Four Deck SCORE, Compared to Six Deck?

Great work! This is exactly what I want to compare: playing solo and playing 3rd-base of a 5-player table. Earlier, I proposed these equations.
 

For playing solo,

Delta_solo=(TC_1stCard -TC_bet)^2 + 

(TC_3rdCard-TC_bet)^2 

For playing 3rd-base of a 5-player table,

Delta_3rdBase= (TC_5thCard -TC_bet)^2 + 

(TC_11thCard -TC_bet)^2 

The only difference between these two cases is this: the player's two upcards span from 1st to 3rd cards playing solo, but from 5th to 11th cards playing 3rd-base. Do this calculation for a 6-deck shoe only at these five advantageous shoe situations: HiLo betting TC=+1, +2, +3, +4, +5. Average the values at a fixed +TC number. Discard all other TC numbers.

For the solo case the first squared term will be 0 since it is at the betting count. Can add displaying the table for solo to see what the second term is.

For both cases the squared terms averaged you have are variance which is standard deviation squared. The standard deviations are currently listed but I can add variance. I believe standard deviation is usually used to see typical variations though..

Phil

I added those - the column labeled "sum of the variance differences seat # player cards 1 and 2" is the sum of squared terms you have there. If you enter 5 in the seat select field player card 1 is card 5 of round, player card 2 is card 11 of round.

If you leave the seat select field blank or enter 0 in it then it is solo. If you enter 1 in the seat select field it is first base with 5 players.

Phil

I’ve tested your simulator and found that a counter wins an EV=+0.67% when playing solo but an EV=+0.92% when playing 3rd-base of a 5-player table. I’m not sure if such a dramatic improvement is real or not. A similar EV=+0.89% when playing 1st-base is still a lot too.

Your report table on the variance is clean-cut. However, I’d hoped you could add this for the solo case too. Also, quoting you “for the solo case the first squared term will be 0 since it is at the betting count. Can add displaying the table for solo to see what the second term is,” I believe we are referring to slightly different things (pre or after-dealt). Let me demonstrate it is non-zero in all situations, as below.

Consider a 6-deck shoe game. At a penetration of 208 cards (104 cards remaining), the Running Count (RC) is RC=+7, so the True Count (TC) is TC_bet=+7/(104/52)=+3.5.

If the first upcard dealt to the player is a High, the first squared term is

(TC_1stCard -TC_bet)^2 =[(7-1)x52/(104-1)-3.5]^2 =0.22;

If the first upcard dealt to the player is a Medium, the first squared term is

(TC_1stCard -TC_bet)^2 =[(7+0)x52/(104-1)-3.5]^2 =0.0012;

If the first upcard dealt to the player is a Low, the first squared term is

(TC_1stCard -TC_bet)^2 =[(7+1)x52/(104-1)-3.5]^2 =0.29.

So, I’m referring to the after-dealt TC number, in order to conform to later notations. I think this work is wonderful! Thank you. 

IF, IF, IF....IS NONSENSE

It will display it now for the solo case. The difference is 0 at the first card, same for the first card at first base with 5 players. The counts used in calculating the differences are the counts as they exist before the card is dealt.

Phil

Hi Phil, The simulator has become extremely slow (15 min a run) since you added these variance tables. Regardless, I’ve done some research here.

At TC= +1, +2, +3, +4, +5, and +6 respectively, when playing solo,

Delta_solo = (TC_3rdCard-TC_bet)^2

                     = 0.160, 0.213, 0.252, 0.305, 0.341, 0.387;

When playing 3rd-base of a 5-player table,

Delta_3rdBase= (TC_5thCard -TC_bet)^2 + (TC_11thCard -TC_bet)^2

                          =1.19,1.59, 1.89, 2.28, 2.53, 2.88.

Compared to a solo player, a 3rd-base player at a crowded table has more deviation of his card-arrival TC from his betting TC, and this is more true for higher TCs. From this point of view, I judge the True Count Theorem probabaly is invalid for a multiplayer blackjack table. When the TC is high, you should stick to the table, not go restroom, and not answer any ringing cellphone. Does Dog Hand agree with me here?

I notice it is running quite a bit slower on the chrome browser than on safari on my Apple laptop. I'm not sure why this is and not sure if this is the same on a pc. If you are using chrome and want to try a different browser, could try that. I will try to look into it. 

Also, let me know what you are running on, how many decks, hands, etc. when you are seeing the 15 minute runs. 

Thanks,

Phil

I run with Windows Edge on my laptop.  I always use a 6-deck shoe to run 2,500,000 hands a simulation. I think perhaps the statistics tables you recently added about variance and standard deviation may have slowed down the program. For now, I’ve done with this part of research, so you may delete them if you need. 

As for the comparison between playing solo and playing 3rd-base at a 5-player table, I’ve found that  the latter case gives a lower +EV than the former case does. This result confirms what I have predicted. 

The simulator is only playing the hand in the seat that is chosen. Don't know if or how playing out the other hands may affect the results.

Phil

I understand what you are saying. If a counter shares a blackjack table with 4 other players, he may hit on his two upcards but all others may not. This is close enough to the reality, so do not worry about this minor. I compared the total won % numbers at different seat situations using different simulation runs. 
 

To make the simulation even closer to the reality, you may burn 3 cards before the 3rd-base counter plays out his two upcards, as I proposed earlier. However, I doubt it will produce any meaningful results.