[SumZero]

[ QUOTE ]
that's counter-intuitive: if you have three holes, and 52 marbles of four distinct colors to fill them, you will more often have three colors than 2 or 1, reaching blindly in a bag to grab a marble, isnt that so? what am i missing?

[/ QUOTE ]

That isn't so. Assuming you have 13 marbles of each color (say RGBW), than consider what happens when you are picking the third marble when the first two are of different colors. Say you already have a R marble and a G marble. Now there are 26 marbles that will give you 3 different colors and 24 marbles that will give you a two colored set of three marbles. So once you have two different colored marbles you are very slightly more likely to have three different colors (26/50 or 52% of the time. So even when you start with two different color marbles you have three different colors 48% of the time which is more than the 47% you stated in your OP).

But now consider that you don't always start with two different colored marbles, some of the time the first two marbles are the same. How often does this happen? Well once you've pulled a R marble there are 39 non-R marbles and 12 R marbles so 12/51 times you will have the same color. So the correct answer for how often you have at least two of the same color is 12/51 + 39/51*24/50. That is roughly equal to 1/4 + 3/4*1/2 or 5/8 or 62%. It is actually equal to 60.235294% (to 6 decimal places accuracy).

The fact that the site in question is producing about 60% flops is good, as if it wasn't there would be something to worry about.