# Thread: 13 card straight - Calculation correct?

1. ## 13 card straight - Calculation correct?

Hello!

I am trying to compute the Pr. of being dealt a 13 card straight out of a standard 52 card deck. (ie. 23456789TJQKA)

Here's my calculation:

(4/52 * 4/51 * 4/50 * 4/49 * 4/48 * 4/47 * 4/46 * 4/45 * 4*44 * 4/43 * 4/42 * 4/41 * 4/40) * (13! - 4) = ~0.00016%

The reasoning being: Pr. to draw an Ace on the first draw is 4/52, two on the second draw is 4/51 and so on. Obviously this only gives me the Pr. for this exaxt drawing sequence, but any other order would also make a 13 card straight, that's why I think there are 13! ways to draw, which is why I multiply. Because I want to exclude 13 card straight flushes, I subtracted 4 (4 different 13 card flushes possible).

Is this computation correct? Is there a more elegant way of computing this result?

Thanks a lot for any info you can supply!

2. ## 13 card straight

Hello,

I am not sure I agree with your calculation.

If I understood your problem correctly, you are after the probability of getting a 13 card straight, but excluding the four same colour ones, when drawing 13 cards out of a standard deck of 52.

Denominator: how many ways are there to draw 13 cards out of 52 (where the order is not important)? This is the number of combinations of 13 elements out of 52, hence 52C13=52!/(13!(52-13)!)

Numerator: once again, when the order is not important, how many 13 card straights (not of the same colour) are there? 4^13-4.

So, after simplification, this gives you: 28197/266812420~0.000105681

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