Rule of Six question (Single Deck)
Anyhow, this theory caused me to pause:
While perusing Norm Wattenberger's Blackjack charts on the effect of penetration for a Double Deck and Six Deck Shoe (highly recommended), I extrapolated on a thought I had not seen previously mentioned in any literature or on any forum I had thus far read.
The Rule of Six in Single Deck blackjack dictates:
If four players, deal two rounds (4+2=6)
Three players, three rounds (3+3=6)
etc etc.
It occurred to me, the normal expectation of cards per hand is 2.7, yet in a deck heading negative, less cards would be used per round (more 10 value cards) leading to an earlier shuffle if abiding by the rule of six. The reverse should also hold true, a deck heading positive would yield more cards per round (2-6 value cards) leading to a deeper penetration for positive counts.
Does this then lead to some scenario similar to the "floating advantage" or "cut card effect"? Where the rule of six is of benefit? Logically, at least to me, it seems so, yet I lack the programming skills to quantify? Or, is this potential advantage negated by other factors I have not yet considered?
Finally, would a simulation of Rule Of Six for the card counter yield a larger advantage than strict cut card placement within the single deck? Obviously depth of the cut card placement would matter, would rule of six result in a greater advantage for the card counter vs. a cut card placed at 1/2 deck? And rule of six vs. cut card placed at 1/4 deck?
If this has been previously posted online, would it be possible to provide a link to that discussion?
Thank you,
Yes, of course using rule of 6 (or any other method that deals a fixed number of rounds between shuffles) is better for the player (whether he counts or not) than using a cut card. That's the cut card effect.
But, I think the effect is slightly different. Here, the value of the cards has a distinct effect on when we shuffle with Rule of Six, whereas, with the cut card, the values have no bearing? I have missed simple obvious things before... curious if I have here as well.
Quote: LVJackalyet the rule of six does not depend on a cut card.... and true.. i maybe restating it.
But, I think the effect is slightly different. Here, the value of the cards has a distinct effect on when we shuffle with Rule of Six, whereas, with the cut card, the values have no bearing? I have missed simple obvious things before... curious if I have here as well.
I'm not sure exactly what you are saying.
Using rule of 6 (or any other fixed-rounds method) you will deal deeper when the count goes up than when the count goes down. This is the inverse of the cut card effect. The fact that you can't deal that deeply when there's a cut card (and therefore must shuffle away the good counts after fewer rounds have been dealt) is exactly the cut card effect.
The ultimate question, does the rule of six provide superior results than a cut card? From the player's perspective, I think YES... but by how much?
Quote: LVJackalThe ultimate question, does the rule of six provide superior results than a cut card? From the player's perspective, I think YES... but by how much?
The answer is definitely yes -- that is the cut card effect.
As for how much, I'm not completely sure of this. The wizard has a table here that says that its .113% for a single deck game, but he doesn't go into details about how he got these numbers (in particular, where was the cut card placed for the comparison to the cut card game?)
I'm not sure how much the placement of the cut card matters, actually. It seems that placing it deeper would lead to worse situations for the player, but that would be mitigated by the fact that more rounds would be dealt on average (so the negative expectation would be averaged over more hands). But without running simulations I can't really be sure.
Average # cards dealt at 2.7/hand. So even distribution, 5.4 cards dealt per round heads up with the dealer. Rule of six therefore would lead to 27 cards dealt prior to shuffle on average (5 rounds to 1 player/5.4*5). Average of 1/2 deck cut off. In negative rounds (we not only bet less, but also utilize less cards to achieve the negative count) we could use as little as 20 cards prior to the shuffle (A/K vs. A/K, A/K vs. A/K, Q/Q vs. Q/Q, J/J vs. J/J and 10/10 vs. 10/10). So in our worst nightmare as a counter, the dealer shuffles right at the edge of hell.
Now, the reverse, if abiding by the rule of six: 2+2+2+2+3+3+3 vs. 3+4+4+4+4 (12 cards/1 round), 5+5+5+5 vs. 6+6+6 (19 cards/2 rounds), 6+7+7 vs. 7+7+8 (25 cards/3 rounds), 8+8 (split) +8+9+9 vs. 9+9 (32 cards/ 4 rounds), here we are facing the final round with only 10s and As remaining!!! The wife and her three gorgeous sisters can play with the pool boy all day long.. I'm betting the 401k and anything I can beg, plead or borrow!
Ultimately, I think this is vastly different than the cut card effect. I just do not know how much overall?
Quote: LVJackalFor the basic strategy player, yes, the counter... no.
Average # cards dealt at 2.7/hand. So even distribution, 5.4 cards dealt per round heads up with the dealer. Rule of six therefore would lead to 27 cards dealt prior to shuffle on average (5 rounds to 1 player/5.4*5). Average of 1/2 deck cut off. In negative rounds (we not only bet less, but also utilize less cards to achieve the negative count) we could use as little as 20 cards prior to the shuffle (A/K vs. A/K, A/K vs. A/K, Q/Q vs. Q/Q, J/J vs. J/J and 10/10 vs. 10/10). So in our worst nightmare as a counter, the dealer shuffles right at the edge of hell.
Now, the reverse, if abiding by the rule of six: 2+2+2+2+3+3+3 vs. 3+4+4+4+4 (12 cards/1 round), 5+5+5+5 vs. 6+6+6 (19 cards/2 rounds), 6+7+7 vs. 7+7+8 (25 cards/3 rounds), 8+8 (split) +8+9+9 vs. 9+9 (32 cards/ 4 rounds), here we are facing the final round with only 10s and As remaining!!! The wife and her three gorgeous sisters can play with the pool boy all day long.. I'm betting the 401k and anything I can beg, plead or borrow!
Ultimately, I think this is vastly different than the cut card effect. I just do not know how much overall?
This is exactly the cut card effect. The lack of a cut card allows you to play those last hands at the positive count. If a cut card were being used, you wouldn't get to play them.
