blackjack weighted averages

What is the mean average value of 13 cards?
1 2 3 4 5 6 7 8 9 10 10 10 10 11 =

96
--

Do we divide by 13 cards = 7.38

or 14 values = 6.85.


?


thanks

blackorange

You cannot answer that question unless the value of an ace is defined. I am also not sure how this information will help you in any way. For example, if you are considering hitting a 16, the mean is not relevant. What is relevant is that you will get 17 1/13 of the time, 18 1/13 of the time.... bust 8/13 of the time. But if you forced me to answer your question, you could say the mean has a 'range' of 85/13 to 95/13, depending on the frequency that an ace is 1 versus 11.

I would only consider hitting on a 16, relevant to what the dealer has got. If Im gonna lose 8/13 by throwing, so be it, if the dealer has an 8/13 of winning. If the dealer was looking to lose 9/13, I wouldnt need to throw as that would only be worsening my own odds.

And so to answer: The value of the ace is defined isnt it, by definition it has a designation, albeit, two designations. If it can be defined two ways, does it count as an extra unit, this 14 values? But, no, since there are only 13 cards, its therefore necessarily got to be divided by 13. So do we consider the average between the two? 90/13, which is 6.92.?

I am trying to figure the average of what a 50/50 average may be, so one could estimate wether theres a 50/50 chance of being under or over a certain figure. wether it be 6 or 7 or 8, or a fraction of that.
Then I can estimate where the dealer may lie 50% of the time, or better, and knowing the option of 4/13 for a 10, one can try to ascertain wether the dealer will land in the stand zone.

My train of thinking is that there are only 13 cards, no matter how many decks. Even if there an infinity of decks, as you know only 13 cards.

I say a guy play once, and he won like crazy.
He only ever bet a 10th of his purse, thus eliminatig wild betting, and being able to track his winnings, and he always bet the same way, no matter how high the stakes. He also didnt seem perturbed when he lost, because he knew when to double, and his 21's ended up putting him way in front. It got me thinking a lot about his strategy. Also he didnt look at anyone else cards, because in my estimation, with 306 cards in the shoe, and only 10 removed, its hardly worth the headache of calculating the .002 change in odds. I'm sure he wasn't card counting, and it would be quite useless as a mechanical shuffler was in play after every hand.

So I'd rather stick with whole numbers.

And 13 being odd, it seems that one can eitehr be on the high side or low, ie 7/13 comp. to 6/13.

I figure if the dealerr only has 5 places to land that he can stand on, surely there must be potentially 8/13 games to be won. ?

The other thing to consider is that there are a number of extra games that can be won and lost at the ends of the bell curve. ONe may forget that on 12, theres 4/13 games to throw away, and many players would unnecessarily lose these thinkingthey are 'low', with out evaluating the dealers potential. Similarly, to be on 18, one would think that to throw would be insanity, but, if the dealer had an 11/13 of wining, well, it would be a loss of a game not to throw, as there are 3/13 games to be picked up. And so it goes against common sense, but these extra games make up the winnings edge, couples with doubling and blackjack payout.
Hope you got this far. I havent seen anything written anywhere re this stuff, every talks about card counting...

Wow! This was intense ...
Just look here: https://wizardofodds.com/blackjack/strategy/calculator.html
Or buy a strategy card in a casino gift store, it will just tell you what to do.

I'll just comment on one thing - betting 1/10th of "your purse" *is* pretty wild.

I figured that while you could lose 10 games in a row, as your purse goes down, so does your bet, so in some ways its still running at a constant. Its too easy to put it all upon a hand and lose it all. No one knows of they are gonna win or lose the next hand, so why go 'hunching'? riduculous. So eliminate that by betting a constant value. 10% is not actaully so wild. i found 20% sometimes is safer, but any less and it takes too long to make progress...

please forgive me for the poor typing in the previous post.

Thanks for the tip on betting cards, but I dont believe they are 100%

blackorange

Does the calculator shows house margin of winning per 100 games, or coin margin, based on a constant bet? if it only showed win margin, does it necessarily follow that the house will also make more money, even there is potential for splits and bj payouts?

I wasn't really trying to calculate the house margin, as opposed to calculating the potential for the dealer to land safe, or be forced to throw.

How, under wizards simple strategy, does 'cost for incorrect play at 0.53%'? Cost for really incorrect play can be a hell of a lot more costly if one seriously deviates from his suggested strategy.

If he reveals the process by which he formulated the table, there may be a way of memorising the process, so one can calculate thus with each hand, thus not 'playing incorrectly one hand per 12 hours of play' (seriously)..

Quote: blackorange

10% is not actaully so wild. i found 20% sometimes is safer, but any less and it takes too long to make progress...

It has been shown that overbetting your bankroll like this will cause you to lose all (read: most) of your money pretty quickly, even if you have an advantage! The Kelly bet criterion usually involves you making a bet around 1-2% of your bankroll, with an advantage. You should make bare minimum bets without an advantage, or enough that you have fun.

Quote: blackorange

I would only consider hitting on a 16, relevant to what the dealer has got. If Im gonna lose 8/13 by throwing, so be it, if the dealer has an 8/13 of winning. If the dealer was looking to lose 9/13, I wouldnt need to throw as that would only be worsening my own odds.

You're chasing your own tail. For one thing, the dealer will win more than 3/4 of the time if you stand on a stiff vs. a 7 thru Ace. That alone would suggest why you hit that 16, but you don't WIN 5/13 of the time; very often you make a 17 or 18 and lose anyway.

What hitting a hard 16 vs. a 7 or higher actually does is improve your chances of winning from lousy to slightly less lousy. That's all. Hard 16 is a bad hand.

Sorry, what I meant earlier was not 20%, but 1/20th. If the overall purse goes down, so too does the wager. Why would one want to vary the gamble? Seeing that odds for any particluar round of play do not change in the overall scheme of things, irrespective of how much money is at stake.

And yes, 5/13 is not a guaranteed win, thats for sure, but it's also a certainty that we will defintely bust on 8/13 hands.

If the dealer has 10, and we've got 16, well the dealer has got an 8/13 of winning straight up, and if we throw we've got an 8/13 of losing straight up.

So do we throw the game by handing it over to the dealer, or try to inprove our own odds?

I would say it's safer to not lose more than we already will in that scenario, and let the dealer get the 5/13 cards that will force him to throw, and then throw the game.

Seeing that the dealer has a 5/13 of getting 10 or 11, we would really likely need to get a 4 or 5 to still be in the game, therefore we are reducing our chances to around 2/13.

So standing, and letting the dealer get 5/13 of bad cards, then does give a better than 50/50 of busting out for us.

that to me is better probability.

Any takers?

After reading your subsequent posts I now think I understand what you are asking. You are asking what is the best way to play to maximize your chance of winning. There is a concept, called basic strategy, that answers your question. There are slight variations depending on the rules of the table. For example you will play slightly differently if the dealer hits a soft 17 versus standing on a soft 17. The companion web site, wizardofodds.com, has a section on blackjack, and there are many small laminated cards you can buy with basic strategy. If you are even more interested and have the time and inclination, you can learn to count cards and thus increase your bets when there is an advantage for you, or decrease when the opposite is true. As far as your math goes, it is too simplistic. You will have to trust me (and those that have developed it) that the full math analysis of all possible combinations is what has lead to what is now called 'basic strategy'. Good luck.

Thanks.
I know of basic strategy, and it wasnt invented 300 years ago..or was it.. the game was the same, therefore the calculations were the same to determine the profitability of the game.

I appreciate your suggestions.

At our local casino, all the cards go straight back into the machine after each and every hand, basically eliminating any use for card counting, as all the cards are available all the time..And if Im the first player to recieve the cards, i believe I have the best odds, as the deck is untainted by loss of cards.

Please forgive me, but which part of my math is too simplistic or incorrect in the above example regarding playing 16?

law of averages states that the above conclusions will occur that many times with those plays.

Some hands have better margins, some are losing hands.

I'm just trying to illustrate that example, and if you can comment on it that would be great!

If a dealer had to hit on 17, that would be great as it means more chance to win:)

blackorange

I will try and be polite- but if you believe that by getting the first cards gives you the best odds then you need to start from the beginning in your understanding of probability, statistics, etc. My using the term 'basic strategy' includes the sometimes not inherently apparent plays one must use to maximize your chance for winning. Do you split 6's against a 7? Will you double a soft 18 against a 5? Choosing the incorrect play gives the house a slightly greater advantage. You are correct in that at your casino you cannot count cards if it is a constant shuffle. Dealers never hit a hard 17, but there are some places where they hit a soft 17. That is to the dealer's advantage, not the player's. And as I said, there is no one basic strategy. Since there are different rules which are played, there are by definition different basic strategies. Rules that can change are- number of decks, BJ paying 3/2 versus 6/5, how many times can you split, on what totals can you double, can you surrender, do you get a bonus for obtaining 6 cards, etc.

While you can't average the blackjack points values like you suggested in your first post (both your options are wrong), I think for your purpose you should always count ace as 1. You won't be applying your calculations to hands that are less than 11 anyway, since you can't bust if you can still count an ace as 11.

So, count an ace as 1, use 13 cards, and average = 85 / 13 = 6.54

I hope you don't lose too much money trying to reinvent blackjack strategy...

I believe that getting the first cards gives one the most consistent probabilitys. Yes, if one happens to be last player, there could be 30 cards on the table, and one may very well be able to spy an opportunity to deduce wether they are inn a good position or not. However one could also be lead to believe that nearly all the good cards are on the table, and play differently. I would rather play with an unadultered deck, knowning that that every 13th card is an ace, no more or less, regardless of how many decks.

By apparent plays, do you mean standing while still on a low value, or drawing cards while on a high value? that would seem to be counter-intuitive, yes.

With regards to splitting 6's against 7's, or doublings, these are decisions to maximise winnings. While we all want this, that is not the course of this particular thread/query.

I am only concerned here with the calculation of the win itself.


Yes, I appreciate that a dealer throwing on soft 17 is to the house advantage.

Regarding number of decks, I feel that more decks means less change to the ratios, so if one card is taken out of a thousand, it has less impact than 1 from 100. #/2 pays better than 6/5, but again im only interseted atm in calculating winning angles, not the maximising of funds. That is for a different thread.
And yes if the casino does have a 0.5 advantage or whatever they publish, and that therefore anyadvantage in doubles et is the only to forge ahead, then yes, those things matter.

How is the casino edge calculated?

Thanks

I see that wether if I chose 1 or 11, it's still valued at 85 for the deck over 13=6.54.
Now I can estimate wether one will be over or under this quantity.
Thanks. Now i have my answer.


Haven't lost a cent yet.
Not going to a casino till I see whats going on.

Yes, of course I don't need to account for this while I'm under 11.


A question that relates to a previous poster: If the dealer is on 5, and the question is wether to double or split or whatever, how can one project the likely outcome of the dealers (indeed anyones) progress from a 5?

My math current math says that a dealer will get 21.5 on average.

The casino edge is calculated by figuring out, using best strategy, how much you would expect to lose over an infinite number of hands, divided by how much you bet. So if you bet $100 and best strategy would have you getting $99 back, then the house edge is 1%. You can see on the wizardofodds.com website various house edges for different blackjack rules, or for craps, roulette, etc. The importance of YOUR hand being hard or soft cannot be understated. You would never hit a hard 17, and would always hit a soft 17. There are situations where you might double a soft 18, while you of course would stick with a hard 18. And i reiterate- getting the first cards is no better or worse than getting the last cards while sitting at a table. If you cannot be convinced of that then i would surmise that the rest of your understanding of the game will be limited, too.

A question that relates to a previous poster: If the dealer is on 5, and the question is wether to double or split or whatever, how can one project the likely outcome of the dealers (indeed anyones) progress from a 5?

My math current math says that a dealer will get 21.5 on average.

the 21.5 average is irrelevant. what is relevant is the frequencies of the discreet possibilities-
17 18 19 20 21 bust.
it is easily figured out, if i had the time or inclination- i am sure someone will respond with the exact odds.

As far as 'whether to double or split or whatever?' the answer is called BASIC STRATEGY,

if you believe that by getting the first cards gives you the best odds then you need to start from the beginning...

THanks forthe quick reply.

But, you stated here that my opinion of the benefit of the 1st cards to be errenous, while you later state that it makes no difference..

Do forgive me for my laziness re soft and hard hands... Im not thinking so well at 1am... Im quite soft in the head with somethings..

Yes, we really only want to know the dealers potential to land in the sitting zone, I totally agree.

I understand that 'basic strategy' relates to 'what to do when thins look good', but, I want to know, how are these things calulated to see that it looks good.

So, I probably need to see the math you mention. Surely there is acres of it on the web. Perhaps you may be so inclined as to direct me to a possible site that deals with such matters. I would not think to suggest that you type it all out for me long form..

Perhaps you know of a few choice links..

What I really want to know is the margins on winning and losing, not the money margins relating to choices of doubles, BJ payous etc..
They are a separate matter for now.

cheers

Start with the wizardofodds.com site. I am not skilled enough to do a basic strategy mathematical analysis for blackjack. I will try and be clearer- there is no advantage to getting the first cards, and no disadvantage, either.