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Thread: Why is the expected return sometimes greater with more players in single deck?

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    Why is the expected return sometimes greater with more players in single deck?

    I intuitively guessed that playing a single deck game was generally more profitable when 1 on 1 with the dealer, than at a full table where you might get 2 hands before a shuffle. This is assuming that the decisions made for the hand incorporate all the visible cards from the current deal (is that a safe assumption for the sim?). I ran a sample set of sims for 1 through 7 players using hi opt 1 with 6-5 payout and qtr deck resolution and got surprising results. Am I reading the results incorrectly, and is there an intuitive explanation for why the returns are not progressively better or worse as you go from many to one player?

    Ranked by worst to best DI, I get:

    4P : 2.18
    2P : 2.90
    5P : 3.36
    1P : 3.65
    3P : 3.86
    7P : 4.17
    6P : 4.40

    _Custom Hi Opt 1 6-5 Pay : Qtr deck TC : 1P.jpg_Custom Hi Opt 1 6-5 Pay : Qtr deck TC : 2P.jpg_Custom Hi Opt 1 6-5 Pay : Qtr deck TC : 3P.jpg_Custom Hi Opt 1 6-5 Pay : Qtr deck TC : 4P.jpg_Custom Hi Opt 1 6-5 Pay : Qtr deck TC : 5P.jpg
    Last edited by bjoe; 08-21-2019 at 12:47 PM. Reason: incorrect ordering of worst to best DI

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  3. #3


    2 out of 2 members found this post helpful. Did you find this post helpful? Yes | No
    Just a little note to let you know it's been a few minutes since you started a new thread.

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    thank you.

    I do appreciate the responses you've given, though. It's very enjoyable here.

  5. #5


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    So, you're confusing two separate issues. It goes without saying that, at a full table, the game slows to a crawl, and you will play a fraction of the hands per hour that you would if playing alone. So, your hourly win rate will suffer greatly. However, CVCX doesn't display the results that way. In each chart, it assumes that you play 100 rounds per hour. Obviously, you need to make an adjustment, because, at a full table, you aren't going to get 100 rounds per hour, so it will take you much longer to achieve those 100 rounds, and your hourly win rate will suffer.

    The other principle is that, for these sims, it assumes that you are sitting at third base. So, all else being equal, the more players, the more cards you are able to see before making the play for your hand, which should definitely increase your win rate.

    Clear?

    Don

  6. #6


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    Thanks for that clarification! So I can take the "hourly rate" to mean the "per 100 hands" rate and all will be fine when making various analyses as long as I understand the impact to how long it will take to complete those hands because of the larger number of players. A few followup questions:

    1) Since the Desirability Index is a function of win rate per 100 hands and std dev--and not of rate per hr--I can probably apply some rudimentary time factor such as the proportionate number of players to scale the win rate, i.e. if 3 players has $30 win / hr reported in The Bottom Line chart and if 6 players has a $40 win / hr, maybe it's roughly close enough to figure the 3 person table to be more like $60 : $40 (versus $30 : $ 40) in comparison. Do I have that right? I know it's not perfect and maybe you have a better idea what the playing time scales to as num players increases.

    2) The player-count order from worst to best was 4251376. Intuitively from your comment about the sim running the player as 3rd base, it makes sense that the "6" with 5 players ahead of you, could be best (on a win rate per hand basis), and better than "7" because of the times that the deck might only see one deal before a reshuffle, but are there other broad factors that would explain why "4" isn't better than "3", or is it mainly the competing forces of "number of players to act ahead of you" and "number of hands the table might get in before a reshuffle" pulling the higher num players and lower num players toward better win rates respectively? Intuitively speaking, seeing 6 is better than 7, but 5 is not better than 6, but 3 is better than 4 etc etc makes me feel there may be other high level reasons to help understand why these win rates (per hands) land this way.

  7. #7


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    Quote Originally Posted by bjoe View Post
    Thanks for that clarification! So I can take the "hourly rate" to mean the "per 100 hands" rate and all will be fine when making various analyses as long as I understand the impact to how long it will take to complete those hands because of the larger number of players. A few followup questions:
    Yes, right.

    Quote Originally Posted by bjoe View Post
    1) Since the Desirability Index is a function of win rate per 100 hands and std dev--and not of rate per hr--I can probably apply some rudimentary time factor such as the proportionate number of players to scale the win rate, i.e. if 3 players has $30 win / hr reported in The Bottom Line chart and if 6 players has a $40 win / hr, maybe it's roughly close enough to figure the 3 person table to be more like $60 : $40 (versus $30 : $ 40) in comparison. Do I have that right? I know it's not perfect and maybe you have a better idea what the playing time scales to as num players increases.
    I'd make the three-player game (four total hands) $70, since the six-player game (seven total hands) is $40, and 7/4 x $40 = $70.

    Quote Originally Posted by bjoe View Post
    2) The player-count order from worst to best was 4251376. Intuitively from your comment about the sim running the player as 3rd base, it makes sense that the "6" with 5 players ahead of you, could be best (on a win rate per hand basis), and better than "7" because of the times that the deck might only see one deal before a reshuffle, but are there other broad factors that would explain why "4" isn't better than "3", or is it mainly the competing forces of "number of players to act ahead of you" and "number of hands the table might get in before a reshuffle" pulling the higher num players and lower num players toward better win rates respectively? Intuitively speaking, seeing 6 is better than 7, but 5 is not better than 6, but 3 is better than 4 etc etc makes me feel there may be other high level reasons to help understand why these win rates (per hands) land this way.
    It may not be a very satisfactory answer, but SD is somewhat quirky, and trying to know what the ultimate order ought to be may not be intuitive. I'm sure no one would look at this and come up with the final order that you did. I also didn't bother to look at standard errors. It could be that some of them were close enough such that there may be some statistical insignificance between or among some of them. Don't think I'd worry too much about it.

    Don

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