Don suggested that this discussion be posted on the MB, so here it is! =) My original email to Don has Don's pargraph by paragraph responses interspersed between my own. These are followed my my resonse.

Me:

Yep, the operating principle on the two box idea
would be to spread one unit over two boxes through negative counts. This is, of course, is usually only possible with a unit that is 4 times the table minimum since most places I've been in only allow the play of 2 boxes at 2x minimum each.

Don:

So, what's the point? Why use a unit four times as large as it has to be, just to spread to two boxes, when you can bet the table min on one box?

Me:

This is probably something you already know about, but I haven't heard of it before: Suppose we flat bet many times the table minimum. (7 spots times 2 units each is 14, so 14x the min could be a good working figure) We index the number of boxes used to the count such that as the count becomes more negative the number of boxes increases. (say 1 box at T 0+, 2 at T -1, 4 at T -2 and 7 at T -3) I'm not sure how to do the math on this, but could this effect generate an advantage all by itself? It, if it works, would be kind of like a 'seated Wong' except instead of sitting out negative counts, we burn them away. Perhaps this has already been explored... if not perhaps it could be useful to you or someone else. The idea came to me while thinking out the logical extention of the two box theory.

Don:

I'm sorry, but you're not making any sense. Why do you insist on betting MORE money as the count get smore negative. Instead of betting one unit on one hand you want to bet 14 units on seven hands? Why would you want to do that? The first way costs one unit for 5.4 cards, while the second costs 14 units for 21.6 cards. On a dollar-per-card basis, the second way is 3.5 times as expensive as the first. Makes no snese at all.

My response:

I suppose I didn't explain this properly. The _total_ bet on each round is _exactly_ the same. If we were betting 12 times the table minimum and the table minimum was $5, then the bet on every round would be $60. If the TC is greater than +1, then we bet one box of $60. If the TC is between 0 and -1, then we bet 2 boxes of $30. (Note that the bet hasn't changed, just the number of boxes.) If the count drops further to T -2, we then spread to 4 boxes of $15 and so forth.

The idea is to use the card eating effect to burn our way through negative counts. On average, we would receive 100 rounds per hour when betting $60 on one box, 66.6 rounds per hour with 2 boxes of $30, 40 rounds per hour with 4 boxes, etc. We are still seeing the same number of _cards_ on each TC that the normal distribution calls for but, and this is the key, our _effective_ wager on each -TC goes _down_ because each unit wager uses more cards. Thus, if we see a TC of -1.5, on average, 6 out of every 100 hands we would have an anticipated turnover of 6x$60=$360, on average, in every 100 rounds. However, due to the card eating effect, we actually only receive 2/5ths as many rounds if we have that same $60 wager on one box. Thus, our total turnover at TC -1.5 becomes (6x$60)x(2/5) = $360x0.4 = _$144_. This, statistically speaking, has the exact same effect as reducing our wager to $24 on TC -1.5.

In the most extereme theoretical form, we would spread to 7 boxes (if the casino's tables have 7 boxes), on TC's equal to or lower than 0. We would use only one box at TC +1 and higher. In this instance, the total loss at all negative counts would be multiplied by 2/7. (ratio of minimum card usage to maximum card usage) This is a reduction in loss at -TC's of 5/7th's or 71.4%... a rather significant reduction.

According to some preliminary calculations I did, this effect can yield a very slight advantage even on an 8-deck shoe with S17, D11, DAS, nS. On more favorable games the gain would be larger.

Now for practicality... First off, how often do we bet twelve or fourteen times the table minimum as our main bet? Not too often. Also, if we spread from 1 box straight to 7 and then back again we would most likely attract some unwanted attention. But this is an extreme example meant so show potential value. More practical use would be for someone who wants to make a reduction in his losses if he is a play-all and bets 4x the table minimum as his lowest bet. On any TC lower than +1 they would spread to two hands. This alone would reduce losses when at a disadvantage by 33%. This is, I think, significant.

KOD