...why the bs is different for 6D vs DD?
An example: bs for DD, H17, no DAS for 6D and DD (at least in my strategy charts) differ in three instances: 9 vs 2, A,3 vs 4, and 6,6 vs 2.
The proportion of the different types of cards remain the same regardless of the number of decks so why should the bs be different from a fresh shuffle? From a practical standpoint, it doesn't really matter much to me, but I really am curious.
Lessee, before any cards are dealt, the proportion of 6s in two decks is 8/104 = 0.0769230... With 6 decks, the proportion is 24/312 = 8/104 = 0.0769230... Same thing.
Once you're dealt 6,6 v 2, with two decks, the proportion of 6s remaining is 6/101= 0.05940594.... With 6 decks, the proportion is 22/309 = 0.071197411... No longer the same. The proportions of other ranks also become different.
These plays are very close. Most people just memorize a generic basic strategy. By choosing a generic strategy more correct for shoes, you get a slightly more risk averse strategy, which may be better for your bankroll, even though it doesn't maximize EV, strictly speaking.
ETF
When a BS-player faces say 6,3v2 in a DD-game he has actually a TC of 3/2 = 1.5.Since the index is +1, it's logical he should double.
If he has the same hand in a 6D-shoe, his TC is only 3/6 or 0.5 so he should just hit.
Francis Salmon
"When a BS-player faces say 6,3v2 in a DD-game he has actually a TC of 3/2 = 1.5.Since the index is +1, it's logical he should double.
If he has the same hand in a 6D-shoe, his TC is only 3/6 or 0.5 so he should just hit."
Sorry, but this is not a valid answer, as your reasoning is circular. Expectations determine what indices should be for a given play, not vice-versa. You don't start with an index and then note that, with two decks, the TC is 1.5, whereas with six decks, the TC is 0.5, therefore, one play is a double and one isn't. That makes no sense at all. (In fact, often indices are different for DD and six decks, for the same play!)
You start with the correct observation that the proportions of remaining ranks are different for two decks than for six decks, and it is THIS mathematical fact that drives the relative expectations to be different, as stated above. Then, with this knowledge, indices are created after the fact. In essence, the indices simply "come along for the ride."
If you reread your answer, you ought to realize that it really isn't an explanation at all.
Now, dhays, you should know something ahead of time: Francis isn't going to agree with me, but that doesn't make my response to him any less correct! :-)
Don
Like most indices,the index for 9v2 happens to be the same (+1) for DD as for multideck.The TC is a measure for card distribution which is the main point raised be dhays.I just wanted to point out that an RC of +3 leads to a different TC in DD than in 6D hence to a different card distribution and a different decision:More chances to get a high card and more chances for the dealer to bust.I don't see anything circular here.
Francis Salmon
"Like most indices,the index for 9v2 happens to be the same (+1) for DD as for multideck."
That's true, but it's just "coincidental." By that, I mean that the indices do not, of necessity, have to be the same, and if they weren't, how would you argue then?
"The TC is a measure for card distribution which is the main point raised be dhays."
An index is a blended value, obtained by averaging advantages over all levels of penetration. Rarely, but not never, a correct BS play off the top of the deck will actually contradict the TC and index given for that play (see BJA3, bottom of p. 44 and p. 45). The point is, the indices are simply tools. You can't invoke the true count to demonstrate why or why not a particular BS play is correct or incorrect. For that, you need to invoke uniquely expectations,, after removing the player's two cards and the dealer's upcard -- and let the TC and the alleged "correct" indices be damned!
"I just wanted to point out that an RC of +3 leads to a different TC in DD than in 6D hence to a different card distribution and a different decision"
See above. Your observation isn't incorrect; it's simply that it isn't a valid mathematical explanation of why we make one play for DD and another for six-deck. You simply cannot invoke indices to explain that. You have to invoke expectations!
"More chances to get a high card and more chances for the dealer to bust. I don't see anything circular here."
Well, look a little harder! :-)
Don
Miss one closing sign (>), and the whole text gets screwed up.
Sorry!
Don
I never claimed to give a mathematical explanation for the BS plays in question, only a logical one.
dhays asked why there were differences in BS for pitch and shoe games and the generic index is a perfect tool to make these differences plausible.Since the situation in question produces an RC of +3, it logically is BS to double in pitch but to hit in shoe games.Otherwise the index would be mistaken.
Note however that at a neutral count anywhere in the deck or the shoe one should always just hit.
Francis Salmon
