• Blackjack Card Counting Efficiency Calculator
• Blackjack Card Counter Calculator
• Blackjack House Advantage Chart
• Blackjack Hand Calculator
• Blackjack Payout Calculator
• Blackjack Odds Calculator

BLACKJACK STRATEGY CALCULATOR. This calculator generates a blackjack strategy table based on the programmed set of rules. Select the Switch to Advanced Calc button to add support for less common rule selections including 5-card 21 bonuses, charlie bonuses, 777 bonuses; split restrictions; and peek on 10. See the blackjack page for more information about the rule options. BjBustOdds - High-Power Odds Calculator, Hands Generating Software for Blackjack Published on August 19, 2010; last update June 2014. Version 21, June 2014; New Software. BjBustOdds precisely generates all favorable cases (busted hands) and all possible cases (total blackjack actions). Thus, mathematically precise calculations of the blackjack odds and house edge are possible for the first. The house usually has a slight edge over the player in Blackjack (but not by much!). This house edge is an important consideration and often one that is ignored by the player. Our strategy calculator will help with this. We have used mathematical probabilities to suggest the. The house edge is half of one percent so if we take $100 million and multiply it by.005 we get $500,000 which is how much the casino expects to make off of you in the long run if you continue to bet $100 a hand. So essentially each bet you make is worth about 50 cents to the casino. Obviously you don’t just hand over 50 cents every round.

ssho88

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) ?gordonm888

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.

Blackjack Card Counting Efficiency Calculator

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.

Blackjack Card Counter Calculator

ssho88

Blackjack House Advantage Chart

gordonm888

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

Blackjack Hand Calculator

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.ssho88ksdjdjgordonm888

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?

House edge means the percentage of the player's bet the casino wins on average. This is worth figuring out since the size of house edge has everything to do with how likely you're to win. Educated players always find the games with the least house edge possible and therefore win the most - or at least lose the least.

For example, if house edge is 1.89%, the player loses $1.89 on average out of every $100 bet he makes. Obviously the player doesn't lose that amount on every single bet; you might win two hands and then lose six hands in a row but in the long run the loss will be about $1.89 per bet. One of the goals of Gaming the Odds is to teach you all about perfect blackjack strategy and to minimize the house edge. You can find several house edge percentages for blackjack game variations below in order to help you to find the best games.

The Amount of Decks

Firstly, what kind of an effect the amount decks has on casino's advantage? The table below displays the house edge for a standard blackjack game: blackjack pays 3:2, the dealer stands on soft 17, doubling is allowed for any two cards and splitting to four hands is allowed.

Number of Decks	House Edge
Single Deck	-0.03%
Two Decks	+0.25%
Four Decks	+0.38%
Six Decks	+0.42%
Eight Decks	+0.44%

Under those rules it would actually be profitable to play according to basic strategy with a single deck. It's always optimal to play according to basic strategy but in the vast majority of cases you're still going to have negative expectation.

Game and Rule Variations

Blackjack Games

Let's move on to the next table, which features other blackjack game variations and their house edges. In order to make it easier to compare these games, all the house edge percentages are for six-deck gamesunless otherwise stated.

Game	House Edge
Atlantic City Blackjack	+0.42%
Blackjack Switch	+0.58%
Double Attack Blackjack *	+0.61%
Double Exposure Blackjack	+0.67%
European Blackjack	+0.62%
Multiple Action Blackjack **	+0.42%
Pontoon Blackjack	+0.45%
Spanish 21	+0.37%
Super Fun 21	+1.40%
Three Card Blackjack	+2.10%
Vegas Downtown Blackjack	+0.62%
Vegas Strip Blackjack	+0.53%

* Played with a specific amount of decks (which isn't six).
** Multiple hands played but probability equal to standard blackjack.

The table above was made to give you some idea of which games are better to play than others. It's also important to remember that some casinos may operate with slightly different rules which either increase or decrease the house advantage of the game.

Blackjack Rule Variations

What about other rule variations, then? I'm going to list some of the more common blackjack rule variations and their house edges. The tables below consists of changes made to standard blackjack rules:

Dealer Hits Soft 17
# of Decks	House Edge
Single Deck	+0.15%
Two Decks	+0.45%
Four Decks	+0.59%
Six Decks	+0.63%
Eight Decks	+0.66%
Player Can Only Double 9-11
# of Decks	House Edge
Single Deck	+0.11%
Two Decks	+0.36%
Four Decks	+0.48%
Six Decks	+0.52%
Eight Decks	+0.54%
Player Can Only Double 10-11
# of Decks	House Edge
Single Deck	+0.26%
Two Decks	+0.48%
Four Decks	+0.58%
Six Decks	+0.61%
Eight Decks	+0.63%
Dealer Doubles on 17
# of Decks	House Edge
Single Deck	-0.03%
Two Decks	+0.25%
Four Decks	+0.38%
Six Decks	+0.42%
Eight Decks	+0.44%
Player Can Resplit Aces
# of Decks	House Edge
Single Deck	-0.06%
Two Decks	+0.20%
Four Decks	+0.32%
Six Decks	+0.35%
Eight Decks	+0.37%
Blackjack Pays 6:5
# of Decks	House Edge
Single Deck	+1.36%
Two Decks	+1.62%
Four Decks	+1.75%
Six Decks	+1.78%
Eight Decks	+1.80%

Blackjack Payout Calculator

A couple of conclusions: first of all, the last section ('Blackjack Pays 6:5') shows you how unprofitable it is to play those games. Never play a game where blackjack pays 6:5.

Secondly, games where the player can resplit aces are preferable for the player. Try to find those games. It's also good for the player when the dealer doubles 17.

Blackjack Side Bets

And finally, blackjack side bets and house edges for them.

Blackjack Odds Calculator

Side Bet	House Edge
21+3 Blackjack	+3.20%
21 Madness	+23.00%
Bonus Blackjack	+24.00%
Match the Dealer	+3.10%
Perfect Pairs Blackjack	+4.10%
Royal Match Blackjack	+6.50%
Super Match Blackjack	+2.60%
Super Sevens Blackjack	+11.70%
Bust It Blackjack	+7.00%

No, casinos didn't include the 'side bet' option just to give players a better chance of winning. As you can see, side bets are good for the casino and bad for the player even if they might make the game a bit more exciting.

Favourable Blackjack Rule Variations for the Player

Here's a list of blackjack rule variations favourable for the player:

• The less decks the better. (Games with one deck are the best.)
• Double down on any 2 cards.
• Blackjack pays 3:2.
• Resplitting aces allowed.
• Dealer stands on a 17.
• Early/late surrender.
• Low deck penetration (for card counters).
• Insurance (for card counters).

Favourable Blackjack Rule Variations for the Casino

• Side bets.
• Double down on 10 and 11 only.
• Dealer hits a soft 17.
• The more decks the better.
• Blackjack pays 6:5
• Low deck penetration (against card counters).
• No doubling down after splitting.
• Not allowed to resplit aces.

I suggest trying to memorize these lists and look for games with beneficial blackjack rule variations for the player. Rule variations in favor of the casino should obviously be avoided.

Blackjack House Edge: FAQ

Do bet sizes impact house edge in blackjack?

It makes no difference whether you bet $10 or $10,000 - the house advantage stays the same. The amount you lose or win per bet changes, of course, depending on how big of an edge either you or the casino's got.

Which blackjack game has the smallest casino edge?

Suggesting all games are played with six decks - which is a common size for a blackjack shoe - Spanish 21 has the best house edge for the player according to the blackjack house edge table on top of this page. Standard 21 Blackjack is good too since you can actually have the edge by playing perfect basic strategy with a single deck.

How big is the house edge if I count cards?

This depends on many variables, such as which blackjack card counting systems you're going to use. In case you're using a highly complicated system, play perfectly and manage to find a good game to play, you may have a significant edge (even 3% or 4%).

Additional Resources: