For simplicity, let us use a deck of 52 cards. Dealer’s up card can be: 2, 3,4,5,6,7,8,9,10, ace. For each dealer’s up card, each of the two player’s simultaneous hands can be: ace, 2, 3, 4, ...19, 20, 21, 22, ..., 29, 30, 31. Use a computer to list all possible permutations for each situations, and then calculate the expected values for each permutations. Then you will find the exact value of covariance. This is a lot of calculations though.
Then I lay down the gauntlet to you, as I have done on multiple occasions to the forum, to determine the underlying theory which led me on my path. The clues may be in your own playing records as they were in mine, they are certainly buried in my posts and well before those posts revealing theories on intermediate density.
There have been no takers.
A player has never been advised to play more than two hands because the variance on the expected value will be too huge to handle. Also, the player may waste the 3:2 payout for being under bet. In addition, I prefer play solo. I really donot know how to calculate the covariance of two simultaneous hands.
Wong's Pro BJ has optimal bet sizes (which rely on covariance) for all simultaneous hands from two to seven. You seem to ignore a great deal of the research and literature that has been around for ages. In particular, use Table 86, page 204 of the latest edition, with explanations on page 203.
And while variance obviously increases with optimal bets on multiple simultaneous hands, so does e.v., by the same percentage, leaving risk of ruin the same.
Don
I actually read this part of Wong's book carefully, but my impression is that the result of multiple-hands playing was based on assumption*assumption. We haven't cleared out the covariance problem of two hands only yet, but we have used it to degenerate to multiple hands. Practically speaking, I would not count cards when there are two or more other players on the same table. The real question I have been pushing is this: When the remaining deck is rich with Aces, I would play one hand with a large bet; when the remaining deck is rich with Tens, I would play two hands whenever I have an edge. Is this the correct strategy?
What I can see here is that aceside tries to avoid the problem of multiple hands associated with a dealer Blackjack. The strategy could be applicable to Ace sequencing... Play only one hand and share the Ace with the dealer (on average) instead of playing a "buffer hand" and lose both to a dealer BJ. This problem doesn't exist with decks that are ten rich.
Is that what you mean aceside?
G Man
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