Standard card distribution.

PlayHunter

PlayHunter

Active Member
I have the following questions (which would create me a description over how the cards are fairly distributed in general):

1) How often a player would be dealt 30 to 32 cards of the same rank (5s for example) out of an 8 deck shoe with 60% penetration ?

2) How often a player would be dealt 30 to 32 cards of the same rank out of an 10 deck shoe with 50% penetration ?

3) How often a player would be dealt more than 32 cards of the same rank out of an 10 deck shoe with 50% penetration ?

PS: Sorry if this is not the right place to post this thread. I was thinking that Mr. Gronbog software can solve these easily if he have the time for it.
 
I could easily add the collection of this sort of data to my sim. Before I do, I need to clarify exactly what you're asking for.

When you say "How often a player would be dealt ...", do you actually mean that these cards are dealt to the player, or is it that the cards are dealt in general (either to the player(s) or to the dealer).

I'm guessing from the specific nature of your question that this has happened to you in online play. Bear in mind that just because an event has a low probability of occurring, it doesn't mean that it won't happen, or that it won't happen more than once in a short period of time.
 
There is probably a formula some where on the web that can calculate the situation. As a place to start I would go to the Wizard of Vegas site http://wizardofvegas.com/ (join it if you are not familiar with it), go to the math forum and ask your question. One of the math experts could probably tell you.

Larry
 
Yes, cards dealt out of the shoe, either to the player(s) and/or to the dealer as well.

Yes, it did happened online .. but it is frequently happening, all I want to see is if it happens more frequently than it should be.

Basically I have found a game which does use a RNG software and does not shuffle the decks after each hand.

But something is wrong with it. I believe it deals out too many cards of the same kind. The game is said (in the rules)to have 8 decks and to deal 5 decks before the shuffle is done. The problem is that I am sure it uses at least 10 decks, but I wonder if there could be more than that.. thats why I need this info.

Hopinglarry, thank you I know WoV, I asked this already there and got no response.. Anyway, people seem to not trust the casino software in cause.

Anyway, if anyone is interested about where this game can be found I think would be better if we talk more details on PM ?
 
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Hoppinglarry thank you, that calculator it aims to calculate what I need, but I think it is not good on its results. For example, I have inputted the following:

Population size: 520 - (total number of cards)

Number of successes in population: 40 - (maximum number of cards which have the same rank in the shoe)

Sample size: 260 - (penetration)

Number of successes in sample (x): 39 - (minimum) number of cards of the same rank dealt out between the shuffles

And the result shown was:

Hypergeometric Probability P(X = 39): 8.42....

and

Cumulative Probability P(X =/> 39): 8.60....

And if I lower the "Number of successes in sample (x)" from 39 to 38, it says the result will be:

Hypergeometric Probability P(X = 38): 1.91....

and

Cumulative Probability P(X =/> 38): 2.00.... (and this is impossible - the number should be higher than 8.6 - what I am missing ?)
 
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You are missing the "E annotation" at the end of the results.

For 39, the result is .00000000000842, very small chance
For 38, the result is .000000000191, but much bigger than 39:)

These very small numbers are to be expected. Just think of the odds of going from 38 at 259 cards vrs going to 39 at 260. You only have 2 chances in 261


Look at numbers that might come up such as the expected mode 20.
For 20, the result is .13 (13%)
For 19, the result is .1238 (12.38%)
For 21, the result is .1238 (12.38%)
For 18, the result is .1056 (10.56%)
For 22, the result is .1056 (10.56%)
Roughly 59% of the time you will come up with one of these numbers. You can keep expanding this with 14-26 coming up will happen about 93% of the time.

The graph of the different numbers is not your "normal" bell shaped curve. It drops off on each side of the "mode 20" very quickly.

If Gronbog did a simulation, then after some large number of iterations the results should start conforming to these types of number if the calculator is working the way it is supposed to.

You might be better looking at the Wizards page http://wizardofodds.com/games/blackjack/appendix/13/ on determining the number of decks used in an online game.

If I really wanted to know, I would play one hand and then start the game again and continue doing this until I got enough of a sample to determine what percentage of suited pairs were coming up in the first 4 cards. I would be playing forever if I played until the machine shuffled.
 
By the way when I use 20 as the expected mode, this is not exactly correct. There are actually 41 possible results when you include zero (just as likely as 40), but is close enough to the mode.
 
Hopinglarry, thank you very much ! Yes, I did not read what E annotation means, sorry for my fault ! I guess the calculator is very good indeed.

Well, as I see the probability of being dealt 30 or more cards of the same rank in a 10 deck shoe with 50% penetration is only 0.000736 and I have played about 30 shuffles and been dealt 30 to 32 cards of the same rank around 18%. A few times 33 but thought I missed something since the rules said there must be eight decks.. and last time I have been dealt 38 cards of the same rank !!! And they have passed a third party Technical System Testing audit. Nice!
 
I don't know what they are doing.

If you have an infinite deck where the probability of getting a card never changes, then with normal distribution and 5 decks dealt (260 cards) the probability of getting 30 or more of the same card is only 1.756%.

They are doing something strange.
 
I suppose they use way more decks in the shoe (16?) or their RNG is simply working faulty. Either way, they shouldn`t have passed the third party fairness audit.
 
Black Diamond / Box24 / Spartan Slots - all uses Top Game platform and are owned by Deck Media, but the same games can be found at any Top Game casino.
 
I wouldn't play the game at all.

That being said the game might be beatable if they consistently deal more than the expected number of face cards. I have never thought about a strategy where the deck would basically be negative most of the time, but as the deck is going negative by quite a bit a person probably wins more hands than normal and surely has more pushes.

When you get a 10 count card you do not bust very often and you should have just as many 10 counts as the dealer. Dealers advantage is your busting. Might be the type of game where you play 10-20 hands and start a new game before the shuffle.
 
A little more to say on the thing.

I guess it is possible that the RNG is treating K-10 as the same card and picks Ks vrs Q,J or 10 for some reason or other. If 4/13 of the total cards dealt are one of these then it should make no difference in the play.

If the excess of Ks is not being offset by one of the other 10 counts, then that could be bad. Who knows it might not be dealing as many Aces as it should, cutting down BJ possibilities. Then again it might not be dealing as many 5s as it should and hurting the dealers chances of turning that 16 into 21.

In any event, I wouldn't play it.
 
What I can say is that about 75% of that 30 full shoes (shuffle to shuffle) it went negative all the way. - I don`t know if this is normal ? I`ve had only one single shoe which went positive all the way, but only with a true count lower than 3. And of all positive true counts I believe I`ve only had half of them at +2 or higher. (considering 8 decks) And never had a true count higher than +5. - I do not know if this is how an 8 deck shoe blackjack game should behave or not ?

What I have noticed was the fact that many times when I was playing on 4 hands at once per round, streaks like winning and losing 3-4 rounds in a row (winning or losing on all 4 hands in the round for a total of 12 to 16 hands) were happening quite frequently. Comparing it to other multihand versions, it felt very streaky.
 
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