How do you find the EORs for an infinite shoe?

[NotEnoughHeat]

Just a curious question,

how do you find the effects of removal when dealing with an infinite deck? I'm not looking for a comprehensive answer that would include the standard procedure for calculating EORs (though I wouldn't mind someone doing so as I am too certain I'd be able to describe it accurately myself). Really, the motivation behind my question here is a mention of the Wizard's Appendix 7(Link) in a blackjackinfo thread I was reading. Conceptually it just seems a bit odd to talk about the effect of removing a card in an infinite shoe. With a finite shoe, you can calculate EV before, with all the cards, and EV after with, for example, all the 6's save one. I've never really learned my infinity arithmetic but isn't infinity minus one still infinity? I'm having a hard time wrapping my mind around how the Wizard went about calculating his numbers. From his description on the page he seems to really mean the effect of removing one card as opposed to removing every card of that rank in an infinite shoe.

[Three]

I would go out on a limb here and say the EoR of all cards in a true infinite deck situation is 0 because in effect cards are never removed.

[ZenMaster_Flash]

If you confine your research on this question to consulting the fine tables in
"The Theory of Blackjack" and "Blackjack Attack, 3rd ed." you'll find that one
needs to extrapolate the MULTI-DECK figures from the Single Deck which is
easy as can be. e.g. if you have an E.O.R. figure of X for a single deck and you
want to approximate an infinite deck by stipulating a 100 deck shoe, the E.O.R.
is 2% of X.
Thus, the E.O.R.'s are too insignificant to have ANY value. An interesting topic is the
E.O.R.'s of the ranks with a deck composed of 13 cards - one of each rank. Note:
Pair Splits will be impossible.

As Tthree implied, and I am elaborating upon, as the number of decks grows, the E.O.R.
of all ranks are progressively reduced, in linear fashion, until ZERO is approached.

[NotEnoughHeat]

Ok, from what I can tell, my intuition that a truly infinite deck would have EORs of 0 is correct. So perhaps the Wizard here has just used some sort of approximation. It still seems odd his EORs only seem to be around a fifth to a seventh of that of a single deck considering that the closer the approximation the closer to 0 the EORs are. In this case, with such a rough approximation, why bother calling it infinite at all?

I suppose I'll just leave this at that unless someone wants to throw out a guess, bug the Wizard or can read his mind.

[ZenMaster_Flash]

" ... seem to be around a fifth to a seventh of that of a single deck."

Yes, that would be correct for standard shoe games.

[ACFERRET]

I think by removing the number of cards "per deack" that you want to find the effect of removal of, applying that to a compositions of which you have unlimited "decks" for your simulation.

More simply put, if you want to use an infinate deck model to find the effect of removal in a 4 deck game, create one deck, that has the number of cards in 4 decks, and take out the one you want to analyse, then run the sim with an unlimited number of that "deck" and by deck i mean a composition of 207 cards.

Make sense?

[NotEnoughHeat]

I think by removing the number of cards "per deack" that you want to find the effect of removal of, applying that to a compositions of which you have unlimited "decks" for your simulation.

More simply put, if you want to use an infinate deck model to find the effect of removal in a 4 deck game, create one deck, that has the number of cards in 4 decks, and take out the one you want to analyse, then run the sim with an unlimited number of that "deck" and by deck i mean a composition of 207 cards.

Make sense?

So what you're saying the Wizard is doing here is instead of running the post-removal sim by taking an infinite set and subtracting a finite set (one card) from it he is taking an infinite set and subtracting a smaller infinite set (eg. one 6 for every deck) or something of the sort? It seems plausible if it's the case that EORs aren't calculated but simmed (if they were just calculated using a single shoe would do). Again, I don't know enough to really comment.

[Three]

It seems plausible if it's the case that EORs aren't calculated but simmed (if they were just calculated using a single shoe would do). Again, I don't know enough to really comment.

I never generated EoRs either but I have been privy to discussions about it. I believe what the person was removing was using the same number of cards from the same number of decks. Let me see if I can find the Email about it. Well that communication may be lost. Finding it is bare minimum a needle in a haystack as it is not marked. I can't believe I didn't save it. I remember he was removing more than one card and the dividing the EoR by the number of cards removed. Fuzzy memory though. I filed it away for future reference but I may not be able to find it. The guy, a top AP and tops at game analysis, was saying his technique was more accurate than what others do. ACFerret technique sounds like it may be the same technique. It is not surprising as I know ACFeret and I are in the same super-network composed of a few sub-networks of AP's that share info and bounce ideas off each other.

[Freightman]

Just to simplify things
How can EOR's possibly be relevant on an infinite deck.
1/infinity is an infinite fraction - it has no relevance.

[Norm]

Well, this could matter. I hear that Adelson is in the process of building an infinite shoe, with his infinite bankroll. It will cost an infinite amount. But, he figures it'll save money in the long run since all dealers in all of his casinos (eventually he'll own all casinos) can simultaneously deal from the same shoe.

[Dog Hand]

Well, this could matter. I hear that Adelson is in the process of building an infinite shoe, with his infinite bankroll. It will cost an infinite amount. But, he figures it'll save money in the long run since all dealers in all of his casinos (eventually he'll own all casinos) can simultaneously deal from the same shoe.

Yeah, but then his moronic PC's would screw it up by making the tables NMSE

Dog Hand

[Freightman]

Yeah, but then his moronic PC's would screw it up by making the tables NMSE

Dog Hand

That's actually very funny