What are the odds?

Our finally project for computer science is to write a game. I am picking a Black Jack game. I have found most all I need, I was going to stop at just using the charts for correcting wrong moves. But it would be a much more impactful if I could give the what the math says: Does it not sound better to say?

The correct decision was to double down because there was 30.8% chance of a 10 counter, 7.7% chance of a 9 and 7.7% chance of a 8. A 10, 9 or 8, was a high percentage winner against a 6 showing for the dealer. Why? With a 6 showing there was again about 46.2% chance of having a 10, 9 or 8 under cover. This means that the dealer will have to draw again, making a 46.2% to 68.8% chance of busting.

Well something like that does anyone have the equations, preferably in Excel, but I take anyway I can get. Also if I am right it does not matter how many decks, because the proportions remain the same. ANY other suggestions would helpful.

Buttercup

Welcome to the forum! Everyone here is eager to help.

However; my first suggestion would be for you to find someone with a better understanding of the English language to help you re-write this post. With your poor grammar and other choice of words, it's almost impossible to understand what you're trying to ask us; almost to the point of sounding like gibberish. Sorry to have to be so harsh on you.....

I think you are trying to be funny, so I guess HA,HA. I have a full 4.0 GPA and English is one of my best subjects! I grew up in San Jose, California and already accected to UC Berkeley in the fall. It is true I may not be using the correct lingo for this forum. If that is the case I am sorry, I will try to explain a different way.
Way #1
I am writing a Black Jack game using (HTML, PHP and mySQL) I have already written the whole game. It plays fine. I still have about 3 weeks left, so I want to make it better. As you play it will use the basic statagey charts to tell the player if they are making the best decisions. I can already tell the player that: When the dealer shows a 6 and you have 10 and a 5, the correct action is STAND. I want to make my explaination better. What is the math behind the correct action? Why is that the best decision?

Am I correct that it is based on a set of percentages? In the example above there is a high percentage the dealer already has a high count card, but will be forced to HIT anyway with a 6. After the dealer takes a card there is a high percentage that card will be a high count card, causing the dealer to bust.

Does anyone have those percentages? I.E. the dealer has a 58.2 percent busting after you STAND.

Way #2
Without saying the “Chart says so”, Why is STANDing the best action when the dealer has a 6 and you have 10 and 5??? I am looking for the math behind these actions.

TY, Buttercup
PS – Better?

I agree with Sucker when he said that the OP was poorly written. Anyway...

Cant you calculate these numbers by yourself using the program? You know how many decks were used, how many of each card was taken out, therefore you can use the probabilities of certain cards coming out to determine the probable outcome; one would use a recursive function, I would think.

I think you will find what you are looking for in Carcarulo's work.

Thank you BJ Bob, I searched for posts from Carcarulo. I only found 1. It was interesting but very little information. It only covered 1 possiblity A7 vs 2. This is what I am looking for but I need more if it exists.

Hey guys I guess another child lost to the school system. I get good grades and I can’t even write simple questions.

In trying to do my own calculations in my example above (which I guess is gibberish) the chance of drawing a 10 counter is 30.8% (this is 96/312.) The chance that the dealer has a 10 counter is the same 30.8% So please English / Black Jack Gods, how would you finish a response to a player:

The correct action to 10,5 vs 6 is STAND. Because ...

TY, Buttercup

Try this

(Dead link: http://www.blackjacktactics.com/blackjack/odds/)

And this (look at the appendices)

http://wizardofodds.com/blackjack

For complete Carcarulo:http://www.bjmath.com/bjmath/ev/ev.htm (Archive copy)

I'd think twice about it

It's somewhat more complicated than that. The number of decks, and the precise rule variations both have an impact (on the numbers and on which of the possible actions is consequently best for certain decisions).

There are no equations to give you, just the results of a very convoluted computation: basically play out every possible hand in every possible way and note which action wins the most (or loses the least) money at each stage.

The action to take (hit/stand, etc.) at each stage is the one with the highest 'Expected Value'. That's defined as the percentage return on the initial bet (bearing in mind that splitting and doubling require you to add to your initial bet during the play of the hand).

There are some tables of Expected Values for different rules/numbers of decks (from Carcarulo) listed here: http://www.bjmath.com/bjmath/ev/ev.htm (Archive copy)

Available at the same site, there is also a C++ library, licensed under the GPL, which you might be able to make use of: http://www.bjmath.com/bjcomputer/computer/gamegen.htm (Archive copy) (You could take a look at the included sample game to get some ideas on how to present the information.)


It might be better not to bother with any of this, though. Once you start down this road, you'll realise that there are more and more complications to consider.

For instance, you have probably adopted a total-dependent Basic Strategy table in your program. You'll see in Carcarulo's tables that specific, two-card starting hand compositions are all that are listed. The Expected Values (and therefore sometimes the best action) are not quite the same for different, multi-card hand compositions.

The C++ program I referenced uses (by default) 'perfect play', which means that every decision is based on the precise Expected Values of the given hand composition. That's not practical for a human player. Humans use either an entirely total-dependent strategy, or add in just a handful of composition-dependent variations (such as standing on a multi-card 16 versus a dealer 10).

So all the above begs the question: What figures should you display and should they be allowed to contradict what your program is saying is the correct move?


It would not be the work of a mere three weeks to implement such a thing from scratch. (I've been tinkering with my own additions to Eric Farmer's C++ library, referenced above, for about three years, and I still haven't got very far. )

THANK YOU very much I am still reading, but wanted to say a quick TY. I do believe it is impossible or nearly impossible to do ALL calculations. But I think with what I am seeing, I can make better reasons for the actions taken. Please if there any more thoughts I am still reading.

TY,TY,TY
Buttercup

If you stand you will win the hand 42.3% of the time and lose 57.7% of the time.
If you hit you will win only 29.4% of the time, lose 66.2%; and push 4.4%.

And yes; the rewrite made it MUCH easier to understand. You may have noticed that once you reposted, that's when the responses started to come in.

I don't see any other basis of such conclusion.

I've never been there, but I hear that "they've got a lot of space" there.

wizard of odds has a HUGEEEEE chart with every hand listing the evs for each action.

You are attemting to explain why each action is better simply by looking at the rate of busting, and that is not the case.

once your dealt a hand of XX vs Y you are confronted with options on how to play it.

Option A will result in 100000 permutations of different ways it will play out, some being the same, some winnign some losing, in totall, there will be a total dollar amoutn won or lost in sum of all possible permutations, and when divided by the number of possible permutations, there is a single average dollar amount won of lost by making that action.

Option B will result in a different 100000 permutations and result in a different average amount of money either won or lost.

Since you cannot predict which one of the millions of permutations your hand will play out to be when you choose to hit or stand, all you can do is make the best guess based on sound math, so you pick the option that has the highest averag dollar win...or the option with the lowest average dollar loss.

Another way to view it is maximising your ROI.

here is some info on average returns for different hands
http://wizardofodds.com/blackjack/appendix9.html