Multi Armed bandit tests need even more traffic, as there are more variations being tested. I think you have to be careful with false positives in AB testing - drawing conclusions too fast can nullify it's usefulness.
The different between "traditional" A/B testing and Multi-Armed Bandit has nothing to do with the number of treatments. A/B is really shorthand for A/B/n.
In an A/B test, the probability of selecting an "arm" (a treatment to show to the visitor) is equally distributed. Google Optimizer differs by adjusting the traffic distribution, sending more traffic to better performing options, what's usually called MAB approach.
The difference is that MABs will more quickly converge on the "winning" variation, but are more likely to get stuck in a local minimum. EG, if an "worse" option performs better right off the bat, the MAB might send most traffic to it. This would take a while for the algorithm to "recover".
The major advantages of the MAB approach are minimizing opportunity costs and the ability to capture seasonality because you can continuously run tests. Traditional split testing runs for a while, gets a result, and moves on. With a MAB, you can assign an "explore" budget that keeps tests running in the background to capture the seasonal/periodic change in conversions.
That comes with a cost: every visitor who doesn't see your best page is lost revenue.
