[defen]

See my reply lower in the thread - I worked out the numbers using Bayesian inference to find the exact probability that B is better than A, subject to a number of assumptions. The benefit of this approach is that it's exact so you don't need a certain number of samples to properly approximate a normal distribution. The answer is that B is almost certainly better than A. Here's the calculation I plugged into Wolfram Alpha:

2835 2837 choose[2834,6] choose[2836,24] NIntegrate[(f^6) (1-f)^2828 (g^24) (1-g)^2812,{f,0,1},{g,f,1}]