Four Deck SCORE, Compared to Six Deck?

How about this? Consider a 5-player table including a third base counter. You deal out two cards face-up to each player in the dealing order of a real casino, then you burn 3 cards, and then you play out the counter’s hand. This is equivalent to giving 2.75 cards to each of the remaining 4 players, and it should be close enough to the reality.
 

All of the above arguments will be resolved by this simulation. 

There is no need for approximation. The concept is not new. Accurate simulations have been done. There is nothing to resolve.

I understand you have done such simulations, but what I propose for Phil is to modify his current simulator with the least amount of work. I want to quantitatively find out, is True Count Theorem valid for a 5-player table? 
 

Furthermore, there are no accurate simulations. Most players do not play basic strategy after all. 

A tc plus 5 is plus 5......

Halves 16...9 = 5 h/st

Regardless hdup or full table

You’ve got what I am saying. If heads-up TC=+5, I bet $300; if at third base of a 5-player table, I bet $200 because I am not sure of the TC=+5 accuracy here. 

+5 with one deck left

probability of a high card 23/52 probability of a low card 18/52 assuming 11 medium cards, didn’t assume 12 so that I didn’t have to say 22.5/52 and 17.5/52) 

There is a 44.2% chance of getting a high card,

34.6% chance of a low card, 21.2% chance of a medium card. These change as the cards go out but if you use these % over the 4 cards that need to come out before you get your first card then on average of the 4 there would be 1.77 high cards out, 1.38 low cards, .85 medium cards.

And if a high card came out first the probability of diluting another high card drops so the above % are more likely to get closer, so using the above %s probably favor your thought of the TC dropping. 
 

So on average when the first card gets to you the true count on average should drop from 5 to around 4.61. Then 5 more cards for you to get your second card. And all the while the probability of true count dropping being a little less likely as high cards are a little more likely to have been used. So on average the TC may be around 4.25 or probably a little higher when you get your second card. (I was also ignoring the lower divisor for TC as cards come out).

So maybe not too bad leaving a higher bet out there, maybe lowering it a little like you are doing.

If the TC started lower, say at +2, the TC should move lower at a slower rate. If the TC was higher, say at +8 then maybe it drops on average to 7 or even if went to 6 your high bet is probably ok.

But if you look at a high bet of $200 or $300 a hand and you look at some of the worst case drops over the course of several hundred hands I don’t doubt that you could easily be down $10k or so depending of course how often betting at this level and what your other bets are. Or even typical fluctuations like one standard deviation, could be, I am just guessing maybe $4k or so up or down depending on how long you play and how often you place high bets.

It is so random so there is a lot of variability and higher risk when raising bets even in advantageous situations. 

I think the True Count Theorem is invalid for counters because they spread their wager to (equivalently) play only advantageous shoes.

To simulate a counter at a multiplayer table, you just deal out two upcards to each player, then burn a few cards, and then play out the counter's hand,  just like that in 1-player situations.

What is important here is this. For example of a 5-player table, the 3rd-base counter receives the 5th and 11th cards dealt, and the dealer receives the 6th and 12th in that round. 

I used to get angry w/the true count theorem"e nonsense. Now I find it comical.

Address my question of why you guys aren't satisfied w/Blackjack Attack calculations, and further research is needed?

Not for me and associates w/over 100 yrs f/t success 

Let Phil say first. I test his simulators and provide feedbacks. 

I added tracking of the exact count at beginning of each hand and at each card arrival. There is a chart at the very bottom of all the results (scroll way down) that shows the average counts and standard deviation of differences in counts. Am seeing very little difference at all in counts at the beginning of hand and at each card arrival. Let me know what you find.

The simulator plays your hand as usual and just deals the initial 2 cards to each of 4 other seats. It doesn't play the hands in the other 4 seats. There is a seat select field under the ace side count entries. If left blank the simulator doesn't do any of this. If you select seat 1 or 5 (it only does seat 1 or 5) then it tracks the counts at the beginning of the hand and at each card arrival at the seat selected. 

Thanks,

Phil

I roughly tested everything on my cellphone. My focus was on the Total Won % number. When I set these numbers

the total hand number was 2,500,000 hands per simulation.  If I play at 3rd-base of a 5-player table, I will consume almost 3 times of shoes as that in the 1-player case. Is this right?

Also, you did a lot of statistics on the average TC at three different dealing points of a 3rd-base counter at a 5-player table, but I’m not sure the meaning here, because they should be close. However, I’d like to compare things between a 5-player table and a 1-player table. 
 

Let me try it more and think about this. This is tricky. 

It shows the average exact count at the start of the hand being dealt. Then the average exact counts at each card arriving at the player. Then the standard deviation of the difference between each arrival count and the count at the start of the hand. 
 

You can select seat 1 or 5 for your hand that gets played.

Phil

I noticed some misunderstanding here.
 

If I say a 5-player table, I mean a blackjack table that is packed with 5 players each playing one-hand;  if I say a 1-player table, I mean a blackjack table that has only one player playing one-hand with the dealer. 
 

I am not interested in comparing the +EV results between 1st-base and 3rd-base in a table packed with 5 players. That difference should be negligible. Instead, I want to compare a counter's +EV results between playing solo and playing at a crowded table. 
 

Thank you for your patience! 

If you leave the seat select field blank it is one player playing solo.

if you select 1 or 5 in the seat select field you are playing in the selected seat at a table with 4 other hands. Only the initial 2 cards are dealt to the 4 other hands. 

That is what I thought. Before further test, I need to clarify this. If I set a fixed total hand number of 2,500,000 for a simulation, I will consume a lot more shoes (almost 3 times) if playing 3rd-base at a 5-player table, than that if playing solo at a 1-player table. Is this correct?  Thank you again.

Yes, also a lot more shoes if playing 1st base at a 5 player table.

One more thing.  If I select 5 in the seat selection field, a 3rd-base counter at a 5-player table will receive the 5th and 11th cards  in that dealing round as his two upcards, and the dealer will receive the 6th as her upcard and the 12th as her downcard. Is this correct?

I think this work is fantastic! 

That’s correct. Thanks!

Phil

I will test the simulator in a few days. However, I’ve been thinking about your averaging on these TC numbers at three different dealing points. Probably it makes more sense to find the sum of two squares of the player’s offset TC from the betting point TC. For example of a counter at 3rd base of a 5-player table, the equation should be,

delta= (TC_5thCard -TC_bet)^2 + 

(TC_11thCard -TC_bet)^2 

Also, statistics should be done on advantageous shoe situations (TC>0) only. Discard all other situations. 

The sum of squares goes into the calculation of standard deviation. It's part of calculating variance and standard deviation is the square root of variance. Yesterday, I had an error in how the differences were being recorded. That should be fixed now.

The differences between the average count at the beginning of hands and the average counts at the cards arriving at the player look low. The standard deviations of these differences however seem large. This was with 2 decks. Not quite as large with 6 decks. 

For the differences it takes each exact count difference at the beginning of each hand and each card arrival at the player at the selected seat. These differences are then squared and are added together (sum of squares). This is divided by the number of hands -1 as per the formula for variance. The standard deviation is then the square root of the variance.

Also, I changed the program so the playing hand can be at any seat 1-5.

Thanks,

Phil