How to make this bet fair? A person bets $1$ dollar to $b$ dollars that he can draw two cards from an ordinary deck of cards without replacement and that they will be of the same suit. How to find the value of $b$ so that the bet will be fair? 
My effort: 
There are a total number of ${52 \choose 2} = 26 \cdot 51$ ways of drawing two cards oout of a deck of $52$. 
And, there are ${13 \choose 2} = 13 \cdot 6 $ ways of drawing two cards of any given suit, say, hearts. 
Now since there are four distinct suits, the number of ways of drawing two cards of the same suit is $13 \cdot 6 \cdot 4$. 
So the probability of drawing two cards of the same suit (assuming that the deck is well-shuffled  so that each card is equilikely to be drawn) is $$ \frac{13 \cdot 6 \cdot 4}{26 \cdot 51} = \frac{4}{17}.$$ 
Is it correct? And if so, then what next? 

It is correct.
So the probability of getting different suits is $\dfrac{13}{17}$.
So the odds should be $\dfrac{4}{17} : \dfrac{13}{17}$ or $4 : 13$ or $1:3.25$.
There are other ways of getting the same result.  
For example, given the first card, there are $12$ other cards of the same suit and $39$ cards of other suits, making the odds $12:39$.
