help with the math

[notes1]

I have 2 questions that hopefully the math folks can answer. As i am a simple guy, please use simple language, thanks.  When i draw and hit a 4 of a kind, why is it that it seems more likely, i will draw 2 matching cards than when i draw to a 3 of a kind and only need to hit one card?  Has anyone else noticed that when drawing to a premium hand, if you do not get the card you want, that you will often draw an EIGHT? If the answer is that an eight comes up more often, then why do i not get 4 eights more often?

[onemoretry]

Even though it's around 15 times more difficult to complete a quad drawing to a pair than to trips, that route to a quad happens more often because you're almost 20 times more likely to be dealt a pair than trips.

Is that the kind of answer you're looking for?

[notes1]

onemoretry, i appreciate you trying to keep it simple, but i am still confused.  are you saying that from a statistical point of view, that out of 47 remaining cards, it is more likely to draw a matching pair than to draw one matching card? 

[Eduardo]

I don't understand what you mean about drawing a matching pair. Can you explain with an actual example?

[notes1]

sorry, if i am not being clear.  if i am dealt J-J-2-5-7 or i am dealt J-J-J-2-7. it has been my experience that i am more likely to draw a matching pair (J-J) to eample #1, than i am likely to draw a single J in example #2. i understand i have 3 card draw in #1 and only 2 card draw in #2. as a non math person, it just seems more likely it would be to draw one matching card out of two cards than to draw two matching cards out of three.  

[alpax]

Chances of converting a dealt pair to a quad is 1 in 360.33
Chances of converting dealt trips to a quad is 1 in 23.5

Chances of a dealt trips is exactly 20 times less frequent then being dealt a pair; but the chances of connecting trips to a quad is only 15 times better. Hence when you hit Quads, its more often you connect it from a pair than a trips in terms of your experiences.

[FloridaPhil]

As humans, we tend to remember those things that turn out differently than we expect and forget the things that we consider common.   For example, if we draw to an inside straight 6 times and we don't get it, we don't remember it.  If we draw once and the right card comes up, we think "Man I'm really hitting those straights today!".   In video poker anything can and will happen. Math will only get you so far in this game. 

[onemoretry]

as a non math person, it just seems more likely it would be to draw one matching card out of two cards than to draw two matching cards out of three. 
That is absolutely correct, as confirmed by the numbers in the post from alpax.

If you think you are consistently more successfully completing a quad on a 360 to 1 shot versus a 22.5 to 1 one, it is either a very small sample, or your memory is off.

Do you actually record the number of these draws and their outcomes?   

[BillyJoe]

I hate eights..

[notes1]

alpax, thanks for the explanation, makes sense.  billyjoe, can you expand upon your statement, i hate eights?   onemorereply, no, i do not keep stats on my play, i am there to have fun. I should have phrased my original question better. I should have stated that i appear to get more quads from starting with 2 of a kind than from 3 of a kind. alpax's numbers cleared that up. Sorry, if my question offended you.