Some Thoughts

*the overall EV (EW, in your terminology) can't be greater than 10% x $100 = $10, with the $100 house limit in your hypo. *

I'm using EV in the way it is described in BJ21 glossary - as a percentage. I am also using EW the way it is described in the glossary - as a dollar amount over a period of time. In this case the period of time is one week. You are correct that EV cannot be greater than 10%. In fact, in this game the limit is about 4.4%, and only if you are making a single bet each week. However EW (which is different that EV) can be greater than the limit you suggest, because we are making multiple $100 bets during a week.

*Here is the problem I have with your calculation. You made the original EVS calculation for one wager -- that was fine -- but then ou made the same calculation for multiple wagers. Your
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calculation would have some basis if the EVS applied on every wager.

My intention is that EVS (EV of Strategy) represent the overall EV for whatever number of wagers the strategy (weekly series of bets) calls for. It could be one wager or many. EVS for the "Stop at +1 or -1" strategy would incorporate only one wager/week (excluding pushes). EVS for the "Stop at +3 or -3" strategy would incorporate a minimum of 3 wagers, an average of 9 wagers, with no theoretical maximum (although it would be under 30 wagers about 98% of the time). Under this strategy we do not know in advance the number of wagers that we will make each week, therefore we cannot calculate an EV per wager.

*If your calculation: "EW = 0.0367 x $300 = $11.01" was accurate, the player should increase his action as high as possible. For a "Stop at +10 or -10" strategy, we have "EW = 0.0367 x $1,000 = $36.70" *

The value 0.0367 in your above equation "EW=0.0367 x $1,000 = 36.70" is not a constant, but depends on your stopping point. See my post above entitled "Table of Strategies and Outcomes" for a summary of what happens at different stopping points. This table shows that if you play more hands, your chance of being behind at the stopping point increases. When the stopping point is 10, you are playing an average of 100 hands per week, and your chance of being behind is significantly greater. Your equation would become (roughly) EW = -0.01 x $1,000 = -10 (in other words you lose $10/week).

*The other problem I have with your calculation is that the total action isn't necessarily $300 with a +3/-3 strategy. (Nor is it $1,000 for +10/-10.) *

You are correct that by the conventional meaning of "total action", it is not necessarily $300 The conventional meaning of "total action" is the total amount of money you put in the bet circle. In a conventional blackjack game, every time you put money in the circle you are risking it. So in a conventional blackjack game you are risking your "total action".

This strategy is different. For any given week, you are saying "I will quit when I am either up $300 or down $300". Essentially you are only making a single $300 bet in any given week, even though that "bet" is spread over a variable number of blackjack hands. So you are only risking $300 in any given week.

*I think you did do a sim, because I think your +3/-3 strategy is probably right, as DD' points out. If you can get your sim to report the average win per week, over several thousand weeks, I think you'll find $4 < EW < $10.*

The sim for the +3/-3 strategy is showing an EW of about $11/week over about 50,000 weeks (assuming a table limit of $100). The +3/-3 strategy works because it effectively allows the player to circumvent the $100 table limit by combining a number of table limit bets into a "strategy" which is effectively equivalent to a larger bet. The EV decreases by a small amount with this strategy (from 4.43% to 3.67%), but because the effective bet size increases a larger amount (in this case from $100 to $300) the overall EW increases.

One final point that deserves amplification: If a player has a limited bankroll (they cannot bet above the table maximum) they should be using the +1/-1 strategy, which has the highest EVS. However if they have a larger bankroll, and can comfortably exceed the table maximum, then they should consider using the +3/-3 strategy. The +3/-3 strategy has a slightly lower EVS than +1/-1, but it has a much greater EW, and will therefore enable the player to win more money each week.