to as independence here, of the result.
The 11th roll is dependent on the server seed, client seed, and nonce and the previous rolls.
Example:
roll 1: 0.65
roll 2: 0.23
roll 3: 0.99
roll 4: 0.55
roll 5: 0.09
roll 6: 0.13
roll 7: 0.33
roll 8: 0.67
roll 9: 0.04
roll 10: 0.97
I would be willing to bet that the next roll will be higher then 1. But without the knowledge of the previous 10 bets I wouldn't.
At the same time I would like to see a server seed, client seed, nonce produce rolls anywhere close to what I listed.