Countability - Effect Of Removal - question when designing a Blackjack like game.

Please forgive me but I am wondering whether anyone can give me some general advice on protecting a multi-deck game from countability and how one can measure it at the design stage or do you just ask the casino to use a CSM?

I'm designing a Blackjack based game, as normal you're trying to beat the dealer without going bust, but it seems Aces have a large effect on the edge. The basic House Edge comes out (using six decks) at 1.61%, but removing just one ace (i.e. 23 rather than 24) increases it to 1.83%, whereas removing a 5 decreases it to 1.54%. Based on wizard's analysis of Blackjack ( https://wizardofodds.com/games/blackjack/appendix/7/ ) it seems this game is more suspect to card removal.

Obviously Blackjack starts from a smaller number, so statistically sometimes there can be an advantage (and counters detect this and take advantage). However (i) is 1.6% sufficiently high not to worry about it, (ii) is the difference of 0.22% for one card in 6 decks a concern, (iii) should I aim towards using fewer decks and an even lower HE?

Many thanks (ps hope to be at Coventry in May).

Let us count :-)

shuffle after each round :-)

It seems that counting might be effective in this game, except it will be more volatile than counting blackjack. I would at least develop a hi-lo count and run simulations where you track how often you hit each count and what you won/lost at each count.

Many thanks for the excellent idea - it took a while to develop the program and iron out some bugs but I eventually managed to run 10 million shoes (338m hands) with 60% penetration (I have to assume the same player strategy all the time as it takes me ages to work it out). It got the House Edge from various small runs at nearer 1.66% (rather than the 1.61% I'd worked out). However it gave the following results.Essentially unless only betting when the count is high (i.e. back-counting), the player would have to jump from a small bet of 1, to a large bet of 39, to show a long term profit. (I'm not sure what happens at larger counts as there were few instances).

Since I've never analysed Blackjack in similar detail, is this spread of advantages similar to that in Blackjack? I also think, starting from a higher initial House Edge, perhaps the count has to be relatively higher before the advantage kicks in.


Many thanks

Do you have the return tracked by count? I'm not sure that is necessary because the return will follow the count even if you don't have the details of the count. At 60% penetration, I think a spread of 1 to 39 is too aggressive for counters and likely too volatile. I recommend trying this at different penetrations, including 4/6 and 5/6.

If you know the EOR for every card, then I would use that data to make a hi/lo count and track your simulation data by the count. This way, you can play with different bet spreads to see if it is profitable. if it takes a spread of more than 1 to 15 or 20, then you are probably safe. You can also recommend the maximum penetration and if they should disallow mid shoe entry.

Quote: charliepatrick

...I'm designing a Blackjack based game... The basic House Edge comes out (using six decks) at 1.61%...

lol and casinos want to pretend we're the "thiefs." 1.61% basic house edge, how to protect that game? Sit on your ass and don't worry, that's an awful game and even the ploppies will figure it out. Shame on anyone promoting a 1.61% HE game as a game of "blackjack."

Thanks - yes I keep a running count (based on the EOR figures and decks left in shoe) and store the results in an array for each count value. I tried your suggestion as it seems 5/6 penetration does give the counter more or a chance, the count-in-favour opportunities occur more often (nearly 16%) and the spread only needs to be 1-11 to make a profit. Like standard Blackjack the advantage gets to about 5% and then reduces as the count increases.

Quote: Romes

Shame on anyone promoting a 1.61% HE game ...

You are right and agree that for a simple Blackjack variant I should be aiming south of 1%. btw the "ploppy" House Edge at the moment is about 2.5%.

My feeling is that I possibly need to introduce a bonus which counteracts the count and both reduces the House Edge and countability factor. I am very grateful for everyone's help. Thanks

Don't go too low on the HE........remember, you only get/keep a game on the floor and get paid for it if the game is winning more than the BJ table it is replacing. If the house BJ game HE is set at 0.6%-0.7% and is actually realizing closer to 1.2-1.3% due to player errors, your new BJ variant better be around 1.8-2% with player errors in order for it to make more money. I think it is difficult in a BJ variant to increase the HE adjusted for player errors by more than 80%-100% of the optimal play HE (although Spanish 21 is such a game, due to the participation rate in the Match the Dealer side bet). To me that means you need your base game to be right around 1%-1.2% with a goal of actual play HE of 1.8-2.4%.......about double what they property is experiencing at regular BJ.

Your average player that is likely to be engaged and entertained by a BJ variant is not going to be put off by the higher HE if in exchange they are getting game features they enjoy. The typical Forum member is not the demographic that will drive the success of a new proprietary BJ variant..

Quote: Paradigm

Don't go too low on the HE........remember, you only get/keep a game on the floor and get paid for it if the game is winning more than the BJ table it is replacing. If the house BJ game HE is set at 0.6%-0.7% and is actually realizing closer to 1.2-1.3% due to player errors, your new BJ variant better be around 1.8-2% with player errors in order for it to make more money. I think it is difficult in a BJ variant to increase the HE adjusted for player errors by more than 80%-100% of the optimal play HE (although Spanish 21 is such a game, due to the participation rate in the Match the Dealer side bet). To me that means you need your base game to be right around 1%-1.2% with a goal of actual play HE of 1.8-2.4%.......about double what they property is experiencing at regular BJ.

Your average player that is likely to be engaged and entertained by a BJ variant is not going to be put off by the higher HE if in exchange they are getting game features they enjoy. The typical Forum member is not the demographic that will drive the success of a new proprietary BJ variant..

Well said.

Quote: beachbumbabs

Well said.

Well said, as well

Quote: Paradigm

...you need your base game to be right around 1%-1.2% with a goal of actual play HE of 1.8-2.4%...

Many thanks, a excellent way of thinking of it.

It's been very enlightening looking further into the countability issue. So I created a Blackjack simulator (UK rules, player stays at the same standard strategy throughout - to be consistent with my existing methods) and I looked at the percentages of advantageous positions and the size of the bet needed to break even.

I was trying to use an existing game and establish a benchmark for a quantifiable comparison how risky my game was. You can see, using the bet-size method as a quantifiable value, that the adverse conditions are with fewer decks and larger penetration. The player has a 1% advantage (usually when count>3) between 1 hand in 16 (6, 66%) through 1 hand in 6 (4, 83%).

I'm guessing most casinos are moderately happy with 6-decks and 66% penetration, although prefer CSMs, but have to accept that some hi-rollers prefer shoes. This seems to imply that any similar game has to require at least a 1-5 spread, and ideally nearer 1-10 or better. Also I'm not sure how often casinos allow advantageous conditions, or just prevent jumping-in using a no mid-shoe entry rule.Thanks again for everybody's help - it's an intellectual trip trying to get this game designed!
Edit results - previously it didn't allow re-split or Aces or splitting of 9s. Also nice that it now corresponds to WoO's figures!

im looking to obtain a spanish 21 program to run sims with. would you be willing to help me with that?

The method I use is scripting, so isn't the best solution. The experts use faster programming languages, so if you know these, they would be better.

Essentially if you already have a normal BJ simulator, then just adjust the creation of your decks to remove the 10's. If not you will need a few routines
(i) Random Number generator - using Mersenne seems OK
(ii) Fair un-biassed shuffling routine
(iii) Dealing mechanism
(iv) Methods to gather the data and put it into readable form

For Blackjack you need to develop a strategy (unless you're developing on on the fly - in which case best of luck!), look at EoR's and develop a count, track results by the count, evaluate the House Edge at different counts, look at countability issues.

Personally at this stage of my game development I'm only really interested in an estimate so I can tweak the design and identify potential pit-falls. In this case I wanted to know how risky it might be to counters and confirm my House Edge estimates.

Quote: Romes

lol and casinos want to pretend we're the "thiefs." 1.61% basic house edge, how to protect that game? Sit on your ass and don't worry, that's an awful game and even the ploppies will figure it out. Shame on anyone promoting a 1.61% HE game as a game of "blackjack."

And yer the fastest growing blackjack 6 deck game has a HE of 1.98%. Its called 6/5 BJ. Evidently the boycott that bj websites called fur in 2004 has been less than successful.

do you have your own personal eor's and a developed count for spanish 21 hit soft 17 that you wouldn't mind sharing with me?

Sorry I didn't analyse Spanish 21 so have no figures on it.