for those of you with math skills

[jee_pack]

can anyone estimate the proportion of cards in a dealer hand compared to cards in a player hand. knowing players can split and dealer's can't, there will be more cards on average dealt to each player that to the dealer. Also the rules are not the same as you all know.

my guess is that a dealer would draw on average 5% less cards than the players in a hand. (of course that is if you play millions of hands and then taking the # of total cards dealt to the dealer/player, then do: ((# of cards dealt to you) - (# of cards dealt to dealer))/(# of cards dealt to you).)

I'm sure someone could just run a simulation of a heads up game with AC rules and playing BasicStrategy (with a giant bankroll), and then the exact # from that simulation...........

So if you can make an educated guess or if you have the exact #, please let me know, thanks!

 

[Renzey]

The Other Way Around -- I Think

Can anyone estimate the proportion of cards in a dealer hand compared to cards in a player hand. Knowing that players can split and the dealer can't, there will be more cards on average dealt to each player than to the dealer.

Somewhere in the blackjack literature two or three decades ago, and I can't remember where, it sticks in my mind that I read the dealer's hand will, on average, contain 3.0 cards as opposed to only 2.7 for the player.

This is because the dealer draws to all stiffs and never limits herself to one hit by doubling down. Notice that although the basic strategy player splits around 2.2% of his multi-deck starting hands, he also stands on 12.8% of all his starting hands (those where he has a stiff against the appropriate dealer's up-card) that the dealer would hit. The player also limits himself to one hit by doubling down on 8.5% of all starting hands (A/6 and A/7 excluded), but then, unlike the dealer, takes extra cards with A/6 and A/7 on 2.1% of all his starting hands.

 

[jee_pack]

nice! how sure are you about this number?

 

[Renzey]

nice! how sure are you about this number?

Apparently, not sure enough. I posted this question for Don Schlesinger on another site, and he answered it saying that dealer and player are both just about 2.7. It seems it could be calculated with a little spare time, but I suppose the exact answer would be of only academic interest.

 

[jee_pack]

Apparently, not sure enough. I posted this question for Don Schlesinger on another site, and he answered it saying that dealer and player are both just about 2.7. It seems it could be calculated with a little spare time, but I suppose the exact answer would be of only academic interest.

I'm not too sure about this... Pretend you are in a situation where where you want to keep your same EV but wanted to MINIMIZE THE RISK factor without changing the size of your bankroll or unit bet. I could very well tell you exact percentage of the 1 hand bet to place to minimize the risk while NOT REDUCING THE EV. It might be something like spread to 2 hands and instead of 50% of the normal bet on each hand, place 63% of the normal bet on each hand (this # actually is mostly always closer to the optimal bet (73$ x 2) than the minimal risk bet (50$ x 2) because of the hand depletion rate. But if I don't have the correct proportion of dealer cards vs player cards in the furmula, the 63% could have came out as 67%, which means your were betting below the point where you EV is equal, therefor, thinking you are Decreasing risk but not EV, you are actually deceasing EV also. Of course it may not be worth it for someone to simulate this if they don't care about minimizing risk, but the truth is if you want to know how the reduce your risk by the biggest amount possible without changing your EV, I have NO choice to use the EXACT proportion in my formula...

 

[jee_pack]

And on top on this, the # can change with the TABLE RULES!@#*(!#&(

 

[jee_pack]

ok, I got it, the trick was to place the # 2.7 in a google search, it came up with a couple of posts around the web, and they mostly all said that on average, its 2.7 both for the dealer and the player, that's one thing less I have to fin... thanks for the help guys! the one goes out to Sunny which apparently is the first 1 to have came out with this answer.