Math for BJs in MHBJ

[Katweezel]

Say I averaged 4.5 hands per round, playing MHBJ over a long session. At 1:21, what should my math look like, so as to calculate how many BJs I should have math-got?

Is this 1:21 formula applicable for each of my 4.5 hands per round average figure and for the dealer as well? :cat:

 

[Kasi]

Is this 1:21 formula applicable for each of my 4.5 hands per round average figure and for the dealer as well? :cat:

Well, God himself can't change the fact that ~1 of every 21 initial 2-card hands dealt will be a BJ. Lady Luck is an equal-opportunity employer and doesn't discriminate based on whether you are a player or a dealer receiving the 2-card hand lol.

Look at it this way - if you could play at a 20-spot table with 19 other players and the dealer, a BJ would occur on avg every "round".

If you are only one of the 20 players, your percentage of BJ's received will not be 1 in 21 every round. If you were the only player at a 20-spot table and could spread to 20 spots, you would get 20 out of every 21 BJ's dealt per round.

So the percentage of BJ's you are personally dealt does go down as more players join the table but the percentage of BJ's dealt per round goes up and your BJ expectation is unaltered.

Does that help answer your question?

 

[Katweezel]

Blackjack rate for MHBJ

Well, God himself can't change the fact that ~1 of every 21 initial 2-card hands dealt will be a BJ. Lady Luck is an equal-opportunity employer and doesn't discriminate based on whether you are a player or a dealer receiving the 2-card hand lol.

Look at it this way - if you could play at a 20-spot table with 19 other players and the dealer, a BJ would occur on avg every "round".

If you are only one of the 20 players, your percentage of BJ's received will not be 1 in 21 every round. If you were the only player at a 20-spot table and could spread to 20 spots, you would get 20 out of every 21 BJ's dealt per round.

So the percentage of BJ's you are personally dealt does go down as more players join the table but the percentage of BJ's dealt per round goes up and your BJ expectation is unaltered.

Does that help answer your question?

Yeah thanks K. Let's say I am the only player at the table, playing a different number of hands each round, between 3 and 7 hands and averaging 4.5 hands per round over say, a 3-hour session. Are each and all of my 4.5 hands per round (average figure) still going to score blackjacks at the rate of 1:21? In other words, would my math be correct if it looks like this:
1/21 + 1/21 + 1/21 + 1/21 + 0.5/21 X 4.5 = Total number of BJs.

(Right, that is obviously not correct, seeing as total number of hands played is not in there.) So, how would the calculation look if I told you I played a total of 4 shoes per hour (6-deck) for 3 hours = 12 shoes @ 16 rounds per shoe, and averaged 82 hands per shoe. Mixing the number of hands up at random, so that I averaged 4.5 hands per round, I am trying to figure how many BJs I should get, related to that 4.5 figure.

My total rounds was 12 shoes X 16 rounds = 192 rounds @ 82 hands per round = 15,744 hands. Divide by 21 = 749 That looks too many... I'm getting lost here. Help! :cat:

 

[Kasi]

My total rounds was 12 shoes X 16 rounds = 192 rounds @ 82 hands per round = 15,744 hands. Divide by 21 = 749 That looks too many... I'm getting lost here. Help! :cat:

Happy to try to help. Keep in mind, quite often, I don't know my as* from 3rd base.

Above you seem to have gone from "82 hands/shoe" to "82 hands/round".

I'm gonna assume you mean you played against 192 dealer upcards ("rounds"). I'm also gonna assume you played 82*12=984 originally-dealt 2-card initial hands by the time all is said and done. Ignore split "hands" as a "hand" lol in case you may be including that in total "hands". Not that it would matter much anyway.

Therefore a total of 984+192=1176 initial 2-card hands were dealt including the dealer's initial 2-card hands.

If 6 decks, one would expect 1176*.0475=56 total number of BJ's dealt.
Of those total 56 expected BJ's the dealer expected 192*.0475=9 BJ's and you expected 984*.0475=47 BJ's.

In other words, you would expect to receive 984/1176=84% of all BJ's dealt.

That's more-or-less how I'd approach it. Which doesn't make it right or anything. But it seems logical lol.

Also, this is for "BJ's dealt" as opposed to "winning BJ's" since sometimes you will push against a dealer BJ.

Do you actually know how many BJ's were dealt and, of those, how many the dealer got and how many you got? Just curious lol.

But that's the leading edge of where paranoia can set in and one can lament the incredible unfairness of it all lol. That's a whole other subject - like you expect 56 BJ's, and indeed 56 were dealt, but the dealer got 20 instead of 9 kind of thing. Or maybe only 44 BJ's got dealt at all. Is he cheating? He may not be but I guarantee you will have no doubt whatsoever that he must be :grin:

I speak from personal experience as I used to keep track of my BJ's vs dealer BJ's as an indicator of a fair game being dealt in my internet play. It all worked out in the end but, sometimes, I was on the way wrong end of the variance paddle.

I'd just tell Lady Luck "Beat me again, baby" thereby turning lemons into lemonade :grin: :whip: Other times, she showered me with equal kindness and I only wondered how bad the whip would eventually be. She loved caressing me from time to time just to make the pain all that much worse in comparison. I never really trusted the b*tch to tell you the truth.

I'm guessing you are only asking because you think you got screwed lol ?

Hope this helps as an "approach" to the problem anyway.

 

[Katweezel]

Multi-hand BJs

Happy to try to help. Keep in mind, quite often, I don't know my as* from 3rd base.

Above you seem to have gone from "82 hands/shoe" to "82 hands/round".

I'm gonna assume you mean you played against 192 dealer upcards ("rounds"). I'm also gonna assume you played 82*12=984 originally-dealt 2-card initial hands by the time all is said and done. Ignore split "hands" as a "hand" lol in case you may be including that in total "hands". Not that it would matter much anyway.

Therefore a total of 984+192=1176 initial 2-card hands were dealt including the dealer's initial 2-card hands.

If 6 decks, one would expect 1176*.0475=56 total number of BJ's dealt.
Of those total 56 expected BJ's the dealer expected 192*.0475=9 BJ's and you expected 984*.0475=47 BJ's.

In other words, you would expect to receive 984/1176=84% of all BJ's dealt.

That's more-or-less how I'd approach it. Which doesn't make it right or anything. But it seems logical lol.

Also, this is for "BJ's dealt" as opposed to "winning BJ's" since sometimes you will push against a dealer BJ.

Do you actually know how many BJ's were dealt and, of those, how many the dealer got and how many you got? Just curious lol.

But that's the leading edge of where paranoia can set in and one can lament the incredible unfairness of it all lol. That's a whole other subject - like you expect 56 BJ's, and indeed 56 were dealt, but the dealer got 20 instead of 9 kind of thing. Or maybe only 44 BJ's got dealt at all. Is he cheating? He may not be but I guarantee you will have no doubt whatsoever that he must be :grin:

I speak from personal experience as I used to keep track of my BJ's vs dealer BJ's as an indicator of a fair game being dealt in my internet play. It all worked out in the end but, sometimes, I was on the way wrong end of the variance paddle.

I'd just tell Lady Luck "Beat me again, baby" thereby turning lemons into lemonade :grin: :whip: Other times, she showered me with equal kindness and I only wondered how bad the whip would eventually be. She loved caressing me from time to time just to make the pain all that much worse in comparison. I never really trusted the b*tch to tell you the truth.

I'm guessing you are only asking because you think you got screwed lol ?

Hope this helps as an "approach" to the problem anyway.

Thank you Kasi, you have been a good help. Yeah, that should have been 'shoe' not 'rounds.' And no, I wasn't screwed - as far as I know - I just like playing alone sometimes as it can have its benefits. There are only 13 casinos down here, for 20 million population, and they are all owned by 3 or 4 owners, so competition is not exactly a big factor, which means casino cheating is probably less inclined to be used. Why should they, anyway? There is an abundance of mugs feeding slots at a HE as high as 14% in some places, as well as all the other games. The Big Wheel is a good winner for them as well, which demonstrates gamblers' generally low skill levels.

Yeah I understand that any fluctuations are possible in the short-term, but for some time now, I have been thinking that there is some unknown (to me) factor when I play MHBJ, whereby every hand will not necessarily score what it 'math-should' for blackjacks. Like, for example, if I played all 7 boxes every round, (which I never do) should I get 7 times the Blackjacks that the dealer scores? If that answer is yes, then long-term, each of my 7 hands should theoretically wind up with the same % BJs total, correct?


And I'm also kicking around a style of play that also shows promise on CSMs. I seem to find that instead of getting my EV (for Blackjacks) PER hand, it doesn't seem to work out that way, for multi-hand play. Meaning that if I averaged 4.5 hands per round, why would I not expect to get what I should math-get for each of those hands (or thereabouts)? Is there any reason at all why I should not? Thanks again for your help mate. :cat:

 

[Kasi]

Like, for example, if I played all 7 boxes every round, (which I never do) should I get 7 times the Blackjacks that the dealer scores? If that answer is yes, then long-term, each of my 7 hands should theoretically wind up with the same % BJs total, correct?

I couldn't agree with you more that there is absolutely no reason I'd assume they may be cheating lol.

To answer your question above - yes. You would expect to receive 7/8 of all BJ's dealt. But each of those 7 spots obviously are not receiving 1 BJ in 21 hands dealt. Once each spot has been dealt to 21 times that spot can expect 1 BJ.

And I'm also kicking around a style of play that also shows promise on CSMs. I seem to find that instead of getting my EV (for Blackjacks) PER hand, it doesn't seem to work out that way, for multi-hand play. Meaning that if I averaged 4.5 hands per round, why would I not expect to get what I should math-get for each of those hands (or thereabouts)? Is there any reason at all why I should not? Thanks again for your help mate. :cat:

Well, again, once each of your "hands" on a given spot has been dealt 21 2-card initial hands, that particular spot should expect 1 BJ.

Each and every "spot", including the dealer's, will expect a BJ once that "spot" has been dealt 21 2-card initial hands.

You play heads-up vs dealer, after 10.5 rounds, 1 BJ will be dealt. At that point 21 2-card initial hands have been dealt. Maybe the dealer got it, maybe you did. You have played 10.5 hands and should only expect a half of a BJ at that point as should the dealer.

After 21 rounds, both you and the dealer have been dealt 21 initial 2-card hands and 42 2-card hands have been dealt in total. Lady Luck expects 2 BJ's to have been dealt by then. One for you and one for the dealer lol.

So, when you say "EV (for Blackjacks) PER hand", I think you are getting confused that that hand should receive a BJ once for every 21 total hands dealt.

It will receive 1 BJ after that spot has received 21 hands.

You could prove this to yourself and take a pack of cards and just deal out 2-card hands. You don't have to play them out. Keep track of number of 2-card hands dealt and number of BJ's dealt. After a few thousand hands dealt, you will find that 1 in every 21 2-card hands dealt was a BJ and that it really doesn't matter whether you dealt them out 1 2-card hand at a time or 3 or 5 2-card hands at a time.

Just try to remember that once of every 21 2-card hands dealt, no matter the number of spots or the number of players, 1 BJ will be dealt to someone somewhere.

 

[Katweezel]

Half a blackjack

Kasi quote: "You play heads-up vs dealer, after 10.5 rounds, 1 BJ will be dealt. At that point 21 2-card initial hands have been dealt. Maybe the dealer got it, maybe you did. You have played 10.5 hands and should only expect a half of a BJ at that point as should the dealer."

Now everytime I get a 10 or an Ace, I always automatically assume I have half a blackjack. lol Thanks for your help; much appreciated Kasi.

Regarding cheating, a guy lives near me, once worked for an illegal casino North of Sydney in the bad old days when they were run by organized crime. Every Friday night, the local boss cop (and a few detectives) would present himself for collection of 'protection' cash.
Whenever management noticed a big winning streak, or a 'cheat' (AP), he would be steered down the back to the 'special' blackjack table. Here, several aces and tens had been removed from the decks. Nobody ever dared call for a deck-check there, which would surely antagonize the gang of thugs whose job it was to look menacing and keep order... (the boss's order).

If someone STILL managed, somehow, to stay with his lucky streak, they had a pharmacist who owed them plenty and to work off his debt, one of his little tricks was to supply some pills that would cause you to really want to piss bad, 20 minutes after you drank your spiked coffee. This was supposed to break up your lucky streak! lol Good thing they don't cheat like this, these days, right? :cat: