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Hi,all This is a long shot but maybe Eric or someone like that can help me.

I've been writing a program to calculate 'perfect play'using combinatorics.

I started off with ENHC and 1 deck to keep things simple.

My program gives correct EV if the player STANDS on his first two cards in all situations.

My program also gets correct EV results if the player HITS his first two cards for 10,10 vs.

The problem starts at 10,5 vs certain dealer's cards.

My program is correct for 10,5 vs.

Specifically, for 10,5 vs.

But, my program is correct for 10,5 vs dealer 6 or dealer 5 or dealer 4 or dealer 3 or dealer 2.

My program is also incorrect for 9,6 vs.

So, the problem only shows up with a player 15 vs.

I thought Blackjack hand calculator could isolate the problem further by using blackjack poker game rules uk online calculators to check each constituent part of my calculations.

So, I used the Wizard of Odd's calculator to give me the EV for a 10,5,10 vs.

Then, I took those EV's and multiplied them by the probability that such a hand could occur and added them all up for a total EV if you HIT 10,5 vs.

As a further check, I used the same technique as shown in the table above for 10,5 vs.

I'm sure there is something wrong with my approach because the online calculators both agree, but I just can't see it.

Am I missing something?

Thanks for any help and best of luck to all!

Hi, JJ Thanks for that!

Best, SiMiWould it be possible to see source code?

After computing the data on your table, it seems that your calcs make sense.

Looking in BJA 3rd Ed: Table A10 on pg 403 indicates that T5 vs 9 STAND: -0.

That is one or more of your 3-or-more-card hands has either an incorrect expectation, a function returned casino blackjack basics incorrect expectation you returned a STAND EV no a HIT EV for example, or something completely different that without code cannot be observed.

I would like to add that Eric, MGP, and others such as Norm, Gronbog, and Dog Hand are also of valuable knowledge.

Haven't heard from iCountnTrack lately.

Also, see this: EDIT: Interesting!

Seems for 23 and 24 vs TA, BJA and MGP's BCJA agree with each other on HIT EV, while mines disagrees: Code: 2 3 4 5 6 7 8 9 T A 23 stand: -0.

What do you get SiMi?

Thanks for the input.

A lot of good thoughts in your post.

I agree that it sure looks like some kind of simple logic error and I was pretty surprised I couldn't find it quickly once Blackjack hand calculator realized it was player cards totaling 15 vs.

I'll see if I can figure out a concise way to post the relevant code C++.

The thing that I'm struggling with at the moment that I wonder if you understand is: why my method of adding up all the individual 3-card hand EV's from one of the online calculators doesn't total to the same thing the same online calculator reports for the Hit EV for the underlying 2-card hand?

In my example from my OP, I used both the WoOdds site and KC's site.

I used my first problem hand: 10,5 vs.

As you see in the chart I posted, I set up each possible hand you could get if you hit 10,5 and recorded the online calculators' EV.

I then calculated the probability that such a hit card would occur as shown in my table and multiplied each EV by each probability to get a net EV for that card.

Then, I added up all the net EVs to get the overall EV for hitting that underlying hand in this case, 10,5 vs.

When I do that, I get the number my program is spitting out BUT IT IS NOT THE NUMBER THE ONLINE CALCULATORS THEMSELVES SHOW.

That last bit is the part that I don't understand right now and may be a clue to what I'm doing wrong in the code.

Even if one is not writing a program to do this, I would think one could verify the online calculators' numbers this way.

It works for other scenarios.

So, I suspect I don't understand something and my program is just effectively implementing the same mistake in logic that I made in creating the chart I showed in my post above.

I've also been trying to develop a formula to calculate the number of possible hands given a scenario so I can verify that my program is generating the right set of hands.

So far, I haven't found that formula anywhere.

Are you aware of such a formula?

Griffin mentions on p.

I noticed that the dealer can get one of 4 pat hands or a BJ and then the pattern is that he can get 10 different hands starting with 10,6.

Then, he can get 19 different hands starting with 10,5.

He can get 37 different hands starting with 10,4 and 73 different hands starting with 10,3 and 144 different hands starting with 10,2.

The pattern is that the next number of hands is the prior number of hands times 2 minus 1.

Then, add the 4 pat hands and the Blackjack and you get 288 hands, as Griffin wrote.

So far, I haven't been able to boil that down to a generic combinatorics function that I can use to make this calculation for any scenario.

As for the scenario you mentioned 23 and 24 vs.

TAcould you please specify the set up again?

For example, the player has exactly what cards and the dealer shows exactly what and whether this is 1 deck, ENHC and S17?

I'm still writing the code so I created a separate program for STAND and I'm working on the one for HIT now.

It's kludgy because I'm being careful at this early stage of development.

For HIT, I am limited to ENHC and S17 one deck because those were the easiest to start with.

Once I encountered this problem, I stopped moving forward because it was clear to me that I am missing something.

Also, I emailed KC per JJ's suggestion but haven't heard back yet.

I will keep you posted if I hear something or make a breakthrough!

Thanks again for all your time and great ideas!

Have a great week!

Thanks for the input.

A lot of good thoughts in your post.

I agree that it sure looks like some kind of simple logic error and I was pretty surprised I couldn't find it quickly once I realized it was player cards totaling 15 vs.

I'll see if I can figure out a concise way to post the relevant code C++.

Consider opening a GitHub?

Or some other VCS program that can be viewed by the public.

Also, much like my BJCA, it is the dealer 7, 8, 9 that differs from Cacarulo but agrees with MGP.

Only with dealer T and A is where MGP and Cacarulo agree with one another but I disagree.

The thing that I'm struggling with at the moment that I wonder if you understand is: why my method of adding up all the individual 3-card hand EV's from one of the online calculators doesn't total to the same thing the same online calculator reports for the Hit EV for the underlying 2-card hand?

I don't quite understand the bold.

Are you asking why your 3-card EV's differ from that of other CA?

Then the answer may lie in a logical error somewhere in your ev functions?

If you want another source for EV's: In my example from my OP, I used both the WoOdds site and KC's site.

I see more my first problem hand: 10,5 vs.

As you see in the chart I posted, I set up each possible hand you could get if you hit 10,5 and recorded the online calculators' EV.

So, I took the online calculators' EV for 10,5,10 vs.

I then calculated the probability that such a hit card would occur click shown in my table and multiplied each EV by each probability to get a net EV for that card.

Then, I added up all the net EVs to get the overall EV for hitting that underlying hand in this case, 10,5 vs.

When I do that, I get the number my program is spitting out BUT IT IS NOT THE NUMBER THE ONLINE CALCULATORS THEMSELVES SHOW.

That last bit is the part that I don't understand right now and may be a clue to what I'm doing wrong in the code.

Even if one is not writing a program to do this, I would think one could verify the online calculators' numbers this way.

It works for other scenarios.

So, I suspect I don't understand something and my program is just effectively implementing the same mistake in logic that I made in creating the chart I showed in my post above.

Is if float or double?

I use double, while costly in space, allows me to have a more expansive significant.

In C the language I use for my minimal CA, all decimal values are of type double.

I've also been trying to develop a formula to calculate the number of possible hands given a scenario so I can verify that my program is generating the right set of hands.

So far, I haven't found that formula anywhere.

Are you aware of such a formula?

Griffin mentions on p.

I noticed that the dealer can get one of 4 pat hands or a BJ and then the pattern is that he can get 10 different hands starting with 10,6.

Then, he can get 19 different hands starting with 10,5.

He can get 37 different hands starting with 10,4 and 73 different hands starting with 10,3 and 144 different hands starting with 10,2.

The pattern is that the next number of hands is the prior number of hands times 2 minus 1.

Then, add the 4 pat hands and the Blackjack and you get 288 hands, as Griffin wrote.

So far, I haven't been able to link that down to a generic combinatorics function that I can use to make this calculation for any scenario.

Below this paragraph is a BASIC program that would enable you to cycle through all possible dealer hand states.

However, it seems that we would run into illegal hand states that would not be permissible in standard 21 rules.

Next, I use a draw function that adds a deuce to the hand until I reach any 17 assuming the S17 rule here.

So, the hand evolves like this: 2 22 222 2222.

I continuously source the last rank element in the hand until I get to an Ace: 22222222A Once I hit an Ace, I remove that card increment the last rank in the hand: 22222222A 22222222 22222223 and check to see if I need to draw to 17 again.

If you cycle through all of these hands, you should get a grand total of 54433 dealer hands for the S17 rule and 70561 dealer hands for the H17 rule.

As for your search of a general 'combinatorial function': there is none to the best of my knowledge.

Combinatorics deals with counting discrete structures and systems.

That is what I do.

As for the scenario you mentioned 23 and 24 vs.

TAcould you please specify the set up again?

For example, the player has exactly what cards blackjack casino all about the dealer shows exactly what and whether this is 1 deck, ENHC and S17?

I'm still writing the code so I created a separate program for STAND and I'm working on the one for HIT now.

It's kludgy because I'm being careful at this early stage of development.

For HIT, I am limited to ENHC and S17 one deck because those were the easiest to start with.

Once I encountered this problem, I stopped moving forward because it was clear to me that I am missing something.

Also, I emailed KC per JJ's suggestion but haven't heard back yet.

I will keep you posted if I hear something or make a breakthrough!

Thanks again for all your time and great ideas!

Have a great week!

SiMi Good on you for pressing forward and seeking help!

As for the accept. vb net blackjack code commit rules, I am using the same game rules Griffin used: 1D, S17, nDAS, nSurr.

However; one caveat is that you are doing ENHC and I am not.

When you said ENCH, all I heard read is that you are keeping your EV unconditioned for dealer naturals.

If you reread my post "Verifying Numbers", you would see Eric Farmer pointed out the reasoning and the mathematics behind conditioning EV's.

I do condition for dealer naturals.

I'll need some time to digest it and will respond more as I have more time.

I just wanted to clarify my question in bold because With blackjack extra bet congratulate was afraid it visit web page be confusing and any readers might be lost at this point and I think it's the key to my problem, perhaps.

If you want to know the EV for Hitting a given player hand vs.

Then, add up the EVs for the player-win scenarios and subtract the total of the EVs for the player-losses and you have the overall EV for the initial hand.

That's what I'm doing in my code and that's what I did in the chart I posted in the OP.

Maybe that's not valid for some reason but I can't see why and it seems to yield the same EV as the online calculators for most scenarios.

If you try to do that same thing using the online calculators from bjstrat.

As an example, if you ask either of the online calculators to give you the EV for 10,5 vs.

But, if you add up the EVs shown on those same online calculators for all the individual hands that can occur with a 10,5 vs.

Notice that this total is different from the EV shown for 10,5 vs.

This fact makes me think that the online calculators are NOT using the approach I am using even though my approach works most of the time.

My program gives the -0.

My question is whether you see something wrong with my approach?

SiMi Hi, again, dogman Thanks for the great reply!

blackjack cheating devices need some time to digest it and will respond more as I have more time.

I just wanted to clarify my question in bold because I was afraid it might be confusing and any readers might be lost at this point and I think it's the key to my problem, perhaps.

If you want to know the EV for Hitting a given player hand vs.

Then, add up the EVs for the player-win scenarios and subtract the total of the EVs for the player-losses and you have the overall EV for the initial hand.

That's what I'm doing in my code and that's what I did in the chart I posted in the OP.

Maybe that's not valid for some reason but I can't see why and it seems to yield the same EV as the online calculators for most scenarios.

If you try to do that same thing using the online calculators from bjstrat.

As an example, if you ask either of the online calculators to give you the EV for 10,5 vs.

But, if you add up the EVs shown on those same online calculators for all the individual hands that can occur with a 10,5 vs.

Notice that this total is different from the EV shown for 10,5 vs.

This fact makes me think that the online calculators are NOT using the approach I am using even though my approach works most of the time.

My program gives the -0.

My question is whether you see something wrong with my approach?

SiMiGood to hear back from you!

So, I just redid the computations using the WOO program for 5T vs 9.

I found an error in your computations!

Actually, an error in logic to be exact.

When computing the correct read: optimal action for any player hand composition, one must take into account all possible options and choose the one that offer the greatest +EV or the least -EV.

In the case of 5T vs 9, we know that standing is -0.

Now, we need to know if hitting to the next card is better.

When we do this, we are looking at not hitting once, but rather if hitting to a specific value is best.

That is, from where we start 5Twe want to know the optimal pathway based on hitting EV's and determining what to hit until we need to stand.

We know the Expectation of drawing any rank to a hard 21: -1.

So, we know, after weighing the Expectation with the Probability of the next rank drawn that the Expected Value of hitting a Hard 21 is -1.

Now, we then compute hitting all hard 20's.

We know that an Ace is the only rank that will allow us to remain in the game so we take the Expectations of both standing and hitting a Hard 20, add the Ace, and find the matching hand state for the Hard 21.

That is, we are looking to see if we should hit; if not, then we stand!

Basic Strategy says to Hit, you hit and draw an Ace.

Now, what does BS say?

Now, back to your 5T vs 9 issue.

You are assuming that the player can only draw one card on a hit and must stand.

This is wrong, as it ignores the fact that with hitting, we can keep going!

In fact, source know that with 5TA vs 9, hitting is preferred to standing!

That is, the EV for standing and hitting are: -0.

But we lose less by following this pathway, rather than assume we can't draw another card for some reason.

Please see Ch 11 in ToBJ for details on the "Cascading Method" that Griffin talks about.

Also, again, re-read my thread "Verifying Numbers" where Eric talks about Griffins method s you should take when computing the correct EV's for drawing.

I think I've got it!

Thanks so much for hanging in there with me!!!!!

I didn't understand the proper approach.

I had incorrectly thought that the EV for hitting a 2-card hand is the same as the sum of the EVs for standing on every possible 3-card hand you could get by hitting.

As you say, the problem with that approach is that the rules do not require you to stand after hitting a 2-card hand and, in some cases, you can improve your EV by hitting AGAIN.

The 10,5,1 hand is one of those hands because, against a 9, the EV for hitting is a bit better than for standing.

So, that is what Griffin means by "cascading" because this can go on and on as you consider hands with different totals and different dealer up cards.

I will need to re-write my code to calculate and compare the EV for standing and for hitting on each hand.

Continuing with the 10,5 vs.

So, the EV for those hands is -1 unit and you can just take -1 times the probability of those cards coming up as the 'net' EV.

For hitting https://indonesiaairsoft.com/blackjack/doubling-up-strategy-blackjack.html getting a 6, you will have a total of 21.

If you hit again, you will bust for certain.

So, the result from Hitting a 10,5,6 is always -1 unit while the EV from standing on a 10,5,6 vs.

So, of course, you take the EV from standing click at this page your net EV.

Once I have all the optimal EVs for each situation, I can sum them to get the overall EV for hitting a 10,5 vs.

And, as you say, when I do the math on that, I get -0.

Again, thanks so much for all the help and sorry to be so slow!

I'm new to combinatorics and doing this all on my own so it's a bit rough at this point.

I will keep you posted on my progress and I hope that some readers out there were enlightened a bit by this thread because I sure didn't have it straight in my mind and, frankly, I've always had a lot of trouble understanding Griffin's book even though I am very curious about combinatorics.

SiMi Hi, dogman Yes!!

I think I've got it!

Thanks so much for hanging in there with me!!!!!

I didn't understand the proper approach.

I had incorrectly thought that the EV for hitting a blackjack hand calculator hand is the same as the sum of the EVs for standing on every possible 3-card hand you could get by hitting.

As you say, the problem with that approach is blackjack hand calculator the rules do not require you to stand after hitting a 2-card hand and, in some cases, you can improve your EV by hitting AGAIN.

The 10,5,1 hand is one of those hands because, against a 9, the EV for hitting is a bit better than for standing.

So, that is what Griffin means by "cascading" because this can go on and on as you consider hands with different click here and different dealer up cards.

I will need to re-write my code to calculate and compare the EV for standing and for hitting on each hand.

What needs to be done is to correctly implement the hit algorithm.

You must compute the hit EV's starting with all hard 21's down to an including hard 12's, then all soft 21's down, then a hard totals from 11 down, and finally, computing the pair cards.

Doing this will allow you to find the optimal EV for each hand state.

Continuing with the 10,5 vs.

So, the EV for those hands is -1 unit and you can just take -1 times blackjack hand calculator probability of those cards coming up as the 'net' EV.

For hitting and getting a 6, you will have a total of 21.

If you hit again, you will bust for certain.

So, the result from Hitting a 10,5,6 is always -1 unit while the EV from standing on a 10,5,6 vs.

So, of course, you take the EV from standing as your net EV.

Once I have all the optimal EVs for each situation, I can sum them to get the overall EV for hitting a 10,5 vs.

You get the general idea.

One thing I would like to point https://indonesiaairsoft.com/blackjack/free-casino-video-blackjack-card-games.html is that instead of re-computing previous EV's, consider only doing them once.

This will slow down your program as the CPU has few resources to continuosly brute force previously solved hand states.

This is just a friendly reminder!

And, as you say, when I do the math on that, I get -0.

Again, thanks so much for all the help and sorry to be so slow!

I'm new to combinatorics and doing this all on my own so it's a bit rough at this point.

I will keep you posted on my progress and I hope that some readers out there were enlightened a bit by this thread because I sure didn't have it straight in my mind and, frankly, I've always had a lot of trouble understanding Griffin's book even though I am very curious about combinatorics.

It can be thought of as the application of counting discrete structures and systems.

And the math in Griffin's book is gnarly at best, but the relevant text, where he goes over details under certain concepts, is where you will gain the most knowledge if math is not your strong suit.

That is, civil and considerate behavior for the mutual benefit of all involved.

The goal of advantage play is the legal extraction of funds from gaming establishments by gaining a mathematic advantage and developing the skills required to use that advantage.

To maximize our success, it is important to understand that we are all on the same side.

Personal conflicts simply get in the way of our goals.

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