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#1
11-28-2007, 09:05 AM
 denks Junior Member Join Date: Nov 2007 Posts: 4
Blackjack q - continuous shufflers - can they be beaten?

Hi All, first post so be kind please!

I have a q that needs some maths analysis on it (Im in the process of running several mill simulations but don't have the mathematical background to also run a statistical analysis as well).

To provide some history - over several years I have been toying with the concept that blackjack was perhaps beatable using BS, with emphasis on bet size management rather than using single bets where obviously the house will win in the long run. After much playing with ideas I was actually playing around writing up an AI engine for predictive purposes for another interest when I came across a few concepts which I believed could have been fitted back into BJ. To cut a long story short, with a decent sized roll (roughly 300x the min table bet) I hit the casino and made a bit over \$10k in about a month - without counting - on \$25 tables. What happened was I would lose most tables, but have a huge win on roughly 1 in 3 tables which more than overcame the losses on the previous tables. Yes the variance was high and rather scary at times but overall everything appeared to be working. Due to other circumstances in my private life I have had to unfortunately use most of my winnings elsewhere and have thus reduced my roll to a level which cannot handle any variance and so have had to stop for the moment.

Now for the maths whizzes - is it possible that the 400 bet win (winning over 50% of the days I played) was just a statistical outlier and cannot continue in the long term? Keep in mind that out of the 30 days of playing I won over 20 days.

I am keen to listen to other peoples findings here based on either the statistical maths, computer simulations or hundreds of hours play (last two I have done).

Here are some basic findings that I have observed in a live casino environment with a continuous shuffler:
Winning and losing streaks tend to happen more often and go for longer than what would be statistically expected in a truly random game
Small and large cards tend to be clumped together - ie it is very common for a stream of picture cards to come out followed by a stream of bad cards - giving almost the entire table 14s and 15s against a dealer 10, or 20s and blackjacks all round against a dealer 8
It is disproportionately common for a dealer to keep busting repeatedly
It is disproportionately common for the dealer to hit high totals on bad cards (eg 4 or 5) repeatedly in a short space of time
I also am finding that I have a greater chance of winning if there are more players on the table than if it is myself heads up against the dealer - I have never won heads up and only once with a single other player. I have won many times on a near full table. I believe this may be due to moving through the cards at a greater rate so as not to get stuck on a batch of 'bad' cards. I know this goes in direct contradiction to the above statement regarding rolls going for longer but I am only going by observations.

Overall what I am getting at - rolls of wins or losses appear to be much more common using continuous shufflers than I would have expected.

Keen to hear any thoughts on this - about to complete a simulator which I believe most closely resembles what a truly random continuous shuffler would deal (not a random card each deal - 50 cards in the discard tray with 10 - 20 cards in a buffer about to be dealt, rest of cards randomly shuffled). Will post the results if anyone is interested?

Would be keen to know what betting strategies would be best suited if a long run were more likely than a purely random game (no doubling every win is not usable, you need a massive roll to overcome the variance).
#2
11-28-2007, 10:14 AM
 SheetWise Senior Member Join Date: Jul 2005 Location: Phoenix Posts: 2,384
Re: Blackjack q - continuous shufflers - can they be beaten?

From my testing, CSM's work. Most are truly random -- you can't even reliably "count" the last hand played. If your club is using a single deck discard rack, and you know the next deal is buffered (none I've seen do this), you can obviously count what's in the rack.

I think the "clumping" you're observing is simply normal patterns, even from a full shoe. I assume you're going to run simulations counting with a one deck penetration.

There will be patterns, but I don't believe they're predictable.
#3
11-28-2007, 04:23 PM
 Poshua Senior Member Join Date: Dec 2006 Location: New York, NY Posts: 508
Re: Blackjack q - continuous shufflers - can they be beaten?

Congratulations on your good luck. You cannot systematically beat a CSM.

As for what you observed, see:

http://en.wikipedia.org/wiki/Confirmation_bias
http://en.wikipedia.org/wiki/Availability_heuristic

Edit to add: what was your system for bet size management? It is easy, with bet size manipulation, to create a situation where you'll have small losses at most table sessions and large wins at a few. The house edge is unchanged and you will still lose over the long term.
#4
11-28-2007, 05:25 PM
 denks Junior Member Join Date: Nov 2007 Posts: 4
Re: Blackjack q - continuous shufflers - can they be beaten?

Thanks for the input. My big concern is that I happened to hit an extremely 'lucky' streak (I hate that word - I believe in probability, not luck) and just happened to sit at tables where the cards were set in my favour and in the long run things will even out.

To give an indication on the simulation Im completing, It will be 0 - 52 cards in the discard tray (some of the dealers go up to 2 decks consistently in the discard tray), with 1 - 11 cards in a buffer to be dealt. Any cards inside the machine will be randomly shuffled each round. I am not sure the exact model of CSM used, it consists of a large wheel inside which rotates with roughly 20 - 30 slots for the card to be dropped randomly into in a first in first out manner. It appears these slots are then dropped into the buffer to be dealt (hence why Im counting on up to 10 cards in the buffer). I will add this slot functionality in the next version of the simulator I write using 30 slots.

So far the simulations have supported the above that a CSM cannot be beaten, I am going to see if there is any difference in number of boxes playing or seating position.

As an aside, based on several million games of simulation per betting strategy I have performed over the past month in what appears to be roughly a 1% likelihood - my lucky month I guess [img]/images/graemlins/smile.gif[/img]

Edit: As I made more than the average amount off the BJ tables meaning I had a better than average run it is quite likely that I did indeed observe the above rather than it being cognitive bias. However that is not to say that in the long term my observations will hold - it is likely that what I observed will balance out in the end and prove to be an exception rather than the rule. Will keep you posted as to the results of the simulations. Curious on thoughts - is 1 mill simulations enough per situation?
#5
11-28-2007, 07:57 PM
 SheetWise Senior Member Join Date: Jul 2005 Location: Phoenix Posts: 2,384
Re: Blackjack q - continuous shufflers - can they be beaten?

[ QUOTE ]
My big concern is that I happened to hit an extremely 'lucky' streak (I hate that word - I believe in probability, not luck)

[/ QUOTE ]

If you hate the word luck -- then just think of it as a fortunate fluctuation. [img]/images/graemlins/wink.gif[/img]
#6
11-28-2007, 11:16 PM
 denks Junior Member Join Date: Nov 2007 Posts: 4
Re: Blackjack q - continuous shufflers - can they be beaten?

Thats exactly what I was thinking of it as [img]/images/graemlins/smile.gif[/img] Either I was onto something, or I had hit a very profitable statistical outlier. My main focus is actually in trying to work out the mechanics behind if these outliers can be predicted in any way. Theoretically winning and losing streaks should follow a bell shaped curve, with the y-axis being 0. My personal experience was that the outer edges of the bell shape seem to occur marginally more frequently than is expected in a perfectly random deal - both winning and losing streaks. This is definitely anecdotal still as I have not been able to reproduce this in a simulation, hence why I was to try to model as exactly as possible the CSM in use. Was wondering if anyone here has any experience or knowledge with 'clumping' - what exactly is it? And is it applicable to CSMs?
#7
11-29-2007, 04:59 AM
 Photoc Senior Member Join Date: Sep 2004 Location: center of my own universe Posts: 7,368
Re: Blackjack q - continuous shufflers - can they be beaten?

[ QUOTE ]
and just happened to sit at tables where the cards were set in my favour and in the long run things will even out.

[/ QUOTE ]

No...they won't. You will lose long run, not even out. It's not possible to beat a CSM using basic strategy and counting into them has proven impossible as 99% of the games I've seen load the cards after each played hand.
#8
11-29-2007, 05:17 PM
 denks Junior Member Join Date: Nov 2007 Posts: 4
Re: Blackjack q - continuous shufflers - can they be beaten?

I should have been more precise about my above statement - by 'even out' I meant 'return to normal' (I am very aware of the house edge, out my way it is approx 0.4%). The dealers at my local in many cases deal out between 1 and 2 decks before placing back into the shuffler. Not all of them but a large enough number. I still not convinced a 2 deck penetration will provide a good enough count into 6 decks though am def running a few sims on it. In the process of doing other things so my model of the shuffler is taking a bit but should shortly have a very close model of how the cards are dealt, including a moderately accurate representation of the shuffler. The only part I can't figure out is whether the shuffler dumps an entire tray into the buffer or only pulls out single cards from a randomly picked tray. I do not hear the machine working while the dealer is dealing which lends me to believe that the tray is not continuously spinning each deal and thus lean towards the first - that a tray is dropped in each time it is required. Nobody happens to know which shuffler this would be (a large circle inside with approx 30 trays that rotates)? Or where I could get info on how it works so I can accurately model it?
#9
11-29-2007, 08:19 PM
 SheetWise Senior Member Join Date: Jul 2005 Location: Phoenix Posts: 2,384
Re: Blackjack q - continuous shufflers - can they be beaten?

[ QUOTE ]
I still not convinced a 2 deck penetration will provide a good enough count into 6 decks ...

[/ QUOTE ]

You would need a 12+ running (using a single level count) to make your bet. The frequency of that situation will be so low, the min/max ratio required for your top bet will (in all probability) push you over table limits. At the very least, the spread you need will draw a lot of unwanted attention. I think the zero memory game needs to offer you more than -.004 to beat a 2 deck penetration into a 6 deck game (and my simulations agree with me [or the other way around]) [img]/images/graemlins/wink.gif[/img]

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