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You have two conflicting statements in your scenario -
First you say that you drew the same amount of cards.
Then you said that you ended with the same amount of cards in deck.

If the first is true then Gabe is correct as X/56 is always less than X/50.
If the second is true then Gabe is incorrect as 56/X is always greater than 50/X.

That help?

Ok, If you both ended at the same amount of cards then Stats say that you had a better chance of getting the SoG/NJ combo.
However and I think that this is what Gabe was getting at - He has a better chance of reaching them first because he has less cards between him and SoG/NJ. (Note that I am not a mathmatician and could be getting this completely wrong....)

Gabe, I'm not going to bring up anything we talked about. I was simply asking for a response. If you have a problem, take it to PM. I'm kind of tired of you insulting my sportsmanship on the boards, quite frankly. Please stop. I apologized several times to you saying that it wasn't about winning, I just wanted to know the statistics. And you ignored me and then signed off as I was talking to you. Then you said you weren't looking for a fight but you posted about my poor sportsmanship. Please stop insulting me on these boards, especially about things that I have wrote numberous PMs and hamachi messages apologizing to you. I would like an apology from you for once.

I know there are several math teachers on these boards, so they're input would be great. 

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Bahaha! I know one!

As to the original question, should I assume that both buckets still have both green apples still in there when there's twenty left? If so, it doesn't matter what the buckets were like beforehand, they're at the same state now. They have the same odds, because they have the same present configuration.

The raw statistics are in his favor.  You have a 1.79% chance of drawing any one card at any one time in a 56-card deck, while he enjoys a 2% chance.  So if you each draw 30 cards, you have only a 53% chance of drawing, say, Son of God, while he has a 60% chance.  You seem to have drawn six extra cards during your game, increasing your chances to 64%.  So the extra card draws did increase the basic odds in your favor.

Where it gets hairy, and where the real math whizzes need to step in, is calculating the odds of drawing BOTH SoG and NJ by that point in your deck, which is a smaller percentage.  Additionally, you have to account for the odds of getting your draw cards before you get the Dominants in order to speed up that draw.

In other words, the fact that you actually need more cards in order to get through your deck faster and get the right two cards, offsets the better odds you get by drawing faster.  When the difference is six cards, that effect is miniscule, but it's magnified if you have several draw cards and you try to get through say an 84-card deck before he gets through a 50.  In that circumstance, most people can deduce without crunching numbers that the 50-deck will crush your draw deck.  The only remaining question is what the final numbers say about your odds of getting to your cards first.  But at first glance, I'd say he is correct to say he enjoys the overall advantage because he relies on fewer cards to get where he needs to go.

It also depends on which other cards you draw.  For example, maybe you drew more because he drew no Lost Souls and you drew 6.  I keep forgetting to account for the re-draw on drawn Lost Souls.  So your odds are actually 1/49, or 2.04% and his are actually 1/43, or 2.33%.  The basic premise remains the same, but hey, there's one more confounding factor.

Trust me, they're not exact statistics.  You are correct to say your odds of drawing Lost Souls drops, from 14% to 12.5% per card.  But those vary as you go through the deck and draw more or fewer souls than he.  The flip side, though, you may have more non-Lost Souls, but you also have more non-Son-of-Gods.  It's better for your LS draw but worse for your One Critical Card draw.

You're all wrong.  Here's how the statistics work out...

You have two players (A and B) in the game. Someone, either A or B, has to get Son of God + New Jerusalem First. Since there are two possibilities, the chances are 50/50.*

You're all wrong.  Here's how the statistics work out...

You have two players (A and B) in the game. Someone, either A or B, has to get Son of God + New Jerusalem First. Since there are two possibilities, the chances are 50/50.*

Even when you have two completely different decks? Then speed would be pointless, cause you always have a 50/50 chance? I think I must be misunderstanding you.

Those were the odds of the world being destroyed by the Hadron collider, right? Because either it would be destroyed or it wouldn't?

That was close to my favorite segment ever.

Even when you have two completely different decks?.

I'm fairly certain the rules don't allow you to play two completely different decks. Since you can only play one deck at a time, I don't understand your question.

The odds are 50/50 based on two possible outcomes
- you get SoG/NJ first
- you don't

See, even The Schaef agrees with me. Flip a coin, I tell ya.