# Gambling with the gambler [closed]

You are walking on the street and notice a guy gambling with some other guys and you start to watch.

The game principle is pretty easy. There is a standard 52-card deck and it is being shuffled every time before the game begins. You take five random cards and if at least two of them has the same rank (2,3..., J,Q,K,A) you win, otherwise you lose.

In the long run, you should play or not? (with probabilities of course)

## closed as off-topic by 2012rcampion, Deusovi♦, ghosts_in_the_code, xnor, AzaJan 24 '16 at 5:57

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is off-topic as it appears to be a mathematics problem, as opposed to a mathematical puzzle. For more info, see "Are math-textbook-style problems on topic?" on meta." – 2012rcampion, Deusovi, ghosts_in_the_code, xnor, Aza
If this question can be reworded to fit the rules in the help center, please edit the question.

The probability of the first two cards not matching is $\frac{48}{51}$. Given them not matching, the probability of the next card matching neither is $\frac{44}{50}$, and so on.
Our total probability of no pairs, then, is $\frac{48 \times 44 \times 40 \times 36}{51\times 50\times 49\times 48}=.507$