% question

[JustCuz]

To be quick, I would do the calculations using a slightly different method. I will explain, in detail, exactly what each step does/means, and I will then summarize how I'd think about it while in a hand without the aid of a calculator or pen/paper.

There are 20 broadways cards. The probability of being dealt two of them is 20 out of 52 times 19 out of 51 (you need your first card to be 20 out of the full deck of 52, then you multiply that probability by the the odds of the second card also being a broadway card, which is 19 (number of broadway cards left after you got the first one) out of the remaining 51 cards in the deck).

Whenever you say "x out of y," what you mean is x/y (x divided by y). So, 20 out of 52 times 19 out of 51 is the same as (20/52) * (19/51) = .3846 * .3725 = .1432. Move the decimal point two places to the right to get your percentage, 14.32%.

If I were in a hand, I would think, "20 out of 52 is a little less than 2 out of 5, which can be reduced to 1 out of 2.5, and 19/51 is going to be really close to that same number (note that I am rounding here), so I'll just use it again for the sake of simplicity. (1/2.5) * (1/2.5) is 1/6.25. 100 (basis of percentage) divided by 6.25 is 16%, which I know from my early rounding is a little higher than the true answer, but close for quick mental math. I'd say the odds of being dealt two broadway cards is about 14-15 percent."

I'd be pretty close without ever having to mentally manipluate anything more complex than 100/6.25.