Advanced Math/Blackjack Questions: Calculating House Edge

These questions are for the blackjack experts. To make this simple (or as simple as it can be) I will list the questions in order of easy to most difficult. Instead of knowing the expected results of a certain betting system or wagering amounts, these questions are for calculating win/lose rate only when using any specific counting system with any specific game. I have tried to calculate these myself but have been unsuccessful. I am hoping that there is someone here that is much smarter than myself & much better at math. My goal is to challenge the most experienced blackjack minds of this forum as well as to find the answers myself to these questions that have baffled me. So here are the questions:

What is the (win/lose rate) when using these systems playing these particular games?

System Game Win/Lose Rate

Hi-Lo full indices - 2Deck S17 DAS NS NRA = WR?

AOII full indices - 2Deck S17 DAS NS NRA = WR?

Uston APC full indices - 2Deck S17 DAS NS NRA = WR?

AOII full indices + Unbal. Ten Count - 2Deck S17 DAS NS NRA = WR?

Uston APC full indices + Unbal. Ten Count - 2Deck S17 DAS NS NRA = WR?

AOII full indices - 1Deck H17 NDAS NS NRA Dbl any 2 cards = WR?

Uston APC full indices - 1Deck H17 NDAS NS NRA Dbl any 2 cards = WR?

AOII full indices + Unbal. Ten Count - 1Deck H17 NDAS NS NRA Dbl any 2 cards = WR?

Uston APC full indices + Unbal. Ten Count - 1Deck H17 NDAS NS NRA Dbl any 2 cards = WR?

Penetration on 2Deck games is 60%. Penetration for the 1Deck is 25%.

For example, if a player is using a specific counting system to deviate from basic strategy, how would we determine the win/lose rate?

(I have edited this post.)

Pretty sure that the house edge doesn't change based on the counting system you use.

Your win/lose rate changes when you use the information from your counting system to deviate from basic strategy. Its called Playing Efficiency.

You didn't mention your betting ramp .Each system will perform differently depending on what spread you use.
Or are you asking for flat betting only?

Yes im sorry, this is for flat betting only.

He/she is asking for house edge, same basic strategy will give same house edge. NOTHING to do with counting system or index or betting ramp !

Quote: theOmega623

Yes it does when you use the information from your counting system to deviate from basic strategy. Its called Playing Efficiency.

Improved playing efficiency, from index plays based on count observation, does not change the intrinsic house edge of the game.

The fluctuating conditions which might be exploitable by index plays may not occur, and the house edge will still be intact.

House edge is determined by game rules.

Quote: Dieter

Improved playing efficiency, from index plays based on count observation, does not change the intrinsic house edge of the game.

The fluctuating conditions which might be exploitable by index plays may not occur, and the house edge will still be intact.

House edge is determined by game rules.

well, players want to know when they have an edge, how that is expressed in percentage though

If 2 players are playing the same game, 2Deck S17 DAS about 60% penetration, one player using only basic strategy, the other using AOII with full index plays, both flat betting. They will win/lose the same?

Buy CVCX and simulate it yourself using a flat-bet ramp.

I have done this. But CVCX will not let me use multiple counting systems together, or at least not that I know of. Such as AOII full indices + Ten Count

I will edit my post for calculating win rate instead of house edge.

Have you tried CVData? Basically a CVCX on steroids (or so I've heard, I don't have CVData).

Yes I have tried CVData as well. Its a great program but unfortunately it has the same limitations.

Quote: theOmega623

I have done this. But CVCX will not let me use multiple counting systems together, or at least not that I know of. Such as AOII full indices + Ten Count

I'm a trust the math guy rather than a do the math guy so I have nothing to add.

Would you consider posting your question on Blackjack:TheForum? It may generate some good discussion there or it could bomb. You never know which way the wind is blowing. I'd enjoy reading any response.

Yes I will absolutely do that. Hopefully others will take interest.

Quote: theOmega623

If 2 players are playing the same game, 2Deck S17 DAS about 60% penetration, one player using only basic strategy, the other using AOII with full index plays, both flat betting. They will win/lose the same?

No. They'll be dealt different hands. The cards may fall favorably for one, unfavorably for the other. If applicable, the index plays may help slightly.

They won't win/lose the same, but they'll be quite close - I would expect generally within 1 or 2 bets.

The "main advantage" from card counting comes from placing larger bets when the deck conditions are favorable, and then catching more blackjacks (with the bonus payout), the dealer busting more hands, and making 20 or 21 more often on doubles.


If the counter wasn't flat betting, or was sitting out in unfavorable conditions, or was generally doing anything that made counting worthwhile, we'd expect them to be doing much better.

In the long run they should each be dealt the same hands, not different. The difference would be that the counter would play his/her hands differently than the non-counter according to the specific counting system thus making better decisions. In the long run, the counter should do better but my question is how to calculate exactly how much better? Like if both were playing a single-deck 3:2 game with good penetration, how much would using the full indices of a counting system such as the Uston APC that has an extremely high playing efficiency & insurance correlation change the win/lose rate? I understand the main advantage from card counting comes from placing larger bets at high counts & I understand why, but this is a question of how to lose the least amount possible when only flat betting.

Quote: theOmega623

In the long run they should each be dealt the same hands, not different.

I thought you were talking about two people at the same table at the same time, one playing basic, and one playing basic + deviations.

Quote:

The difference would be that the counter would play his/her hands differently than the non-counter according to the specific counting system thus making better decisions. In the long run, the counter should do better but my question is how to calculate exactly how much better?

Most of the time, the counter will be playing basic strategy, so the results will be very similar.

If we start with the top index play - insurance - it becomes wise to take it when the chances of drawing a ten-value are better than 50% (vs the "natural" composition of about 31%). This index play should come up less than 10% of the time.


The results should be within 1 or 2 bets per hour.

Sorry I should have explained it a little better. Basically my thinking is that since the single-deck game I described has a very low house advantage (about 0.08%) you should theoretically be able to create a neutral or even perhaps a winning game by using such an accurate system. Like for example, if 2 counters were playing this single-deck game together side by side at the same table, one using the UAPC full indices making the basic strategy deviations for both players & the other using the Unbalanced Ten Count system making only the insurance decision for both players, both flat betting $100 per hand never changing the betting amount. Would this system, in the long run, actually show a profit instead of a loss?

Quote: Dieter

I thought you were talking about two people at the same table at the same time, one playing basic, and one playing basic + deviations.



Most of the time, the counter will be playing basic strategy, so the results will be very similar.

If we start with the top index play - insurance - it becomes wise to take it when the chances of drawing a ten-value are better than 50% (vs the "natural" composition of about 31%). This index play should come up less than 10% of the time.


The results should be within 1 or 2 bets per hour.

Insurance becomes correct to take when 33% of the remaining cards are tens not 50%.

Quote: Hunterhill

Insurance becomes correct to take when 33% of the remaining cards are tens not 50%.

Sorry, cranial flatulence struck before coffee did.

The index on the play is TC+3, which would be 19/52 remaining cards being Aces & Faces. (This information can be improved if you're keeping an ace side count.)

This still happens less than 10% of the time, according to some chart I found.

Quote: theOmega623

since the single-deck game I described has a very low house advantage (about 0.08%) you should theoretically be able to create a neutral or even perhaps a winning game by using such an accurate system.

Look up composition dependent basic strategy. That should get you to a neutral or winning game already.

From there, something simple like REKO would put you on track for insurance.

There are still no guarantees - sometimes the cards don't fall in your favor, even when you do everything right.

I think you're over-analyzing this.

I currently use the Advanced Omega II system with an ASC & full indices playing 2Deck S17 with $50-$300 spread. This system has worked tremendously for me & its expected value is a little over $100 per 100 hands played according to CVData. I know that I am over-analyzing this & that is kind of my point, I want to get down to the exact math of the game. The strength of this system along with the game I play would show a small profit even when only flat betting. I have used CVData to determine this, but I would like to know the math & reason behind why this is & I think it is because of the accuracy of the insurance decision as well as the basic strategy deviations. With good deck penetration, my theory is that the strength of the level 2 & 3 ace-neutral systems can overcome the house edge without ever changing the amount of your bet.

Quote: 1BB

I'm a trust the math guy rather than a do the math guy so I have nothing to add.

Would you consider posting your question on Blackjack:TheForum? It may generate some good discussion there or it could bomb. You never know which way the wind is blowing. I'd enjoy reading any response.

I bet least one part of the thread will include Tthree's "I thought I was gonna get backed off, but I got the red-carpet treatment, because they couldn't identify me as a counter because I use 8 main counts and 19 side counts" story.

Quote: theOmega623

I want to get down to the exact math of the game.

There are 52! permutations of a 52 card deck. That's 8 x 10^67, give or take (although many are equivalent for purposes of blackjack, and many more are effectively equivalent because of the shuffle point). That's about a dozen zeroes short of the number of atoms in the observable universe, but it's still a big number.

There are a lot of ways that the cards can fall. Exact math is impractical at best.

25% pen single deck is fairly shallow. That's 1 round with 4 spots in play. It would be difficult at best to use a counting technique to deviate from basic.

Yes anything can happen in the short run but the reason casino's make money is the same reason that us counter's can make money, play the game long enough & the math will prevail. I agree that the shallow penetration of the single deck games available make the game virtually not worth playing. The double deck games on the other hand can be great, with almost 60% penetration they are easily beatable (the only real problem being heat). I ran a sim using the HOII system with full indices playing a 2D S17 DAS game with 55% penetration flat betting $100 per hand. The result was a profit of $13.74 per 100 hands played. I find that very interesting because although it is a very small win rate, you are still effectively beating the game without changing your bet size. A counter could rack up some serious comps while showing a small profit in the end & probably not have to worry about any heat.

Deleted. Wrong thread.

Quote: RS

I bet least one part of the thread will include Tthree's "I thought I was gonna get backed off, but I got the red-carpet treatment, because they couldn't identify me as a counter because I use 8 main counts and 19 side counts" story.

I saw this earlier and I'm still chuckling. Thanks for the laugh.

Quote: theOmega623

I have done this. But CVCX will not let me use multiple counting systems together, or at least not that I know of. Such as AOII full indices + Ten Count

This sounds like a play I've done before... I'm going to assume you and I are on the same page as to why you'd want to do this and that might leave others in the dark, but I'd rather do that right now.

Run your numbers separately and then combine your EV's. If your AOII full indices comes out to $X/hour, and the reason you're applying a second count comes out to $Y/hour, then your overall EV is of course going to be $X+$Y, per hour. You don't have to run them 'simultaneously' with CVCX to either add, or compare them.

Quote: theOmega623

Sorry I should have explained it a little better. Basically my thinking is that since the single-deck game I described has a very low house advantage (about 0.08%) you should theoretically be able to create a neutral or even perhaps a winning game by using such an accurate system. Like for example, if 2 counters were playing this single-deck game together side by side at the same table, one using the UAPC full indices making the basic strategy deviations for both players & the other using the Unbalanced Ten Count system making only the insurance decision for both players, both flat betting $100 per hand never changing the betting amount. Would this system, in the long run, actually show a profit instead of a loss?

To me the question I see is: Given that these systems will help you better decide basic strategy and insurance, what % advantage do they provide in that respect, and is it enough to overcome a naturally low house edge game?

As I mentioned in my (probably confusing) post above, you don't need to run these at the same time to figure out these results. Simply go in to CVCX and sim the game with just basic strategy, flat betting. Then, sim the game with AOII full indices basic strategy, flat betting. This will give your the % advantage to basic strategy AOII full indices gives you. This is half of your answer.

Now, all that's left is to figure out how much applying the unbalanced ten count for insurance is actually helping (over the AOII insurance). This shouldn't be all too hard at all (AOII can be found here: http://www.qfit.com/card-counting.htm , and UTC I believe can be found in Thorp's book, or by using the Google). Since we're not concerned with basic strategy (PE) here, simply just compare the difference in insurance between the two systems. In the game you're referring too, go look up (or sim) how often an insurance decision comes around. If you have your average bet, you should have your average insurance bet. From here you should be able to get a real number difference of insurance between the two systems. This is the other half of your answer.

With all of the number crunching I've done over the years for blackjack, my strongly educated guess would be that you're far better off sticking to just AOII full indices for your game. The difference in insurance correlation (IC) is going to be near negligible, and the errors you'll undoubtedly encounter in running 2 counts (either yourself or with a partner) will by far cost you more money in the long run than sticking to one count. If the deviations AOII gives you brings the .08% HE game to even or a slight player advantage, then adding the 2nd count for the minuscule slightly better IC won't change much. Either you're already beating the game, or you're not.

If were a real life play, one would wonder why you wouldn't just use a 1-2 spread (with big bets like $500-$1000) and just beat it up with one system? Or are you just REALLY looking for a way to get a player edge so you can flat bet and try to avoid any/all heat?

Romes you really hit the nail on the head with your response! Thanks for giving me the information I needed so I now have the ability to do the math myself. I currently use AOII full indices with an ace side count & I have a friend that has played with me a few times in the past, he uses the Zen count. Instead of playing at separate tables, my friend likes to play at the same table beside me simply because its more fun. If or when he decides to travel along with me, I was thinking it could make the game more profitable if I continued to use my AOII system & instead of using the Zen my friend could use the Unbalanced Ten Count (you probably see what I am getting at). This would then create the following system: PE = 0.671. BC = 0.988. IC = 1.00. (We would both be playing 2D S17 DAS with a $50-$300 bet spread each.) My concern is that this type of play could quickly get us the boot lol. If I could find a good 3:2 single-deck game such as the one I described previously, I was wondering if our combined system could significantly beat it by flat-betting or at least with a very small bet spread (such as 1-2 as you suggested). I will certainly use the information you have given me in an attempt to calculate our expected outcome. Thanks again for a terrific & extremely knowledgeable response!!!

Quote: theOmega623

Romes you really hit the nail on the head with your response! Thanks for giving me the information I needed so I now have the ability to do the math myself. I currently use AOII full indices with an ace side count & I have a friend that has played with me a few times in the past, he uses the Zen count. Instead of playing at separate tables, my friend likes to play at the same table beside me simply because its more fun. If or when he decides to travel along with me, I was thinking it could make the game more profitable if I continued to use my AOII system & instead of using the Zen my friend could use the Unbalanced Ten Count (you probably see what I am getting at). This would then create the following system: PE = 0.671. BC = 0.988. IC = 1.00. (We would both be playing 2D S17 DAS with a $50-$300 bet spread each.) My concern is that this type of play could quickly get us the boot lol. If I could find a good 3:2 single-deck game such as the one I described previously, I was wondering if our combined system could significantly beat it by flat-betting or at least with a very small bet spread (such as 1-2 as you suggested). I will certainly use the information you have given me in an attempt to calculate our expected outcome. Thanks again for a terrific & extremely knowledgeable response!!!

I'm glad I could point you in the right direction. I thought we were on the same page =)... Indeed you can make it quite profitable. Do share back once you crunch the numbers to find the exact advantage % you get from AOII full w/ UTC!

p.s. I'd just like to know where this 2D S17 DAS that lets you spread $50-$300 exists lol. Careful with the 'other' part of your play, that might be a bigger red flag than counting. Cover works there as well =D.

I will do my best to calculate the advantage & I will certainly let you know what I come up with. (The largest bet I have placed thus far in my play is $200, but I plan to attempt a spread of $50-$300 in the 2D S17 games at the Monte Carlo, New York New York, the Mirage & the Bellagio (all places I will play very soon). My plan is to keep my sessions short & my act as good as possible. I will do a detailed trip report when I return!

Quote: theOmega623

I will do my best to calculate the advantage & I will certainly let you know what I come up with. (The largest bet I have placed thus far in my play is $200, but I plan to attempt a spread of $50-$300 in the 2D S17 games at the Monte Carlo, New York New York, the Mirage & the Bellagio (all places I will play very soon). My plan is to keep my sessions short & my act as good as possible. I will do a detailed trip report when I return!

Are you planning on playing rated?

Yes I plan to play rated. Do you think a 1-6 spread is too large?

Quote: theOmega623

Yes I plan to play rated. Do you think a 1-6 spread is too large?

That's a tough one. I spread 1-8 at the MGM double deck games and have been backed off more than once, however I wasn't playing rated. I would think 1-6 would be okay and I wouldn't not want to go any less no matter how good the rules. Playing rated concerns me a little, especially within the same chain. Have a backup plan just in case. Off strip maybe.

Yes I originally had planned to spread 1-8 as well & also considered playing multiple hands but I figured that might attract way too much heat. A few questions for you if you dont mind: 1. Do you think refusing to play rated would be an automatic tip off that I am an advantage player? Because im thinking they would wonder why I do not want the comps. 2. Do you think playing my system somewhere like the Bellagio might be the best place because of all the other high rollers? I am thinking my betting amounts might not attract so much attention.

Quote: theOmega623

Yes I originally had planned to spread 1-8 as well & also considered playing multiple hands but I figured that might attract way too much heat. A few questions for you if you dont mind: 1. Do you think refusing to play rated would be an automatic tip off that I am an advantage player? Because im thinking they would wonder why I do not want the comps. 2. Do you think playing my system somewhere like the Bellagio might be the best place because of all the other high rollers? I am thinking my betting amounts might not attract so much attention.

Playing unrated may get you some attention but there are reasons someone may not want to. I say something like I'm not staying long or I'll be betting more at craps and don't want the blackjack to lower my average. I don't know about Bellagio but if you get backed off at one MGM property, the others will know. Do not spread to two hands in these games. You can begin with two and drop one but spreading in good counts is probably one of the worst things you can do. Do you split 10s? :-)

Depending on the day and time, you may not always find $50 minimums at those good games.

Thanks for the advice I will not spread to 2 hands. If they are not currently offering the 2D S17 game for $50 min then I will try to find a 2D H17 game. Yes I absolutely split 10s.

Quote: theOmega623

Thanks for the advice I will not spread to 2 hands. If they are not currently offering the 2D S17 game for $50 min then I will try to find a 2D H17 game. Yes I absolutely split 10s.

"Yes, I play rated." ..."Yes I absolutely split 10s." ...Rut ro =p. Looks like 1BB gave you the playbook for these places, I'd probably recommend to sticking to that. Also, on the no card tip off... It's easy to avoid with a ploppy excuse. Literally last weekend I heard NUMEROUS ploppies sit down at my table and say "I always lose when I use that thing; it's bad luck!" The PB's usually just laugh and say okay. It's my opinion that one of the best skills an AP can have is a good "act." If a guy takes one look at you and determines you're a ploppy, that thought will rule most of his decisions moving forward (until you show too much info and give him a reason to suspect otherwise... like splitting 10's in a TC +4, 5, or 6). :)

Yes 1BB has given great advice & I will certainly keep all of your suggestions in mind! I have had my playing system down to what I think is perfect for some time (due to a ton of practice), but my act is my main focus now. I have always done my best to come off as drunk, careless & overall stupid as possible at the tables because I understand the strength of my system wont count for anything if they wont let me play. I have been working hard to step my game up & I will split 10's, as well as making every other correct basic strategy deviation between true counts of -5 to +10, but since I use AOII splitting 10's against a dealer 5 or 6 isnt a correct play until a true count closer to +10 (+8,+9 to be exact). So its rarely done lol. Romes, both you & 1BB have given me a ton of great advice & I thank you both!

Quote: Romes

I heard NUMEROUS ploppies sit down at my table and say "I always lose when I use that thing; it's bad luck!"

... and to think, some people don't like civilians.