Blackjack House Edge Calculator for Depleted Shoe

Hi,

Is there any Blackjack House Edge Calculator/spreadsheet that can handle depleted Shoe ? Meaning it can calculate the "overall house edge" (and its relevant basic strategy)for any give shoe composition within seconds. With such info, we can calculate exactly(based on Kelly criterion) how much we should bet in next round . . . betting correlation = 1 !

There are 2 methods that can ESTIMATE the overall house edge :-

1) Based on True count - we can estimate the house edge.
2) Based on EOR - Add up all the pre-determined EORs of all removed cards, then add to the full deck house edge to get net house edge.

However, both above methods are not that accurate.

I need exact house edge after each round for online betting(more than 1.5 million daily betting turnover), MGP can handle this but it take too long to calculate it . . .


James

see this thread as it can be quite complicated to write the code depending on how accurate you need the info - https://wizardofvegas.com/forum/questions-and-answers/gambling/34652-blackjack-hand-calculator

Quote: charliepatrick

see this thread as it can be quite complicated to write the code depending on how accurate you need the info - https://wizardofvegas.com/forum/questions-and-answers/gambling/34652-blackjack-hand-calculator

Thanks for your reply.

I found a link here : https://youtu.be/UEA46N9jl00

It's a spreadsheet that can calculate the blackjack house edge. Anyone here can share it ? Is ithis spreadsheet provided by WIZARD(Michael Shackleford) ?

Quote: ssho88

Hi,

Is there any Blackjack House Edge Calculator/spreadsheet that can handle depleted Shoe ? Meaning it can calculate the "overall house edge" (and its relevant basic strategy)for any give shoe composition within seconds. With such info, we can calculate exactly(based on Kelly criterion) how much we should bet in next round . . . betting correlation = 1 !

There are 2 methods that can ESTIMATE the overall house edge :-

1) Based on True count - we can estimate the house edge.
2) Based on EOR - Add up all the pre-determined EORs of all removed cards, then add to the full deck house edge to get net house edge.

However, both above methods are not that accurate.

I need exact house edge after each round for online betting(more than 1.5 million daily betting turnover), MGP can handle this but it take too long to calculate it . . .


James

James,

The EOR method should, of course, provide a more accurate estimate than the True Count method. In general, I think the linearity assumptions in EOR holds up surprising well over depletion of multiple cards, but I agree that its accuracy is limited and becomes "Fuzzy" after depletion of a large number (100s !) of cards.

Let me propose a conceptual framework for a spreadsheet method that should greatly improve the EOR method. Although it would fall short of the perfect calculational precision that you aspire to, I think it would provide the best capability ever developed for real-time calculations of EV/House Edge vs shoe composition.

My Proposed Method
The basic idea is to split the starting hands of blackjack into 13 distinct categories:

1. when dealer has a blackjack and player doesn't
2. when player has a blackjack and dealer doesn't
3. When both player and dealer have a blackjack
4 - 11. When dealer has a 2, 3, 4, . . ., 9 showing and player has any hand other than a blackjack.
12, 13 When dealer has a Ten showing or an Ace showing, but does not have blackjack, and player has any hand other than a blackjack.

a) For a depleted shoe, the probabilities for categories 1-3 can be calculated explicitly from the abundance of aces and tens and the outcomes (EVs) of those hands are unambiguous.
b) For categories, 4-13 the probabilities of occurrence can also be calculated explicitly from the card composition of a depleted shoe, i.e., the higher the abundance of 9's the more you will be playing versus a dealer 9.
c) Use a simulator to calculate the EOR for all ten of the cards ranks for each of the hand categories 4-13, above. Example: do simulator runs where dealer always has a 9 showing and calculate the EOR of all ten ranks of cards for the "vs 9" category (making a rule to ignore any instances in which player's first two cards are blackjack.)

This would give you the tools to calculate the probabilities and player EV for each of the 13 categories of BJ hands defined above, which you can then combine via algebra (on a simple spreadsheet) into a composite player EV at any point in the shoe depletion. The spreadsheet would be small and the calculation would be instantaneous.

The problem with the standard EOR approach for player EV as a function of shoe composition is that you are calculating the EOR of the difference between factors/influences that have opposite effects on Player EV. For example:

Consider the EOR of Ten on the House Edge/ Player EV. An abundance of Tens:
1. increases player EV by increasing probability of BJs (although this element of EOR is clearly affected by the abundance of aces)
2. decreases player EV because the player will be playing versus a dealer Ten more frequently
3. increases Player EV when facing a dealer 2-6, because dealer must hit a hard 12-16, while player will stand on those stiff hands (most of the time.)
4. decreases Player EV when facing a dealer 7-A, because player will be hitting hard 12-16 and more frequently going bust before the dealer has an opportunity to go bust.
5. Increases Player EV when he doubles his bet with a Hard 9, 10 or 11, because that is a very favorable card when doubling. Note however, that this increment of advantage from doubling is reduced when facing a dealer 10 because basic strategy is that you don't double on a 9 or ten vs 10 and the advantage for doubling on 11 vs 10 is small. However, this "the contribution of doubling to the EOR of 10" is more important when facing 2-6, when the advantages of doubling are great. However, when tens are more abundant, you will be placing "vs 10" more often than usual; and less often "vs" 2-6."

So, using the standard EORs methodology, all of these influences on the player EV are combined together and you then look at the effect of removing tens on the net summation of all these influences. It is similar to taking the EOR on the difference between two large numbers each of which are effected in different and sometimes opposite ways by the removal of the card, rather than performing an EOR on the large numbers themselves and then taking the difference.

In my proposed method, you can use straightforward algebra to calculate the probabilities of blackjacks (correctly combining the effects of an abundance of aces with the abundance of Tens), and to calculate the frequency of playing vs 10, vs 6, etc. This takes the probabilities of situations (which are affected by the removal of cards) and removes them from the lumped EOR calculations and instead yields mathematically perfect values for the probabilities of hand categories as I have defined them.

And then, when you use a simulator to calculate the EOR of 10's when facing a dealer 6, you are able to get a much cleaner analysis of how the players advantage from not hitting Hard 12-16 vs 6 and of doubling 9-11 vs 6 is affected by the abundance of tens.

The major drawback of my proposed method is that it will require 110 simulations to calculate the EORs of each of the ten ranks of cards when facing a dealer up card of 2, 3, 4, 5, 6, 7, 8. 9, Ten and Ace (10 baseline calculations and 100 EOR calculations.) But, from what you have posted, I suspect that you are excellent at simulations. ; )

Feedback and comments would be appreciated.

Hi Gordon,

Thanks for your reply.

I will go through your write up and I hope I able/capable to understand it.

Hi Gordon,

This link can generate HE for depeleted shoe : http://www.bjstrat.net/cgi-bin/cdca.cgi


After removed eight "small" card, the no of remaining cards = 408 and the HE changed from -0.715% to -0.184%

See the results : https://ibb.co/wzPq0X3

Quote: ssho88

Hi Gordon,

This link can generate HE for depleted shoe : http://www.bjstrat.net/cgi-bin/cdca.cgi


After removed eight "small" card, the no of remaining cards = 408 and the HE changed from -0.715% to -0.184%

See the results : https://ibb.co/wzPq0X3

I use that Bjstrat calculator all the time, although I had forgotten it had that calculated HE in the corner of its output table. I honestly don't know how that HE is instantaneously calculated! I wonder if it uses EORs?

Maybe that online calculator is the capability you are looking for. Although the user interface for removing cards from the deck is kinda clunky.

Hi Gordon,

I used other software MGP's BJ CA, with removal of same eight small cards, the HE changed from -0.717% to -0.814%, MGP also generated the relevant basic strategy and EORs. However, it take much longer time and not practical for real time online betting.

See the results : https://ibb.co/gD7QVYZ

May be you can help to verify the accuracy of the results ?

Before I started using bjstrat and MGP, here is one that I used in the past >>> http://www.bewersdorff-online.de/black-jack/

Important note: the starting "expected gain" is not the same as bjstrat or MGP, but the EORs are similar, so it may still be helpful.

Main thing I liked about it: fairly quick and easy to use.

Maybe someone on this site can explain why the starting EV is different, could be because the bewersdorff site is using "old estimates from the 60's" (just a guess though, I really have no clue why it is different)

Also, I think I had a better reply almost completed, but my browser closed on me when I was just about finished.

Hope this was helpful or at least interesting

Quote: ksdjdj

Before I started using bjstrat and MGP, here is one that I used in the past >>> http://www.bewersdorff-online.de/black-jack/

Important note: the starting "expected gain" is not the same as bjstrat or MGP, but the EORs are similar, so it may still be helpful.

Main thing I liked about it: fairly quick and easy to use.

Maybe someone on this site can explain why the starting EV is different, could be because the bewersdorff site is using "old estimates from the 60's" (just a guess though, I really have no clue why it is different)

Also, I think I had a better reply almost completed, but my browser closed on me when I was just about finished.

Hope this was helpful or at least interesting

Thank you very much for posting this. I have never seen this caclulator before and it is very interesting.

Regarding "expected gain": It seems this Danish calculator does not allow double on soft hands? Is this correct?

Quote: ssho88

Hi Gordon,

I used other software MGP's BJ CA, with removal of same eight small cards, the HE changed from -0.717% to -0.814%, MGP also generated the relevant basic strategy and EORs. However, it take much longer time and not practical for real time online betting.

See the results : https://ibb.co/gD7QVYZ

May be you can help to verify the accuracy of the results ?

On the BJstrat output you posted, you have not checked the box for DAS. I can't tell what the inputs are on the MGP calculator, but if you are setting the MGP calculator for DAS, that might explain the difference in the calculated HE's? Just guessing.

Quote: gordonm888

On the BJstrat output you posted, you have not checked the box for DAS. I can't tell what the inputs are on the MGP calculator, but if you are setting the MGP calculator for DAS, that might explain the difference in the calculated HE's? Just guessing.

Both setting in MGP and bjstrat is NoDAS, it is just typo in my previous reply, MGP HE changed from -0.717% to -0.184% after removed eight "small" cards. Both bjstrat and MGP give same results. Pls check the attached image : https://ibb.co/gD7QVYZ


Edited, both setting in bjstrat and MGP is NoDAS, 8D, DOA, RS2, RSA2, S17, No Surrender, ENHC.

Quote: ssho88

Both setting in MGP and bjstrat is NoDAS, it is just typo in my previous reply, MGP HE changed from -0.717% to -0.184% after removed eight "small" cards. Both bjstrat and MGP give same results. Pls check the attached image : https://ibb.co/gD7QVYZ


Edited, both setting in bjstrat and MGP is NoDAS, 8D, DOA, RS2, RSA2, S17, No Surrender, ENHC.

Thanks for info. So, now you are not seeing a difference between MGP and Bjstrat -so there is no discrepancy to explain, correct?

Does BJstrat give you the capability you wanted for a very quick calculator for depleted shoe HE?

I think the BJstrat calculator is a marvelous tool with many outputs not available on the WOO calculator. I see that the MGP calculator has even better (more comprehensive) output displays. How long does MGP take to run a HE case? Any other downside to the MGP calculator?

Quote: gordonm888

(snip) Regarding "expected gain": It seems this Danish calculator does not allow double on soft hands? Is this correct?

Yes thanks, it looks like you are correct, but even when I plug "no soft doubles" into MGP it still gives me a different EV figure. With MGP it is -0.8029...% and bewersdorff it is -0.883%, I don't know why.

Quote:

(snip) How long does MGP take to run a HE case? Any other downside to the MGP calculator?

I can't answer for the OP, but on my pc MGP runs slow for things like that.
Another downside for me is when I try to use the "realtime analysis", it gives a significantly different EV*** figure.

***: I get +0.0280819 as the "EV of hand" when I use MGP's "realtime analysis", but I get the same figure as the OP by going to "shoe" and then changing the "forced shoe" to the same as what is in the OP's upload (I am taking out the same 8 cards when using "realtime analysis" ).

Quote: gordonm888

Quote: ssho88

Both setting in MGP and bjstrat is NoDAS, it is just typo in my previous reply, MGP HE changed from -0.717% to -0.184% after removed eight "small" cards. Both bjstrat and MGP give same results. Pls check the attached image : https://ibb.co/gD7QVYZ


Edited, both setting in bjstrat and MGP is NoDAS, 8D, DOA, RS2, RSA2, S17, No Surrender, ENHC.

Thanks for info. So, now you are not seeing a difference between MGP and Bjstrat -so there is no discrepancy to explain, correct?

No discrepancy to explain.

Quote: gordonm888

Does BJstrat give you the capability you wanted for a very quick calculator for depleted shoe HE?

BJstrat can calculate the HE for depleted shoe very quickly and can meet my requirement( for online betting)

Quote: gordonm888

I think the BJstrat calculator is a marvelous tool with many outputs not available on the WOO calculator. I see that the MGP calculator has even better (more comprehensive) output displays. How long does MGP take to run a HE case? Any other downside to the MGP calculator?

MGP take about 16 seconds to calculate depleted shoe HE and give very comprehensive output.

Quote: ksdjdj

Yes thanks, it looks like you are correct, but even when I plug "no soft doubles" into MGP it still gives me a different EV figure. With MGP it is -0.8029...% and bewersdorff it is -0.883%, I don't know why.


I can't answer for the OP, but on my pc MGP runs slow for things like that.
Another downside for me is when I try to use the "realtime analysis", it gives a significantly different EV*** figure.

***: I get +0.0280819 as the "EV of hand" when I use MGP's "realtime analysis", but I get the same figure as the OP by going to "shoe" and then changing the "forced shoe" to the same as what is in the OP's upload (I am taking out the same 8 cards when using "realtime analysis" ).

Clearly, the "realtime analysis" is too approximate to be relied on. That's a terrible discrepancy, especially for the removal of only eight cards.

Edit: When I do a simple calculation for the HE (with those eight cards removed) by summing the 8 deck EOR coefficients for those 8 cards, I get that the HE changes from -0.00717 to approximately -0.001998 -which is in the ballpark of the value of HE =-.001884 provided by Bjstrat and the full MGP calculator.

So, the value of HE = +0.0280819 given by the MGP's "realtime analysis" algorithms is really wacky and most likely involves a programming error.

BTW, my calculation just shows how bad or good the standard "summing the EOR" methodology is: with only 8 small cards removed the error in HE is already 0.11%. When 80 or 100 cards are removed, the errors can become significantly larger.

Quote: gordonm888

Clearly, the "realtime analysis" is too approximate to be relied on. That's a terrible discrepancy, especially for the removal of only eight cards.

Edit: When I do a simple calculation for the HE (with those eight cards removed) by summing the 8 deck EOR coefficients for those 8 cards, I get that the HE changes from -0.00717 to approximately -0.001998 -which is in the ballpark of the value of HE =-.001884 provided by Bjstrat and the full MGP calculator.

So, the value of HE = +0.0280819 given by the MGP's "realtime analysis" algorithms is really wacky and most likely involves a programming error.

BTW, my calculation just shows how bad or good the standard "summing the EOR" methodology is: with only 8 small cards removed the error in HE is already 0.11%. When 80 or 100 cards are removed, the errors can become significantly larger.

I tried to guess what the error with the "realtime analysis" could be by going from 8 deck to single deck (all other rules the same as OP) and then removing the same 8 cards, but it just spat out an EV of between 0.15 and 0.16 for "realtime".

That's good that your calculation is close to the one on the bjstrat site and the full MGP calculator.