Less players have virtually NO affect on EV - ??????????

This is about an article that appears in the Blackjack Insider e-mail newsletter, which is free for a limited time. The title is Number of Players in Blackjack. And if I understand the message right, it seems to be that additional players at the table have almost NO affect on your winnings. Can this be right?

They even admit that it flies in the face of conventional wisdom...that, I'll give 'em!!! I don't doubt the author (Dan Pronovost) at all - heck, I'm barely grasping the whole counting thing, anyway. What I am doubting is my take on this article...am I reading this right? Is he saying it really doesn't matter whether there are 3 or NO players at a single deck game - you're gonna make approx. the same, regardless? I thought that a heads- up game is the ultimate score... and this study seems to cast doubt on this sacred tenent (oooh, that was dramatic, huh? ;) ) All kidding aside, will one of you BJ gurus please spell this out for me....HiLo, Single deck, counting cards (obviously)...what does it mean, from an earnings perspective, if different numbers of players are in the game. And if the answer is that it makes no appreciable difference , then do we stop chasing down the heads-up games, since any game will do just fine?

Please bear with me... I'm simply trying to improve my game. This has not been one of my more lucid post; I hope my question still emerges from all the rambling. thanks. 49.



P.S. The link below is to the above article. This is another first for me. I hope it works OK.

And if I understand the message right, it seems to be that additional players at the table have almost NO affect on your winnings

Untrue. At a heads-up game you will get many more hands per hour. Consequently you will make more money.

Additional players at the table have almost no impact on your expectation per hand. I say almost, I'd leave others to fill in the blanks because its 2am here.

The article uses some premises that aren't quite accurate. First, the author says, "It is a common belief that the less players playing at the blackjack table the better. This belief, especially if you are counting cards, if based on the premise that you will get to play more hands when the count is favorable with less players at the table."

I don't know if what is stated is a "common belief." The primary reason you win more at a heads-up game as a card counter is because you have the advantage and you are playing more hands per hour using that advantage. You aren't going to get either more or less hands at favorable counts in terms of percentages of total hands played in the long run, except in rule of six games or games where only one round is dealt per deck, or in single- and double-deck games where a cut card is used..

The first sim uses a single-deck game with 67% penetration, which is virtually non-existent, and I take it that it sims a cut card. Actually, it belies its own premise when it shows that expectation rises when there are either 2 or 4 players at the table in the simmed game. This is because the number of players in this game directly affects the penetration, which directly affects EV, as the article explains in contradiction to its overall claim.

Now we get to the rule of six sim. The number of players has a direct effect on penetration, as I explained here in a post several days ago. Once you get to four players, with two rounds being dealt, you are in a situation where you are playing the first round in a neutral count and with a minimum bet and you will get one more round, which may be neutral, positive or negative. The net result in this game is that you will be playing more hands in neutral or negative counts, and this will directly affect your EV.

The author used a 1-3 spread for single-deck games. It would be interesting to see how his figures might change if he were using a more aggressive spread. Without simming it, my guess is that even a 1-4 spread would show a bigger difference in EV per number of players. Admitting this is a seat-of-the-pants comment, more aggressive spreads should show a larger difference in EV comparison simply because the ratio of number of rounds played in neutral or negative counts versus positive counts and the larger bet size in positive counts. I'm guessing that the closer your spread is to a flat-bet spread, the less the effect will be in the difference caused by the number of players. The article fails to take into consideration how bet spreads affect EV.

For multiple-deck games, game speed is the primary criterion to achieve higher hourly EV, all other things being equal. In single-deck games, it is speed plus the differences in penetration with different numbers of players that become primary factors in overall EV.