Question from \"Small Stakes Hold’em\" p. 102
 

In the last paragraph on p. 102, it says a hand with one out(after the flop) has a 2/47 chance to improve by the river. For those of us trying to follow along with the math, shouldn’t that really be:

1/47 + 46/47(1/46)

where 1/47 is the chance you get the card on the turn, and 46/47 is the chance you miss the card on the turn and 1/46 is the chance you get the card on the river?

I realize that 46/47 is a little less than 1 and 1/46 is a little bit bigger than 1/47, so when you multiply them together, you get close to 1/47. However, in other parts of the book, the authors use “approximately” when they are not being exact, but here they didn’t.

Thanks.

Re: Question from \"Small Stakes Hold’em\" p. 102
 

1/47 + (46/47)*(1/46) = 1/47 + (1*46)/(47*46) = 1/47 + (1*1)/(47*1) = 1/47 + 1/47 = 2/47

So in other words it's exact.