Yes this is online. I'd rather not state the specific casino just yet, though, if you don't mind.

Below are the exact penetrations and latest data. If you are up to programming it using this, that would be great. If it is too much work, I completely understand. I sincerely appreciate all your help so far, especially related to R.

Just a reminder that the "short" penetration shoes were ones in which I entered midshoe. I never left a shoe early, and I never entered a shoe late based on prior knowledge of the count.

Another way to look at some numbers: Here is the maximum number of any given rank that I have witnessed in a 6-deck shoe:

2: 22
3: 24
4: 24
5: 23
6: 23
7: 23
8: 23
9: 23
X: 82
A: 22

Given the other ranks, we should expect that ~23 of each type of X would have been seen, and a number more like 92 would be appropriate. Even if we had only seen 21 of each (which would be outliers, the lowest 4 in the data set), the number would be 84 instead of 82.

Maybe one time the dealer will forget to place the cut card, and I can get 99%+ penetration.

It would be very unusual if an online blackjack game actually uses "shoes" of a certain number of decks, rather than the illusion of a shoe provided for display purposes only. My understanding is that all online blackjack games use a new shuffled deck before EVERY HAND. And they must, so that card counting has no advantage in an online game. It isn't possible. If an online site were to actually shuffle six or eight decks and deal 75% penetration before a reshuffle, they would get killed by bots and counting programs. It would be pretty stupid for them to do it.

I think you should just count the output of each rank card over time and ignore the groupings of imaginary shoes.

I think you are confusing this with typical online blackjack where you are playing a game against software and a RNG.

Many casinos now offer "live" games where you watch a dealer on video deal. In blackjack, they deal from a shoe. In roulette, they spin a real wheel. The video is fluid and you can tell that the dealer is interacting with you. It is not pre-recorded, and it is not cut or edited in any way.

This is absolutely NOT the casino in question, but here is an example if you care to check it out for yourself: http://www.dublinbet.com

That's pretty cool and I haven't heard of it, but it doesn't change the fact that any remote player could easily use a counting program or bot and achieve an unbeatable advantage against the casino, if the game were what it appears. Casinos aren't in the business of allowing that.

Edit: I haven't looked, but they must use rules that make the game suck, like paying 6:5 instead of 3:2, restrictions on doubles and splits, hit on soft 17, and all the other garbage that the house can do to increase their edge from a normal blackjack game. There's no way they would offer a standard game using a 6-deck shoe, online, for the reason I've given.

Regardless of the debate about the casino...I modified the program a bit to be more flexible to different sized penetrations.

This one is easier to operate as more hands get added as well. All you have to do is add a comma and another penetration number to the pens = c() statement and change the high/low count number and you are good to go.

Oh ya. For this one I get .0268.

Sherman

I agree with what you are saying Spadebidder, but perhaps the reason the OP is so interested in this specific blackjack game is because they do things differently from most and he thinks he can in fact get an edge on the game...or maybe not.

this is wild. i thought you were talking about a B&M casinoit he entire time. this has got me thinking

You're right but I was computing the point count of the cards that had been seen, which tells you whether a player over that period was likely to have been a winner or a loser (in this case, a player was likely to have lost a little more than average). Usually with the point count you're interested in the opposite, the count of the undealt cards. You want to know the future, not the past.

bump

and, there is no way this could happen in a real casino right?

Are you seeing every card? If not, that obviously changes the math.

Also, does the house ever call for an early shuffle? It would change the results if it did so when the count got far in players' favor.

It's also worth testing for specific hypotheses, such as the shoe is short exactly one each of A, K, Q, J and T.

Not sure what to do about Aaron's first two questions, but we can test the "the shoe is missing one of each A, K, Q, J, and T hypothesis." I did something a bit more simplistic and just pretended there were 5 less total "good" cards in the shoe and re-ran the simulation from above. So 115 good cards and 120 bad (72 neutral).

The probability of getting a count of -94 or less was about 93% of 10K trials.

So the shoe might not be quite that bad...but it is probably a reasonable guess at this point that there are some number of "good" cards missing.

Yes. I have never left a shoe early, and the shoes that I have entered late (rare) have all been random. That is, I haven't wonged in or anything like that.

Never an early shuffle. Shuffle always based on cut card.