If I draw $13$ cards from a deck of $52$ cards, the likelihood of getting a straight of hearts from A to K is:
$$P_{52}=\frac{1}{\binom{52}{13}}\tag{1}$$
because there's only one way to arrange a straight of 13 cards of the same suit, and all the possible draws are $\binom{52}{13}$.
My question is: what's the likelihood of the same event but with two decks of cards? My guess is:
$$P_{104}=\frac{2^{13}}{\binom{104}{13}}\tag{2}$$
$\binom{104}{13}$ because now we're drawing $13$ cards from a deck of 104, and $2^{13}$ to account for the fact that each card of the straight could either come from the first deck or the second and all the possible combinations are $2^{13}$.
Is my math righ? Because I'm a bit surprised to find that $P_{104}<P_{52}$ and by a factor of more than $2$. Thanks!