Mathematicians, help me understand why I can never draw a flush.?

Posted on 2016-10-13 18:57:00 in Math by BRYCE

When I play the five card draw version of poker, I have often gotten a near flush, one card shy of a flush. So I always go for the flush. 

I don't know how many times I've gotten four cards of one suit and one card of another suit. It's happened a lot. 

But what has never happened has been that I have discarded the off suit and drawn the suit needed to complete a flush. 

Now under the law of averages wouldn't it seem that every forth hand like that I should be drawing the correct card to get my flush. 

I've gotten "rarer" hands on a single draw. From time to time I get a full house when having two pairs and a junk card. 

I took statistics but just made a C, but that was a few years ago. 

I'm not stupid, but if you could keep the answer simple. 

Full disclosure: I was an English major. Which is why I am now in the Navy. Which is why I am playing lots of poker.

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