Blackjack calculations

Hello BJ lovers!

I couldn't find a free blackjack calculator I thought to ask you this...

What is starting bankroll, winrate and variation (+/- $) to be expected with the following information below:

Minimum Bet = $5
# of Decks = 6 Decks
BJ Payout = 3-2
Double = Anytime
Double after split = Yes
Resplit aces = up to 4 times
Dealer hit on soft 17 = Yes
Late surrender = Yes
Peek = Yes
Penetration = Unknown
Spread = Minimum possible to bring down bankroll (what spread should that be?)
Strategy = Basic Strategy
Counting method = Hi-Lo

Thanks! =)

Oh boy! Well, there's a few things to discuss here Luck. First, you're going to need to know your penetration, or at least pretend you're not going to play anything with less than 75% penetration for the 6 deck games. If you're playing something with horrendous penetration (like online live blackjack) then these games are more/less unbeatable. While technically an advantage could be had, your variance is through the roof requiring a bankroll the size of, well why would you need to be playing if you have that bankroll =p.

Next, you need to define your bankroll, as that will often define your spread... or vice versa. Do you have a specific hourly rate in mind? That would require a spread of X and a bankroll of Y. You can't really say "I dunno what my spread or bankroll is but give me the numbers!"

Lastly, just because you can't find something free doesn't mean it doesn't need done. When you get to the point in counting to make real questions and real decisions (such as your spread based off your bankroll) it's WELL WORTH IT to invest in a simple program that can run simulations and do all of this for you. All you have to do is plug in the information above, your spread, and bankroll (which you can enter different ones to find what works for you) and it'll give you your long term hourly EV and Standard Deviations (SD's) for your +/-.

Lastly lastly, I show how to do this math in my articles... So even if you didn't want to pay the cheap price for this kind of long term investment, you could simply leverage my FREE articles posted in the Articles section of this very site and do a bit of reading/research to find the math you need to do it yourself.

I'm not trying to come down hard on you... but these are questions you yourself can find the answers to several different ways, and in doing so you'll understand the math and game so much more than if someone were to just respond $X +/- $Y. Like anything else in life, with blackjack, you get out of it what you put in to it. It's going to take hard work to be a successful player... No way around that.

https://wizardofvegas.com/articles/A-to-Z-Counting-Cards-in-Blackjack/
https://wizardofvegas.com/articles/A-to-Z-Counting-Cards-In-Blackjack-2/
https://wizardofvegas.com/articles/A-to-Z-Counting-Cards-in-Blackjack-3/

I'm not telling you which one your EV +/- SD's are in, so you'll just have to read all 3 and maybe learn a thing or two =).

Romes! Thanks for your AWESOME reply!

Quote: Romes

Oh boy! Well, there's a few things to discuss here Luck. First, you're going to need to know your penetration, or at least pretend you're not going to play anything with less than 75% penetration for the 6 deck games. If you're playing something with horrendous penetration (like online live blackjack) then these games are more/less unbeatable. While technically an advantage could be had, your variance is through the roof requiring a bankroll the size of, well why would you need to be playing if you have that bankroll =p.

I kept hearing about penetration but haven't learn how to spot it. How would you know how much penetration at the table? Is it a rough guess after seeing the cut? Could every shuffle have different penetrations?

Quote: Romes

Next, you need to define your bankroll, as that will often define your spread... or vice versa. Do you have a specific hourly rate in mind? That would require a spread of X and a bankroll of Y. You can't really say "I dunno what my spread or bankroll is but give me the numbers!"

Ahhh, let's start at the bottom...I would like to solve for bankroll. Let's say hourly rate is $1. For the spread, whichever is reasonable trying to lower bankroll as possible. I saw somewhere that 1:5 is the minimum and up to 1:15 before risking heat. If I understood correctly, the smaller spread, the smaller bankroll needed. If so, I'll shoot for 1:5 to start with.

Quote: Romes

Lastly, just because you can't find something free doesn't mean it doesn't need done. When you get to the point in counting to make real questions and real decisions (such as your spread based off your bankroll) it's WELL WORTH IT to invest in a simple program that can run simulations and do all of this for you. All you have to do is plug in the information above, your spread, and bankroll (which you can enter different ones to find what works for you) and it'll give you your long term hourly EV and Standard Deviations (SD's) for your +/-.

I assume you're speaking of CVCX...I am a Linux user and trying to avoid using Windows apps as possible...Do you know a software for Linux? If not, I'll try doing the math with spreadsheet *gulp* ...else, I'll buy Windows and then grab CVCX.

Quote: Romes

Lastly lastly, I show how to do this math in my articles... So even if you didn't want to pay the cheap price for this kind of long term investment, you could simply leverage my FREE articles posted in the Articles section of this very site and do a bit of reading/research to find the math you need to do it yourself.

I've read your GREAT articles a while ago...I truly enjoyed reading them =) ...I need to re-read it...I don't remember seeing win rate formulas in there but thanks for the reminder!

Quote: Romes

I'm not telling you which one your EV +/- SD's are in, so you'll just have to read all 3 and maybe learn a thing or two =).

*FINEEEEEE* :-P But but would you point to a reliable source that have correct formulas laid out to use? I'll re-read your articles for sure! =D

You can tell the penetration by where the red card is placed in the shoe or in a hand held game in the pack itself.
You need to learn how to judge it for yourself. In a six deck game, imagine the shoe is a foot. Each inch equals a a half deck. When half the cards are dealt, you are at six inches, or three decks. You need to learn to judge by half decks at a minimum. I do quarter decks myself. If not counting cards, the less penetration they offer is best for you. For counters, you want a deep count.

Avoiding the quotes I'll just respond in numbers =P.

1) As pointed out by bill, penetration is how deep the cut card is places after the shuffle. Some places have a notch in the shoe that AUTOMATICALLY cuts 1.5 decks, which in 6 deck is 75% penetration. The Deeper the cut card the more fluctuations in the count you'll see near the end of a shoe and thus the more opportunities you'll have to bet bigger. So more penetration = more big bets from you. Less penetration = less, which usually results in the need to bet harder when you do see a positive situation which drives your bankroll requirements up the wall. I would recommend never playing less than 75% penetration for 6D (In Article 1 I discuss penetration).

2) A 1-5 spread will "probably" be break even, or maybe not even break even. If you're trying to make any money you'll need to spread more. Often is easier to go the other way and say "What can you devote to the game as a bankroll?" If you come back and say $10,000... then your big bet can be about $100. From there you can work a spread that starts at a min and ends at your big bet of $100, thus $10-$100 would be a 1-10 spread. In Article 1 I discuss bankroll requirements like this.

3) I'm not sure if CVCX works for Linux or not. I would recommend contacting Norm and asking him. I would think it works for Linux, and if it does it'll tell you alllll of these things you want to know and more, simply by plugging in the rules and your estimated bankroll/spread. Also, you don't need a spreadsheet to find your long term EV +/- SD. In Article 3 in the Q/A section I show how to calculate your long term EV +/- SD for ANY number of hands. This is how you can find your N0, which is your point of mathematically guaranteed to be positive... Usually around 50,000-100,000 hands (and at 100 hands per hour, the generic 1,000 hours rule).

EV = TotalWagered * HouseEdge = (AvgBet*NumHands) * HouseEdge

OriginalSD = 1.1 * AvgBet

SD(x hands) = SQRT(x) * OriginalSD

BUT... you need to figure out your spread and bankroll first. Then you'll know what your Average Bet is. After that, you just need to plug in whatever number of hands you want to know where you'll be at. Also, the SD(x hands) above is just for 1SD (68% confidence). To be 99.9% sure, you need 3SD's, which would require multiplying that result by 3. Again, this is covered in the 3rd Article in the Q/A section.

4) Take the articles 1 at a time. I have sample spread sheets I posted on Google Docs, which I linked to in the A-Z thread. You can't modify them, but you CAN download them and then modify them for your numbers... Download the spread sheet for 6D. Plug your house rules in to the Wiz's house edge calculator. Plug that number in for TC = 0 on the spreadsheet and update the others for the True Counts (using + or - .5% from the original number). Then update and play with your spread. Your Avg Bet and hourly will automatically calculate. The "Total Gain" will be your Gain Per Hour (per 100 hands). So that's your Hourly EV, but more importantly you can take your Avg Bet and plug it in to the equations above to get your EV +/- SD for ANY NUMBER of hands =).

https://wizardofvegas.com/forum/gambling/blackjack/19491-a-to-z-counting-cards-in-blackjack/5/#post483782

Quote: billryan

You can tell the penetration by where the red card is placed in the shoe or in a hand held game in the pack itself.
You need to learn how to judge it for yourself. In a six deck game, imagine the shoe is a foot. Each inch equals a a half deck. When half the cards are dealt, you are at six inches, or three decks. You need to learn to judge by half decks at a minimum. I do quarter decks myself. If not counting cards, the less penetration they offer is best for you. For counters, you want a deep count.

If you think six decks is a foot I can't imagine what you have told your girlfriend :)

Quote: Hunterhill

If you think six decks is a foot I can't imagine what you have told your girlfriend :)

1st biggest lie in America: I've read and understand the terms and conditions...

2nd biggest lie in America: It's 6 inches.

Six decks equals 12 half decks. As a foot equals 12 inches, and we are dealing with 12 half decks, I find it easier to mentally think of them as inches. When I was learning basic strategy, I used a lot of mental images to help. This was one.

Quote: Romes

2nd biggest lie in America: It's 6 inches.

With facts such as that, is it any wonder why American women haven't shown any interest in pursuing collegiate studies in mathematics???? [Solely intended as sarcasm, so don't bash me for being a MCP]

Quote: billryan

Six decks equals 12 half decks. As a foot equals 12 inches, and we are dealing with 12 half decks, I find it easier to mentally think of them as inches. When I was learning basic strategy, I used a lot of mental images to help. This was one.

Bill, some cards are thicker than others... And while that could be interpreted as a double entendre, I assure you're I'm being serious. I've played at places where 6 decks looked like 8, and others where 8 decks looked like 6. The thickness/quality of the cards definitely comes in to account.

A deck of cards is approximately 5/8" thick.

If not counting or using another advantage play, you are at a disadvantage every hand. Deeper penetration means more hands per shoe and per hour.
An Avantage player generally wants to play with as few people at the table with Deep penetration.
A beginner wants to play at full tables with shallow penetration. The less hands played per hour, the lower your disadvantage.