I was reviewing some calculations for a $4$-card poker type table game and got confused about single vs multiple deck approach to calculating probability. If someone could enlighten me, I would appreciated it.
Lets assume a single deck game, where there is a dealer and a single player, $2$ cards are dealt to each. To compute the probability of having a combined exactly $3$-of-a-kind hand...my approach was as follows:
Denominator of picking any $4$ cards =$\binom {52}4$ interpreted as: choose 4 cards from a single standard deck
Numerator of getting $3$ of a kind exactly: $\binom{13}1 \times \binom43 \times \binom{12}1\times\binom 41$ interpreted as: choose any value for the trips $\times$ choose $3$ out of $4$ possible suits for this value $\times$ choose your unmatched value for the remaining card $\times$ choose the suit for this unmatched value.
Do the odds change in a multiple deck situation and can someone explain the math for such? thanks