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Can The Law of Diminishing Returns Apply to Blackjack?
Certainly, the notion of "loss stops/stop loss" correctly produces scorn from knowledgeable players and statisticians, so this thread is not directly related to that notion, but is similar. After running thousands of sims, and reading hundreds of posts from players and authors much more knowledgeable about the game than I, I fully understand and accept that loss stops have an adverse effect on EV. However, I recently ran a series of sims that made me wonder if the Law of Diminishing returns also applied to blackjack, and if so, was there a way players could capitalize on it...and I think there is, but wonder what others think about this concept.
So, to try and see if I could apply the LDR to blackjack, I used the session options in CV Data to approximate a single player, playing head to head, in a 6 deck shoe with 75% pen, by forcing a shuffle after 43 hands, or forcing a shuffle after session bankroll was lost, or forcing a shuffle at an ODP. I thought this would approximate real world play in a 6 deck shoe based on the average number of cards per hand of 2.7. I used the REKO 6 Deck Full count, and rules 3:2, LS, DAS, DOA, INS, NRSA. I used ODPs and a 1:4 bet ramp of $25:$100. I then ran sims using session bankrolls (which were really shoe bankrolls) of 1 unit, 2 units, 3, 4, 5, ... to 40, then 50, 60, 70, 80, 90 and finally 100. Each sim ran 10B hands. What I found was that using a shoe bankroll of 100 units produced an hourly EV of $25.47 with a 1K Unit Bankroll ROR of .61...and that a 50 unit shoe bankroll produced an hourly EV of $25.42 with a 1K Unit Bankroll ROR of .61.
Here is a chart of the data (I apologize for the poor image quality):
Screenshot_20200403-144835_Gallery.jpg
Notice the similarity between the green Hourly EV line and the line in the LDR image below:
42330578611_5f9009864b.jpg
So after thinking about this, in my opinion, I believe the LDR does apply to blackjack. If I can reach basically the same Hourly EV and ROR with a shoe bankroll of 50 units that I could reach with a shoe bankroll of 100 units, why would I use a shoe bankroll of 100 units and waste time playing longer on a losing shoe just because I had more units to play with when it does not significantly produce greater EV to keep on playing?
Why is it important? I think the stress from a $1250 loss is significantly lower (and thus psychologically better for the player) than the stress associated from a $2500 loss. It is also important to the player because time is of value and should not be wasted on continued play that produces minimal increases in EV and instead should be used seeking opportunities to produce significant increases in EV...afterall, is that not why we "Wong"?
Some will criticize this as simply "lost stop/stop loss" thinking, but I would respond that it is different and valid since it is not arbitrarily determined and instead is based on statistical data obtained by sims and the application of LDR...consider the Hourly EV and 1K Unit ROR numbers for each shoe bankroll...I would be amazed if a difference of 5 cents an hour was statistically significant (granted there would be a larger difference with a larger bet spread and unit size, but I still doubt it's satistical significance).
Thoughts?
As a preventive measure, I should also add that this bet spread and unit amounts are not what I use in live play but were used here simply as an example. Negative commentary in this regard is not necessary.
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