Player bets $10 and is dealt a 10 and a 2 for a total of 12. Dealer is showing a 7. Player hits and gets 6 for a total of 18. Dealer has 17. Player wins $10.
Logically, I can say that the combination of hitting 12, and staying on 18, equals $10. How could I show this, or formulate this arithmetically to get the value of the hands?
Last edited by doffing81; 08-08-2015 at 07:04 PM.
Assuming excel, for all Player 2 card and deale up card combinations, To try and do this thru a series of if then statements would be an absolute nightmare of hard coding etc. it would be far easier to look up the result through a table.
In other words, for example, you would have a concatenation of columns 1 & 2 which for line item in question would be column 1 (12) and column 2 (7), resulting in a lookup value of 127, and subsequent columns showing hit card, dictating further player action (hit, stay) since you can't guarantee a $10 result, you can only dictate a probable result. This would be a start.
Do you want to treat all starting Hand of 12 the same or consider what the two starting cards are?Originally Posted by doffing81
If just a 12
When 12 + x = 18 and dealers hand of 7 + y = 17 then value of hand = bet amount. Assign a few more variable for pler , dealer bet amount etc and you have formular forming. You can use more variables or even an array if programing to store values.
Possibly creat variables of pc1 pc2 pc3. Etc to represent player card 1 2 3. And DC 1 2 3 etc for dealer card 1 2 3. You can also use other logical operators else nor or when/while to form some logic
Not sure if this is what you had in mind...
Mushins comments immediately above could also be incorporated, which could absolutely dictate an end result. Using an array type formula would also assist. I used to be pretty good at this stuff, but I haven't done it in several years.
@DSchles
I am a programming student who is building a blackjack simulator as a personal project. Instead of mathematically predicting the EV, I would like to run simulations that analyze played hands, tally the results, and get the “Actual Value” (AV) as determined by those simulations. I completely understand that this AV is only relative to my simulations, and is not absolute, or that I would need to run billions of simulations to gain any meaningful results. From what I have seen on calculating EV, an original two card hand is compared to all possible outcomes to get that EV. Great! However, only evaluating the first two cards in my situation seems to disregard meaningful data for the strict analysis I desire. For example, in my example of 12v7, where I hit and get an 18v7, if I were to only tally the result for the 12v7 (the first two cards), and say that it resulted in a win of 10 dollars, I would miss out on gathering data for the situation of 18v7, which is seemingly crucial since it is an occurrence of 18v7, and to disregard it as such, to me, is to say that it did NOT occur, when in actuality it did, and as I said before, I am trying to gain the “Actual Value”, however strict I may be, since it would nevertheless be absolutely true (relative to my simulations of course), and THAT is what I am after!
With that said, I would like to refer back to my example of 12v7. The combination of hitting (H) the 12v7, and staying (S) on the 18v7, results in my winning 10 dollars. Arithmetically speaking, how would this look so that I may extract valuable information on the hands of 12v7 and 18v7, or even the information for hitting 12v7 and staying on 18v7? It is this fundamental analysis that I would like to get correct so that I may analyze my simulations strictly, and correctly.
@Freightman
Might I suggest that I am simply looking for analysis of this specific example, which shouldn't require vast calculations, or lookup tables. Refer to the comment for DSchles for clarification, if it is there lol
Last edited by doffing81; 08-09-2015 at 04:44 AM.
@mushin
In essence, with my example, the combination of hitting the 12v7 and staying on the 18v7 has a value of $10. I am looking to distribute that value ($10) either amongst the plays, or the hands. Getting an arithmetic formula for this situation should allow me to do so. if I were to conclude anything at this point, I would say that I cannot conclude that hitting the 12v7 won me $10, and staying on the 18v7 won me $10, because that would be treating them as independent events, for which, in this specific instance, they are not... They are dependent. Hence why I stress the importance of the combination as being equal to $10. If I can arithmetically express this combination, game over... Values can be extracted.
Last edited by doffing81; 08-09-2015 at 06:14 AM.
Are you trying to generate a strategy or evaluate a strategy? These are two very different objectives. When generating a strategy, you must look at one decision at a time. When evaluating a strategy, you must play the strategy as a player would in a casino and measure the overall result. The value of individual decisions is unimportant.
"I don't think outside the box; I think of what I can do with the box." - Henri Matisse
The AND operator joins the the two "hands" and without any form of logical expressions I see no way to do have a straight up formula.
On the flip side I get the impression you are 1) Trying to get the experts of the game to come up with your formula but 2.) Are not willing to accept their advice that you are on the wrong track and 3) that what you are doing is not a viable approch.
Working off the simple fact that in blackjack the goal is to beat dealer there are only three results w l p for each hand.
The values of the decisions are already accounted for in previous work by the afore mentioned experts. This is why basic strategy and index plays exist. That is how people are able to say that failing to hit or stand or split is with +/- a certain amount of money.
Have you considered that the reason you can't come up with an equation and thet the experts that are far smarted than your average student can't provide an answer is that your whole premise may not be applicable to the game of blackjack.
I don't say this to be mean or harsh but some real authorities on the math of the game have replied and you seem to have blown them off of discounted their opinions. I know that if I consult with an expert and they tell me I'm barking up the wrong tree... Well that probably means I'm of track l.
@Norm - THAT is the most beautiful assessment of my problem that I have seen so far! I may indeed be overthinking it, but I would like to question strictly, and scientifically, whether or not the value is indeed shared, since the plays are dependent (in my example anyway), and if they are not, I would absolutely love to be shown that they are not. The purpose of my endeavor is alluded to in that beautiful quote. In answering the question of "Are you trying to generate a strategy or evaluate a strategy?", I could only give the murky answer of BOTH, and I hope I don't lose people here, but my analysis is psychological in nature. What I want to be able to say in evaluating decisions is that this is the absolute truth, giving me the psychological advantage of being able to say that the data I have produced is undeniably true! I want the most strict empirical data, even if the results come to be exactly what theory would have them be! As for those who would doubt that I could make use of this data effectively, I can only assure you that I have a plan, and I would like to not be sidetracked by this since it seems irrelevant to the desired, specific, analysis I am trying to gain HERE, which is already difficult enough to acquire. As for the importance of gaining this ever so subtle psychological advantage, if any of you have been around even the most average of blackjack players, logic can so easily be tossed aside, too often in my mind since I work in table games, and it is often an insurmountable task to convince them to do the right thing, for which I would like to offer this undeniable perspective. I myself, and I believe most here, would not deny the effectiveness of EV, but again, all to often the mere introduction of this concept into a conversation loses people simply because it is theory, and at best, probable. I would like to attempt to rectify this occasion. Finally, and again, in regard to the question "Are you trying to generate a strategy or evaluate a strategy?", all I can say is that the value of individual decisions are absolutely important to me. I hope this a sufficient explanation, and I guess the question to be asked would be, "Can giving a value to each decision be done"? I am assuming that it can. If so, this is my goal, if not, I would ask for an explanation so that I may proceed correctly.
Last edited by doffing81; 08-09-2015 at 10:48 AM.
If it is your goal to convince the average casino player to make the correct plays; I suggest you start with an easier task. Say, teaching a lobster how to ride a bicycle.
"I don't think outside the box; I think of what I can do with the box." - Henri Matisse
"I myself, and I believe most here, would not deny the effectiveness of EV, but again, all to[o] often the mere introduction of this concept into a conversation loses people simply because it is theory, and at best, probable.
That is a patently false statement. The last thing on earth that you want here is empirical data of any kind. It is utterly useless to the discussion. If I tell you the e.v. for the number of heads obtained flipping a coin is 50-50, and you complain that this is theory and that you want empirical data, I tell you that all the coin flipping on the face of the earth is totally uninteresting to me. I couldn't give a rat's ass what results your personal coin flipping produces. All that matters for blackjack is the combinatorial analysis that leads to the perfect basic strategy for each play.
I will grant you this: you are incredibly stubborn, but you aren't going to get what you're looking for here, because, well, it has no meaning.
Don
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