<<I'm still trying to figure out if, say, on a 20 hand Spin machine (100 max
coin in) having draws come from one deck is better/worse in the long run vs.
a 20 (hypothetical) multi-play machine where the draws would come from
different decks.>>
You've been told several times that the expectation is the same.
<<Say you are dealt 3 aces. You draw the 4th ace, but it is drawn in the far
right bottom corner. Mathematically, this is a disadvantage as opposed to
getting that fourth ace on the center line where more of the 20 lines pass
through. This is even more apparent in the 9 line Spin game.>>
That disadvantage is exactly negated by the increased chance of getting the
fourth Ace on the center line when you DON'T draw it in the bottom right.
<<So, I am still just wondering if any "hard" math has been done on this.>>
The problem is well understood. You could bet your house that the
expectation of the two games is identical.
Consider the expectation of each line when drawing one card. The lines that
are filled with the first card off the deck clearly have an expectation
identical to a single-line or regular multi-line game because the method
used to deal the card is identical. Now look at the lines completed by the
second card off the deck. You can see that the expectation of these lines
would be identical to a single-line game if instead of using the very next
card off the deck to complete the draw, one card was "burned" and instead
the second card was used. But since the order of the deck is random it
cannot matter whether the first or second card is used, so the expectations
must be identical. The same argument goes for lines completed by the third
card.
While intuitively it seems that the elimination of two cards from
consideration must affect the outcome, intuition is often wrong when it
comes to probability problems.
Cogno