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There are multiple questions on MathOverflow dealing with Blackjack basic strategy, how to derive the statistics and how to apply them. Though I can't seem to find anything specifically regarding multiple players at a table.

My question comes about from real world experience. If you have ever played at more than a few different tables in your life you will know there are players that get vehemently upset if you do not play the basic strategy (Ex. Not hitting on 16). I always chocked this up to "basic strategy is the best strategy to lose the least money over time". Though, as far as I can tell, basic strategy only applies to you.

But at a real Blackjack table there are usually multiple players each having their own mixed strategies. What can be said about the interaction of players strategies? For instance if two people are playing against a dealer, and 1 is playing basic strategy for the given parameters of the game and the other is not, is it detrimental to other basic strategy players if 1 other player is not playing basic strategy?


From what I've seen in some other answers its tough to calculate basic strategy even for a single player, so I'm don't think I can expect an exact calculated answer to this question (especially given the size of possible mixed strategies one could play in BJ). But maybe there is some intuition or some other math/stats that has been done regarding this?


EDIT: Thinking about it now, I guess the opposite question is applicable too can a set of players form some shared strategy which increases their odds of winning?

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    $\begingroup$ Perhaps I am missing something important about how multiplayer blackjack works, but I thought the separate players are just completely independent of each other (except for providing information for card counting). In other words, the decisions made by one player have absolutely no affect on the outcome for other players. $\endgroup$ Commented Feb 23, 2018 at 19:57
  • $\begingroup$ The connection between players is the deck, I think. For instance, say every player has 15 and the dealer shows 5. By basic strategy every player should stand (The "common wisdom" of this is that the dealer also has 15 and should draw out a 10 and bust). Though if one player hits, draws out a 10, and busts, the dealer could now potentially draw a lower card, not bust, and beat all the other players. In this instance, 1 player going against basic strategy hurts other players. While each player's choices are made singularly, they "seem" to effect others through the deck. $\endgroup$
    – KDecker
    Commented Feb 23, 2018 at 20:18
  • $\begingroup$ Does the dealer continue to draw even if they have beaten all the players? If not then that would create an interaction between the players. $\endgroup$ Commented Feb 24, 2018 at 14:11
  • $\begingroup$ @OscarCunningham the dealer would abide by the rules for the specific game. This relates to my mention of the wild possibilities of rulesets and player strategies. Again, this is why this is a soft question, the formulation of an exact set of strategies and rules which is even close calculable would not be applicable in the real world most likely (2 players, single deck, no insurance, etc). I am seeking any way to even envision an answer the bolded question. // I'm not sure I understand the second part of your comment either? $\endgroup$
    – KDecker
    Commented Feb 25, 2018 at 5:20

2 Answers 2

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In a game where the number of decks is relatively small, the players could use a strategy where all-but-one of the group draw as many cards as possible (while making bets as small as allowed). Then the last player (who bets big) has maximal information about the cards remaining in the pack, and can make better decisions based on this.

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The connection you cite in your first comment is a fallacy in probability. It is true that if a player hits a hand he "shouldn't" or doesn't hit a hand he "should" the dealer gets a different card and the result for the other players may be different. On average, the losses will match the wins as the dealer is just drawing a different card from the same deck, but people get very frustrated if the change in the dealer card is to their disadvantage.

For the question in your edit, the best the players can do is show each other their cards, meaning that each one gets a better count. They each then can make their decisions with better information.

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