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Thread: Can The Law of Diminishing Returns Apply to Blackjack?

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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.
    Last edited by Wave; 04-03-2020 at 04:29 PM.

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    Quote Originally Posted by Wave View Post
    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?
    Wave, you know how you used to quote Don S at the end of all your posts saying something to the effect:

    "That you either do it right or you don't do it at all"

    Well, Don would never approve of those ideas of yours. First and foremost you cannot say that the remaining hands left to be played in the shoe are going to continue losing like the previous hands. You are suggesting that players end the shoe when there are still positive TC hands to be played, a horrible idea. So the next shoe comes along and you are again in a high bet situation but now you make the bets at the same exact TC that you just previously quit the table because of a few of the finished hands in the current shoe did not produce a stop-loss threshold, wonderful, just wonderful.
    Last edited by BoSox; 04-03-2020 at 05:21 PM.

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    Quote Originally Posted by BoSox View Post
    Wave, you know how you used to quote Don S at the end of all your posts saying something to the effect:

    "That you either do it right or you don't do it at all"

    Well, Don would never approve of those ideas of yours. First and foremost you cannot say that the remaining hands left to be played in the shoe are going to continue losing like the previous hands. You are suggesting that players end the shoe when there are still positive TC hands to be played, a horrible idea. So the next shoe comes along and you are again in a high bet situation but now you make the bets at the same exact TC that you just previously quit the table because of a few of the finished hands in the current shoe did not produce a stop-loss threshold, wonderful, just wonderful.

    @BoSox

    Mr.Schlesinger, and his quote (you were close, but you did not use the exact quote I used to use...no matter, you were close enough and it's the idea that counts) are the reasons why I continue to runs sims and try to learn from them. No one, including Mr. Schlesinger, possesses the gift of devine omniscience.

    To your point, I am not suggesting that anyone do anything. It is their money and they can do with it as they wish. What I am suggesting is that there is a better way to play than playing optimally...playing the most efficient way to gain the maximum Hourly EV...and that way to play is for optimization...the most effective use of available resources to gain the maximum Hourly EV.

    Your way, the old way, to play optimally regardless of cost does not utilize all the data available to us from sims. My way, the new way, is to play for optimization...to use sim data to identify the point at which one realizes the objective of reaching the maximum Hourly EV for minimum cost...Effective Expected Value.

    Expected Value, like SCORE, is a standardized measure...so Hourly EV of $25.47 per hour equals Hourly EV of $25.47 per hour regardless of the method used to achieve the Hourly EV of $25.47...and some methods are more efficient than others.

    To demonstrate my point, I ran a couple more sims using the methodology from the OP. Your position is that in order to reach maximim Hourly EV, one must continue playing a shoe regardless of loss, and consequently the more one risks or loses will produce more Hourly EV. In my OP I stated a 100 unit shoe bankroll would produce an Hourly $EV of $25.47 and 1K Unit Bankroll ROR of .61. So, according to the old way, if I risked a 1M unit shoe bankroll I would be rewarded with more Hourly EV and lower 1K Unit Bankroll ROR than risking a 100 unit shoe bank roll. But guess what...the sim with a 1M unit shoe bankroll produced an Hourly EV of...wait for it...$25.48 and a 1K Unit Bankroll ROR of...you guessed it....61. The difference is not statistically significant and due to variance.

    You might respond "Wave, you did not use a large enough shoe bankroll to show why I am right and you are wrong...use a 10M shoe bankroll" (it should be noted that in reality there is no difference between using a 1M or 10M shoe bankroll because both, pragmatically, are infinite shoe bankrolls...it is impossible to lose either shoe bankroll playing the bet ramp/spread in the OP). But guess what, the Hourly EV for the 10M shoe bankroll is...wait for it...$25.47 and the 1K Unit Bankroll ROR is .61...the difference is again not statistically significant and due to varience. Shoe SD for the 50, 100, 1M, and 10M Unit shoe bankrolls is 8.2 and consequenrly the differences in their Hourly EV is not statistically significant and due to variance.

    To simplify, you are only going to get so much Hourly EV from a shoe no matter how much you risk in the form of a shoe bankroll, and that amount is identifiable from the use of sims. The minimum amount you need to risk in order to reach that maximum Hourly EV amount is also identifiable and to "do it the right way" you should play in the most efficient manner by using the smallest shoe bankroll that earns you the maximum Hourly EV. This is not playing using a stop loss, it is significantly different; it is maximizing reward and minimizing risk based on known, sim based, statistical data.
    Last edited by Wave; 04-05-2020 at 09:55 AM.

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    Please note that I have simmed nothing, and that my comments are off the cuff.

    I think what it comes down to is what your goals are. You’ve made it quite clear that your long term goal is longevity to the extreme. Some might call this “aspiring to mediocrity.” Personally, whatever floats your boat is fine with me.

    So, let me play devils advocate. You’re advocating that a 50 unit trip roll is better than a 100 unit bankroll, and with either roll, you can achieve a 1 unit per hour EV with minimal ROR. Further, you are espousing this feat with medium rules, 4.5/6 deck pen, 1-4 spread and utilizing Outbound Departure Points.

    Okay, I’ll buy it, provided you have an abundance of tables to choose from. Now, I play (almost) all, and I wouldn't start a session with a paltry 100 units, let alone 50 units. So, if I play all, then clearly I don’t have an ODP (I have well timed departures timed depending on factors). Further, if I’m playing heads up, I’m going for HPH.

    Now, you’re coined a new phrase - optimization versus optimal play. Sorry, but that’s horseshit. You’ve also espoused that 50 and 100 unit trip rolls are infinite - also horseshit. Sorry to say it, but you’re last paragraph is also - horseshit.

    1 unit per hour EV is equivalent to old philosophies espousing increase of 1 unit for increase in true count, which is now known to be far from optimal. I’m not going to get into my style of play, suffice it to say that

    1. With a shortage of tables, Im not going for optimal departure points with a 1-4 spread
    2. Capitalized well, heads up maximizing HPH, I can achieve significant returns far exceeding 1 unit per hour
    3. Maximizing HPH, I can easily overcome long term variance
    4. And Of course, I need to say something to earn me that unhelpful, an experienced player such as yourself may well discover methodologies allowing you to reduce that negative variance - I know that I have.

    To summarize, you are not maximing EV.

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    Quote Originally Posted by Freightman View Post
    Please note that I have simmed nothing, and that my comments are off the cuff.
    With all due respect Freightman, and I do respect your opinion...however:

    1. There are several inaccuracies in your characterizations of my posts. I'm confident that if you slowly reread and ponder them, an intelligent person like yourself will readily identify the mischaracterizations. For one, I have not "espoused that 50 and 100 unit trip rolls are infinite"...I did say that 1M and 10M SHOE bankrolls, not TRIP bankrolls, were pragmatically infinite SHOE bankrolls. I know the SHOE bankroll is a new concept and new concepts often face a high degree of resistance, so I am partial to granting a high degree of leeway/flexibility until it is fully grasped.

    2. "I have simmed nothing..."

    I included my methodology in the OP for specifically this reason. Replication is essential to validate any form of research. I freely provided my methodology so it could be challenged, replicated, and validated. The only way to validate it is through replication...and not via, with all due respect, anecdotal evidence. I love your posts Freightman, but until you do some sims...you have not done any sims...

    3. I'll take sim data over anecdotal data any day....I'm throwing down the gauntlet, run some sims and prove me wrong.
    Last edited by Wave; 04-03-2020 at 11:14 PM.

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    Quote Originally Posted by Freightman View Post
    Please note that I have simmed nothing, and that my comments are off the cuff.

    I think what it comes down to is what your goals are. You’ve made it quite clear that your long term goal is longevity to the extreme. Some might call this “aspiring to mediocrity.” Personally, whatever floats your boat is fine with me.

    So, let me play devils advocate. You’re advocating that a 50 unit trip roll is better than a 100 unit bankroll, and with either roll, you can achieve a 1 unit per hour EV with minimal ROR. Further, you are espousing this feat with medium rules, 4.5/6 deck pen, 1-4 spread and utilizing Outbound Departure Points.

    Okay, I’ll buy it, provided you have an abundance of tables to choose from. Now, I play (almost) all, and I wouldn't start a session with a paltry 100 units, let alone 50 units. So, if I play all, then clearly I don’t have an ODP (I have well timed departures timed depending on factors). Further, if I’m playing heads up, I’m going for HPH.

    Now, you’re coined a new phrase - optimization versus optimal play. Sorry, but that’s horseshit. You’ve also espoused that 50 and 100 unit trip rolls are infinite - also horseshit. Sorry to say it, but you’re last paragraph is also - horseshit.

    1 unit per hour EV is equivalent to old philosophies espousing increase of 1 unit for increase in true count, which is now known to be far from optimal. I’m not going to get into my style of play, suffice it to say that

    1. With a shortage of tables, Im not going for optimal departure points with a 1-4 spread
    2. Capitalized well, heads up maximizing HPH, I can achieve significant returns far exceeding 1 unit per hour
    3. Maximizing HPH, I can easily overcome long term variance
    4. And Of course, I need to say something to earn me that unhelpful, an experienced player such as yourself may well discover methodologies allowing you to reduce that negative variance - I know that I have.

    To summarize, you are not maximing EV.
    So just how would YOU recommend he maximize ev?

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    Quote Originally Posted by BughouseMASTER View Post
    So just how would YOU recommend he maximize ev?
    I’ve made reference to that, in general terms, in a multitude of prior posts. The above Is likely my post for the month. It caught my interest.

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    Quote Originally Posted by Wave View Post
    With all due respect Freightman, and I do respect your opinion...however:

    1. There are several inaccuracies in your characterizations of my posts. I'm confident that if you slowly reread and ponder them, an intelligent person like yourself will readily identify the mischaracterizations. For one, I have not "espoused that 50 and 100 unit trip rolls are infinite"...I did say that 1M and 10M SHOE bankrolls, not TRIP bankrolls, were pragmatically infinite SHOE bankrolls. I know the SHOE bankroll is a new concept and new concepts often face a high degree of resistance, so I am partial to granting a high degree of leeway/flexibility until it is fully grasped.

    2. "I have simmed nothing..."

    I included my methodology in the OP for specifically this reason. Replication is essential to validate any form of research. I freely provided my methodology so it could be challenged, replicated, and validated. The only way to validate it is through replication...and not via, with all due respect, anecdotal evidence. I love your posts Freightman, but until you do some sims...you have not done any sims...

    3. I'll take sim data over anecdotal data any day....I'm throwing down the gauntlet, run some sims and prove me wrong.
    4. Playing conditions. Ours are polar opposites...I have a multitude of casinos available to me, each with numerous tables, within a reasonable drive that can be played afterwhich a reasonable drive will get me home at night without having to incur lodging and per diem expenses.

    5. I specifically stated in the OP that the unit amounts and bet spread are not what I use in live play but were provided as an example.
    Last edited by Wave; 04-03-2020 at 11:27 PM.

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    Quote Originally Posted by Wave View Post
    4. Playing conditions. Ours are polar opposites...I have a multitude of casinos available to me, each with numerous tables, within a reasonable drive that can be played afterwhich a reasonable drive will get me home at night without having to incur lodging and per diem expenses.
    Okay, my 2nd post for the month.

    Your Point 4, in my view, is your strongest argument. The right act (Float like a butterfly sting like a bee) with an abundance of tables, you can make it work, and you should still achieve better than 1 unit per hour - variable based on HPH and how you ramp that 1-4.

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    Quote Originally Posted by Freightman View Post
    Okay, my 2nd post for the month.

    Your Point 4, in my view, is your strongest argument. The right act (Float like a butterfly sting like a bee) with an abundance of tables, you can make it work, and you should still achieve better than 1 unit per hour - variable based on HPH and how you ramp that 1-4.
    That 1:4 was simply for example as stated in the OP; my live play varies between 1:8 and 1:20 with different 1 unit values...for several reasons I suspect are obvious to you. That being said, all changes in variables (rules, pen, # of players, spread, etc.) will effect the number of units for an optimized shoe bankroll.
    Last edited by Wave; 04-03-2020 at 11:48 PM.

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    Quote Originally Posted by Wave View Post
    That 1:4 was simply for example as stated in the OP; my live play varies between 1:8 and 1:20 with different 1 unit values...for several reasons I suspect are obvious to you. That being said, all changes in variables (rules, pen, # of players, spread, etc.) will effect the number of units for an optimized shoe bankroll.
    Okay, my 3rd post for the month.

    So, what I think I’m seeing is variable bet spreads dependant on house edge, deck pen, and possibly (probably) additional spread based 9n tolerance.

    If that is in fact the case, and further that the 1-4 spread was illusory versus actual, then the 1 unit per hour is also an example versus an actual. Based therefore on assumptions, you should be killing it.

    I would suggest that you quote actuals versus non actual examples. It gets you to the right place faster.

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    Quote Originally Posted by Wave View Post
    I included my methodology in the OP for specifically this reason. Replication is essential to validate any form of research. I freely provided my methodology so it could be challenged, replicated, and validated. The only way to validate it is through replication...and not via, with all due respect, anecdotal evidence. I love your posts Freightman, but until you do some sims...you have not done any sims...
    Positive EV opportunities are positive no matter when they come up. Using a shoe stop-loss as some sort of justification for a form of bankroll protection in the heat of battle does not make any sense to me. Unless your intent was to walk away from the game permanently in disgrace.

    In Don's book to quote the last three sentences starting on page nine:

    "You have to play this game like a machine. What would a computer do now? It would play the next hand-after all, the shoe isn't over."

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    Quote Originally Posted by Freightman View Post
    Okay, my 3rd post for the month.

    So, what I think I’m seeing is variable bet spreads dependant on house edge, deck pen, and possibly (probably) additional spread based 9n tolerance.

    If that is in fact the case, and further that the 1-4 spread was illusory versus actual, then the 1 unit per hour is also an example versus an actual. Based therefore on assumptions, you should be killing it.

    I would suggest that you quote actuals versus non actual examples. It gets you to the right place faster.
    You, obviously, get it...which is a huge form of endorsement, thank you. Personally, I've taken my initial bankroll to +10x it's original value, so I am very happy with my overall results. But I am not going to take personal credit for this, I believe I got lucky and had a lot of + EV early on. That is not to say have not experienced some severe beat downs that motivated me to try and find a better way. I have learned SO MUCH from this forum that I'll say nothing more than my intention of the OP was to try to get some APs to think outside the box and utilize hard data potentially available to them via sims that they might have been missing...Norm has provided us with a valuable tool that, in my opinion, has been underutilized.

    You, and many other APs, are way above my pay grade and ultimately have my respect; I do not think I have what it takes to be a full time AP and my hat is off those that do...I wish I could. But sometimes it takes an annoying "troll" (per Mr. Schlesinger) asshole like me to move people out of their comfort zones and to think outside the box. If that is the case and I can get some APs to further think outside the box, then I'll wear Mr. Schesinger's label as a badge of honor.

    Respect Freightman.
    Last edited by Wave; 04-04-2020 at 02:52 AM.

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