# Probability of doubles on 2 shuffled deck of cards and gaining doubles

I am not asking for questions on homework or anything related to school or work, I am asking for help with a card game I was playing with my friends. I was playing a card game called Tractor(its a Chinese game I think? I wish I don't offend anyone because of this) anyways, good hand to have are doubles on hand, since we have mixed two decks including 2 color and 2 black jokers, which makes it 108 cards total. some were getting way better hands such as having more doubles than others, and we were fighting about how many pairs we would wind up with in total of four hands if it were dealt out in a complete total. It might sound really simple to you guys, but to me a non math major nub, its getting on my nerves :D. What would the probability of the doubles dealt on total of all our hands combined. And doubles meaning same suit and number only. so there can only be 54 doubles including jokers, since it is two decks.
I guessed that it would be 25 percent or just under, so like 13? :D, and others said it should be lower.
I guessed it would be 25 percent because there are four people and when a card is dealt, I feel like the number I have gotten have 1/4 since we are four people should still be 25 percent chance. I think I sound really dumb. So my point was how much doubles would be dealt? Thank you for your help, I appreciate it ;D if you do not think this question is even good enough for this website feel free to down vote and let it rot its just a curiosity that I had that I wanted to get it out:D, no need to think too deeply about it.

• So you have a deck of 108 cards: 4 suits of 13 ranks (two of each rank in a suit), plus four jokers, two of each colour. Now a double consists of both cards with the same suit and rank. Or both jokers of a colour (so, I guess, they don't have suits?). Okay. You seek the probability that when four hands are dealt from this suit, each contains at least one double. Q: How many cards are in a hand? – Graham Kemp Nov 8 '18 at 4:54