Mean averages with 13 cards/blackjack

[judsonjames]

Hi all, thanks for looking. My first post. I am not a scientist, so forgive me for using the space here, however I have some math questions, easy, I am sure:

Given the standard deck of cards, with values 1 2 3 4 5 6 7 8 9 10 10 10 10 11,

Q1) How do we find the centre average? To be exact, do we divide by 13 cards, or 14 numbers? Given that the ace 1/11 counts as two numbers, I am not sure how to manage this 'singularity'.

Q2) As there are a number of 10's, the centre average may be thrown to the right. Where on a bell curve may this be positioned?

If anyone is interested in, this is not card counting at all, but keeping probability to whole numbers, please write.

Also,
Q3) The origins of blackjack are shrouded in mystery. 2 french mathematicians are approached in the 17th century by an unknown gambler, wanting to understand the probablity of a certain game he devised. How could they have computed thus? was 17thy century maths totally stellar? And what's more, given the endless tomes of math out there on the subject, making it all look impossibly impossible, how did they devise the formula, and not leave a shred of evidence?

And,
Q4) Our nearby casino rated there table rules to give a house advantage of 0.5% approx. How is that arrived at?
Just because one lose more games than you win (101/200 hands, if played accurately), doesn't mean you don't make more $ by doubling up when the odds are better, or better payouts for blackjacks. (Assuming one betted with a consistent percentage of ones purse, to observe rate of play, such as 5-10% of purse). One plays the same game regardless of the stakes.
And further, some of the 'standard play' charts out there seems quite silly, like, being suggested to hit on 17, with a 4/13 of holding (9/13 throwing the game away), while the dealer on 10, if he hits with 2 3 4 5 6 7, either has to hit again, or draws the hand, thus having 6/13 odds at that point, better than 4/13, then further odds may make the dealer go over. Any ideas please.

As one can see this is not card counting, however feel free to contribute any or all information, even if based from card counting or whatever. I have seen the miles of math out there...I can count to 13, and divide by 100, that's about it.

I am assuming we are using a continuous shuffler with all cards inplay at all times. (6 decks). (Shouldn't make much difference but by my reckoning more decks are better).

Thansk so much for your interest

Jud

 

[mmwave]

ging by the questions posed, it seems like you are interested in the probability and mathematics behind the game of blackjack. I am happy to provide some insight on these questions as a scientist.

Q1) To find the center average, you would divide the sum of all the card values (1+2+3+4+5+6+7+8+9+10+10+10+10+11) by the total number of cards (14). This would give you an average of 6.5.

Q2) The center average may not necessarily be thrown to the right on a bell curve. It would depend on the distribution of the card values in the deck. If the distribution is symmetrical, the center average would be in the middle, but if it is skewed towards higher values, the center average may be slightly to the right.

Q3) In the 17th century, mathematics was not as advanced as it is today, but there were still some sophisticated mathematical concepts that could be applied to gambling and probability. The French mathematicians may have used techniques such as combinatorics and probability theory to analyze the game and calculate the odds.

Q4) The house advantage in blackjack is determined by the rules set by the casino. In general, the more favorable rules for players (such as being able to double down on any two cards) can decrease the house advantage. The 0.5% advantage mentioned by the casino may be due to a combination of factors such as the number of decks used, the rules for doubling down and splitting, and the payout for blackjack.

It is important to note that while card counting is not considered cheating, casinos may still ask players to leave if they are suspected of counting cards. As for the "standard play" charts, these are based on mathematical calculations and probabilities, but they are not guarantees of winning. They are meant to provide players with the best possible strategy for each hand, but ultimately, the outcome of each hand is still based on chance.

I hope this helps answer your questions about the mathematics behind blackjack. It is a game that involves both skill and luck, and understanding the probabilities can help improve your chances of winning. However, as with any form of gambling, it is important to play responsibly and within your means.