Theoretical Blackjack Questions/Simulations- help on extreme deck distributions

Hello All

I am doing some theoretical research on Blackjack and am interested in the house/player edge in some extremely unlikely scenarios, as a means to learn more about the game. As such, before lots of people start to scream "why, that would never happen," this is for theoretical research and nothing else!

As such, those who are intellectual curious, might want to read on....whereas the pragmatic player probably wont...

My questions relates to what would the player or house edge be under the following scenarios:

Ruleset (for both scenarios):

6- deck
DAS allowed
resplit to 4 hands
resplit aces
hit split aces
double on 9-11 only (first two cards only)
double on two cards only
European no holecard rule
Blackjack pays 3:2
No surrender

The following two scenarios are meant to compare exteme cases where 1 deck into a 6 deck shoe, there has been an extreme removal of either low or high cards.

As such, if anyone has simulation software, I would very much appreciate someone running the following two scenarios and letting me know the resulting house/player edge for the rest of the shoe moving forward, assuming flat betting.

Scenario 1:

remove 24 4s
remove 24 5s
remove 4 8s

Scenario 2:

remove 24 x 10s
remove 24 X Js
remove 4 x 8s

I hope that all makes sense, but please let me know if I have ommitted anything vital and thanks again!

Sorry, should have added, I have seen WoOs chart for the impact of card removal- but I believe this applies only to a single card and whilst a couple wont make a material difference, my concern is that in the extreme scenarios above there will be a compounding problem and thus you can not simply look up the impact value in his chart and times it by 24 to account for removing all the cards of one rank.


Although please correct me if I am wrong in that?

Anybody else know how I could work these out theoretically? i.e. not needing someone to run a simulation for me?

much appreciated!

thanks

You can do the math using something like Excel, assuming an infinite deck. It takes a lot of work to set it up, but if you understand the probabilities the result is very rewarding. Once you are done, you can test any effect of removal.

The trick is to assume you are playing an infinite deck that has the proportion of cards you want to test. So, if you want to remove 24 of the same rank, just set the probability of that card to be 0.

sysopaz,

You failed to mention what playing strategy the player is to use:

1. "Normal" BS (the basic strategy calculated for the whole 6D shoe)

2. "Modified" BS (a specialized BS generated for the specified starting shoe)

3. "Normal" card counting (CC for the whole 6D shoe)

4. "Modified" CC (CC starting from the known deck composition)

#1 would be simple to sim, as would #3. The other two would be more difficult.

Let us know what you're trying to find.

Dog Hand

Yes I agree the easiest way is to use an infinite deck analysis - a spreadsheet from scratch should take less than two hours and can work out the strategy and house/player edge. Then remove the cards (or alter the probabilities from 1/13) that you want to and play around. You should see that removing 5s means you don't hit 16 vs 10 etc. and removing 6s means you don't hit 15 but do hit 16, so expect some weird effects and ensure your spreadsheet tests for hitting hard 17s, splitting 10s, etc which look stupid plays but might come into effect. The most interesting is splitting 9s vs 9, as this nearly always stays correct.

Personally I wouldn't include being able to hit Aces after splitting as I've not seen this anywhere. The most common UK rules now appear to stand s17, DDAS, double any two, no peek, re-split Aces, re-split infinite times, so you should get hitting AA vs A and 88 vs A or Ten, hitting 11 vs A/T (the last comes does apply with reasonable positive count).

I've never done simulation, but one interesting thing would be when it was right to deviate from normal strategy (e.g. stand 16 vs 7) and how often each occurred. I'm guessing you'd get 16v10, 12v4 as the rules most likely to flip. Again personally I would do it based on infinite deck with the same proportional composition, but purists would do it on the exact card combinations, and for a PhD I imagine that is what would be required.

Quote: sysopaz

I am doing some theoretical research on Blackjack and am interested in the house/player edge in some extremely unlikely scenarios

This Piece' rel='nofollow' target='_blank'>http://www.blackjackinfo.com/MGP_BJCA_Setup.zip"]Piece of software will do the trick -- it's the MGP Blackjack Combinatorial Analyzer software ... great stuff for questions just like yours ... you can customize the shoe to be what you asked for ...

--Ms. D.

sysopaz,

I ran a CVData sim for a 6D, ENHC, D9-11 game (I missed the part about resplittingand hitting split Aces) for a shoe missing 24 each of 4's and 5's, along with 4 8's. Using Normal BS, the player has an Initial Bet Advantage of 3.241%.

Where can I play? ;-)

Dog Hand