Free FullBlackjack Simulator: Any Rules + Any Count System + TC Deviations + C-D Calculator

Hi everyone, we are BJTheorem.

We’ve previously shared earlier versions of the platform here, but we recently implemented a major upgrade to both the simulation engine and the overall system architecture. The platform is now significantly more robust and optimized than before, and has evolved into what we believe is one of the most comprehensive tools currently available for analyzing blackjack strategies.

We’d like to invite you to try the current version (available on web and mobile).

The simulator is fully online and currently free to use (you ONLY need to log in to run simulations or compute the calculator’s best bet.).

You can:

• Configure any rule set (S17 / H17, ENHC, DAS, decks, penetration, table spots, etc.)
• Choose any counting system (Hi-Lo, Mentor, Uston, Exact Composition, or custom tags)
• Use full True Count–dependent optimal deviations for each counting system
• Define your own TC-dependent betting ramp (net amount or percentage)
• Run simulations and obtain full distributions including EV, variance, and Risk of Ruin.

In addition, we provide a full Composition-Dependent Calculator that allows you to:

• Follow C-D decisions in real time (hit, stand, double, split)
• Follow C-D betting decisions in real time (based on EV, standard deviation, and bankroll).
• Obtain optimal theoretical utility at any moment based on the exact composition of the shoe.

The goal of the project is to precisely model real casino environments under any set of assumptions and allow users to evaluate the true performance of a specific strategy, so they can determine the optimal approach given their own objectives and constraints.

If you find inconsistencies, edge cases, or have technical suggestions, we genuinely appreciate the feedback. Many previous improvements came directly from community input.

You can try it at bjtheorem 'dot' com.

Thanks to everyone who tested earlier versions and contributed feedback.

Hello, just briefly checked out your website.

To give some advice, I recommend that you change the ruleset to allow players to split up to 4 times. In the USA where I live, this is the standard. There are also many places in my country that let you re-split aces, which I think should also be an optional rule.

Also running 2000 rounds of a simulation is not enough at all. When I do it on your website, the results are very different every time.

Hello, thanks for your reply.

In our rule configuration, 1 re-split means up to 4 hands total, while 1 split means up to 2 hands. The point about aces is a good one, and we will definitely take that into consideration.

Regarding the number of rounds, it’s not 2,000 rounds in total. The simulations consist of tens of millions of rounds, organized into independent sessions of 2,000 rounds each. This structure helps maintain consistency for strategies where the bet size is bankroll-dependent (percentage betting) and where ruin is possible.

Did you obtain dramatically different profitability metrics? Some variation between runs is expected, but the differences should be relatively small in percentage terms, and the overall scale of the results should remain consistent.

I’ve tried this simulator a few times. When you say 2000 rounds of playing each session, do you mean roughly 20 hours of playing heads-up with the dealer? Practically, it’s more reasonable to set it as 500 rounds each session. Players need to go to restroom sometimes.

Also, you distinguish player’s seats #1, 2, 3, 4, and 5, but where is the seat #6? I believe it makes no difference between seat #1 and #6. Why do you put so much effort on a seemingly petty thing?

Hi friend,

What I mean by 2,000 rounds per session is that each simulation run consists of 2,000 consecutive rounds. The actual real-world time that represents depends on whatever rounds-per-hour pace you want to assume.

So it does not necessarily mean “one literal uninterrupted session” at the table. It is better understood as 2,000 rounds of effective play, which in practice could be distributed across multiple blocks, different days, breaks to go to the restroom, etc.


Regarding the seats, those are configured in Table Rules & Conditions, and you can set the number of occupied seats from 1 up to 5. The seats highlighted in green are the ones played by the user, while the remaining occupied seats are played by bots following basic strategy.

And about why that feature is there: it was not a huge effort to add. It was fairly straightforward to let the simulator account for which seats are occupied, and it adds extra flexibility for modeling different table conditions.

I like this simulator because it contains a lot of details. I also want you to say something like this: how much advantage can a seat #6 player get over seat #1?

I’m not entirely sure I understand your question exactly. The simulator currently supports up to 5 seats, so I can’t directly evaluate seat #6 versus seat #1. But you can compare seat #5 and seat #1, which should already give a reasonable sense of how much seat position matters within the supported setup.

For a blackjack table, there are usually 6 seats. I did see a few 5-seat or 7-seat tables, but they are not common. Also, my instinct tells me that there is not much difference between playing seat #5 and #1, so there is no point of putting this feature in an online simulator. Do you agree?

I understand. In our simulator, the number of seats you configure refers to active spots, not the total number of physical seats at the table. For example, if you set 4 spots, you can think of it as a 6-seat table with 4 occupied seats.

I agree that the difference between playing seat #1 and seat #5 is probably not very significant. However, the difference between playing with a different number of active spots is meaningful. That is why this parameter still needs to be specified in the simulation. Otherwise, the setup would be ambiguous.

So while seat position itself may not have a major impact, the number of occupied spots definitely can. And in any case, including this option only adds flexibility to the simulator rather than taking anything away. If we thought it had no value at all, we simply would not have included it.

Another point, there is no advantage playing at a crowded table. So, what I suggest is that you make the simulator one-on-one with the dealer.

very interesting tool!!!!! would this also be helpful for players who are still learning basic strategy and moving toward counting systems?

This simulator is very powerful. I’ve tried it a few times more but found a glitch. When player plays 5 hands a time, the simulator does not produce a result graph.

Also, I haven’t found the report part on EV, variance, and risk of ruin. Where are they?

Thank you very much for your feedback, we really appreciate it. We’re very proud of the quality of the tool, and we plan to keep improving it even further.

Yes, it can also be very useful for players who are still learning and currently playing with basic strategy. You can simulate the performance of playing strictly according to basic strategy and analyze the results under different rules, penetration levels, and other conditions.

That said, moving toward a counting-based approach is highly recommended, since it can significantly increase your long-term advantage. This does require learning some deviations from basic strategy depending on the count, but the simulator allows you to study and test all of that as well.

Thank you very much, we really appreciate it! We’re glad you find the simulator powerful. In fact, we’re currently working on further improvements, and we believe it will become the ultimate tool for modeling optimal blackjack strategies.

Regarding the issue you mentioned: when simulating strategies with 5 player spots at the same time, you’re essentially running one of the most computationally demanding scenarios possible for the simulator. It’s not that it doesn’t work — it’s very likely that the simulation was simply still running. That said, thank you for pointing it out; we’ll definitely look into improving how this case is handled.

As for EV, variance, and risk of ruin: those indicators are located just above the results graph, and they update dynamically as the number of rounds changes using the slider.

I’ve tried this simulator and found it reliable. Using your Hi-Lo strategy and bet spread of $10/$25/$50/$75/$100 at TC=0/+1/+2/+3/+4, I got these EV and STD numbers:

EV=$413; STD=$1840 per 2000 rounds.
EV=$16; STD=$393 per 100 rounds.

However, something I don’t understand here. $16x20=$320, which does not match to $413. Could you please explain this to me?

Quote: Hackergambler

Hi everyone, we are BJTheorem.

We’ve previously shared earlier versions of the platform here, but we recently implemented a major upgrade to both the simulation engine and the overall system architecture. The platform is now significantly more robust and optimized than before, and has evolved into what we believe is one of the most comprehensive tools currently available for analyzing blackjack strategies.

We’d like to invite you to try the current version (available on web and mobile).

The simulator is fully online and currently free to use (you ONLY need to log in to run simulations or compute the calculator’s best bet.).

You can:

• Configure any rule set (S17 / H17, ENHC, DAS, decks, penetration, table spots, etc.)
• Choose any counting system (Hi-Lo, Mentor, Uston, Exact Composition, or custom tags)
• Use full True Count–dependent optimal deviations for each counting system
• Define your own TC-dependent betting ramp (net amount or percentage)
• Run simulations and obtain full distributions including EV, variance, and Risk of Ruin.

In addition, we provide a full Composition-Dependent Calculator that allows you to:

• Follow C-D decisions in real time (hit, stand, double, split)
• Follow C-D betting decisions in real time (based on EV, standard deviation, and bankroll).
• Obtain optimal theoretical utility at any moment based on the exact composition of the shoe.

The goal of the project is to precisely model real casino environments under any set of assumptions and allow users to evaluate the true performance of a specific strategy, so they can determine the optimal approach given their own objectives and constraints.

If you find inconsistencies, edge cases, or have technical suggestions, we genuinely appreciate the feedback. Many previous improvements came directly from community input.

You can try it at bjtheorem 'dot' com.

Thanks to everyone who tested earlier versions and contributed feedback.
link to original post

How to use your bj calculator to find HE of this game ?

I’ve tried this simulator again. In the “Playing Strategy” input part, I haven’t found any mention of insurance. So, do these statistics numbers of EV and STD from this simulator include the insurance contribution?

Quote: aceside

I’ve tried this simulator and found it reliable. Using your Hi-Lo strategy and bet spread of $10/$25/$50/$75/$100 at TC=0/+1/+2/+3/+4, I got these EV and STD numbers:

EV=$413; STD=$1840 per 2000 rounds.
EV=$16; STD=$393 per 100 rounds.

However, something I don’t understand here. $16x20=$320, which does not match to $413. Could you please explain this to me?
link to original post

Hey there. Those numbers don't necessarily have to match, since the risk of ruin means that the expected value doesn't increase linearly over time. However, as you found out when you tested the simulator while writing this, it didn't quite converge, since it only ran up to 60 million rounds. It was updated this week and now runs up to 140 million rounds! Give it a try.

Quote: aceside

I’ve tried this simulator again. In the “Playing Strategy” input part, I haven’t found any mention of insurance. So, do these statistics numbers of EV and STD from this simulator include the insurance contribution?
link to original post

They don't include it, friend. We're planning to add insurance soon!

I’ve tried this simulator. A few things:
1. I don’t understand this “ Pair payout” input box at all. What is this mix6/col12/perf 25? I’ve never heard of this part. I don’t understand “ PAIRS BETTING TABLE” at all.

2. In the betting method, if I chose Hi-Lo, your TC distribution is greater than 37% when TC>=+1. Other people show that about 27%, so there is inconsistency here.

3. I got EV=$237, STD=$2020 when rounds=2000. But EV=$7, STD=$432 when rounds=100. I don’t know how you did the statistics at these two rounds numbers. If rounds=100, do you shuffle the current shoe and then start a new shoe?

Quote: aceside

I’ve tried this simulator. A few things:
1. I don’t understand this “ Pair payout” input box at all. What is this mix6/col12/perf 25? I’ve never heard of this part. I don’t understand “ PAIRS BETTING TABLE” at all.

2. In the betting method, if I chose Hi-Lo, your TC distribution is greater than 37% when TC>=+1. Other people show that about 27%, so there is inconsistency here.

3. I got EV=$237, STD=$2020 when rounds=2000. But EV=$7, STD=$432 when rounds=100. I don’t know how you did the statistics at these two rounds numbers. If rounds=100, do you shuffle the current shoe and then start a new shoe?
link to original post

Pair payout refers to how much the pair side bet pays (mixed pair, colored pair, or perfect pair).

A pairs betting table refers to the strategy for betting on pairs. It specifies two things:

The percentage of hands in which you also place the pair bet
The amount wagered on the pair bet

Regarding the true count (TC) distribution, your numbers are correct (note that this depends on deck penetration). A typical distribution would be approximately:

TC ≥ 1 → 36%
TC ≤ -1 → 36%
TC = 0 → 28%

If, as you mentioned, TC ≥ 1 and TC ≤ -1 were only 27% each, that would imply TC = 0 occurs 46% of the time, which clearly does not make sense. So either there was a mistake in the calculation, or you were looking at a scenario with extremely low penetration.

Finally, simulations are run as independent sessions of 2,000 rounds each, where the shoe is only reshuffled if the cut card is reached.

I’ve tried it again and fount it really powerful! Let me get back to these three things I asked above.

1. In the “pairs betting table,” you set the betting frequency as 10%, but I don’t know how this is related to the Hi-Lo true count. In other words, what triggers the betting of this side bet?

2. The true count distribution strongly depends on how you process the decimal TC numbers into integers. It looks like you use the Round function, but I personally like the Truncate function. Truncate will simplify the HiLo deviation tables and thus works better for card counting.

3. Now, I can easily get a simulation result with 140 million rounds. This is really powerful! However, these 2000-round segments are not totally independent, because you break some shoes into two different segments. What would you say about this?

The Composition-Dependent (CD) Calculator sounds especially interesting. Most blackjack tools focus heavily on count-based strategy, but exact shoe composition and real-time C-D decisions can make a meaningful difference in close EV spots. Curious how deep the calculator goes with betting optimization — does it dynamically adjust recommendations based on bankroll + variance tolerance, or mainly maximize raw EV? Definitely going to test some edge-case compositions.

If I want to compare different card counting methods for the insurance bet, which area should I focus on?

It would be also helpful to add to the simulator a play online option; or create a third tool for that matter. Something similar to this app on Wizard’s site:
https://wizardofodds.com/play/blackjack-v2/

As a mere mortal, I cant afford to play 140 million hands in my lifespan. I got many other things to do :) With wizards tool you can play 200 hands at a time as a real player can do easily. then play 200 again… and again and so on.

Quite a few forum participants complain that 200 hands (rounds) at a time is not sufficient o prove something. Does that mean they’ve never played bj in real life because the impossibility of playing 140 million hands? Cuz any system would require that many bj hands to come to fruition, right? You had a good idea to set a session to 2000. Why not an even more realistic session of 200? If a man can play 2,000,000 blackjack hands in a lifetime, then some 10,000 sessions are possible. Si what happens after 10,000 sessions of 200 hands each?

In any event, your effort is to be commended.

Good question! With less sessions and a small number of hands each session, the variance will become a lot larger, so it becomes more like a gambling.

Quote: aceside

Good question! With less sessions and a small number of hands each session, the variance will become a lot larger, so it becomes more like a gambling.
link to original post

Exactly, much like gambling. Like in real life. We can do it for 100 players, 2000000 hands each. Its like playing some 25 years in a life. I doubt any gambler has ever played that much. I mean 2 million hands at the casino table after tye age of 21. Sure some players will win, others will lose - with the same bj system. Curious what the ratio would be. maybe 55 overall winners to 45 losers. The reverse could also happen, maybe 48 winners to 52 losers.

Quote: toolyp

Quote: aceside

Good question! With less sessions and a small number of hands each session, the variance will become a lot larger, so it becomes more like a gambling.
link to original post

Exactly, much like gambling. Like in real life. We can do it for 100 players, 2000000 hands each. Its like playing some 25 years in a life. I doubt any gambler has ever played that much. I mean 2 million hands at the casino table after tye age of 21. Sure some players will win, others will lose - with the same bj system. Curious what the ratio would be. maybe 55 overall winners to 45 losers. The reverse could also happen, maybe 48 winners to 52 losers.
link to original post

Ok. I just saw fewer simulations for fewer hands (rounds). I tried 50 (the max) simulations of 200 hands each. It is hard to read the graph, even with few sims. Looks like 50-50 or so-close as of winning or losing (related to bankroll). I just say that the mathematical foundation is correct as it confirms the normal probability rule. Counting systems are rated +1% +2% at best. That close to 50-50 prob would give a ratio of no better than 51% winners vs 49% losers. Sure some runs will show ratios like 60% winners vs 40% losers or 45% winners vs 55% losers.

Still, I suggest runs with say, 200 hands (it exists now) with the possibility of 1 mil or 2 or fantasy 5 or 10 or super fantastic 100 mill or bil. Every run should show 2 figures: EV and STD. The user can easily copy to a text file and paste.
1. EV, STD
2. EV, STD
3. EV, STD
…
100. EV, STD

Easy to calculate winning and losing runs and their ratio. That would sum up an average lifetime of blackjack gambling with various systems.

Quote: toolyp

Quote: toolyp

Quote: aceside

Good question! With less sessions and a small number of hands each session, the variance will become a lot larger, so it becomes more like a gambling.
link to original post

Exactly, much like gambling. Like in real life. We can do it for 100 players, 2000000 hands each. Its like playing some 25 years in a life. I doubt any gambler has ever played that much. I mean 2 million hands at the casino table after tye age of 21. Sure some players will win, others will lose - with the same bj system. Curious what the ratio would be. maybe 55 overall winners to 45 losers. The reverse could also happen, maybe 48 winners to 52 losers.
link to original post

Ok. I just saw fewer simulations for fewer hands (rounds). I tried 50 (the max) simulations of 200 hands each. It is hard to read the graph, even with few sims. Looks like 50-50 or so-close as of winning or losing (related to bankroll). I just say that the mathematical foundation is correct as it confirms the normal probability rule. Counting systems are rated +1% +2% at best. That close to 50-50 prob would give a ratio of no better than 51% winners vs 49% losers. Sure some runs will show ratios like 60% winners vs 40% losers or 45% winners vs 55% losers.

Still, I suggest runs with say, 200 hands (it exists now) with the possibility of 1 mil or 2 or fantasy 5 or 10 or super fantastic 100 mill or bil. Every run should show 2 figures: EV and STD. The user can easily copy to a text file and paste.
1. EV, STD
2. EV, STD
3. EV, STD
…
100. EV, STD

Easy to calculate winning and losing runs and their ratio. That would sum up an average lifetime of blackjack gambling with various systems.
link to original post

“45% winners vs 55% losers” sounds kinduv depressing for card counting enthusiasts. The long-run should always show 2% advantage for every counter. Some 20,000 profit after 1,000,000 hands gambled. The longrun started at one million, then went up to hundreds of millions, a billion, then hundreds of billions. Problem was that many sims showed losses, including ruin even at one billion rounds. Then I read one author raising the bar to hundreds of billions of hands to test the validity of any counting system. Since computers couldn’t finish the task in reasonable time, the counting enthusiasts took for granted the 1% or 2% or even higher player advantage.

The authors of this tool deserve special credit. They prove that, for any number of rounds (hands), there is loss, even ruin. Some counters win, some counters lose with the same counting system and for the same number of sims. There is no guarantee that the counter will always win at the end of any length simulation. There are no miracles. Actually it is math and this bj software tool proves it. That’s why I hold the BJTheorem authors in high regards.

They dont distort maths in order to satisfy a point. I remember another bj software author stating that his program had a “predetermined” advantage for a particular counting system. In other words, the sims would increase beforehand the advantage of any counting system. Yet, some sims were negative! The software user would then repeat the sim until a favorable one would result. A false positive!

I believe this tool would prove once and for all the real effect of each and every counting system. I’m sure every result would be close to 50-50. But positive or negative? I suspect negative. From what I saw running this tool. Also from skeptikal reasoning. Every counting system raises the bet automatically every time the true count is positive. But the dealer still has a better chance to win. thus the player still loses more often when the count is positive. Many player’s losses come at higher costs. Some losses are so high that ruin occurs.

Again, kudos to BJTheorem! I am not associated with said group in any way, shape, or form. I heard of them for the first time here.

I agree with you! I like this simulator.

Quote: aceside

I agree with you! I like this simulator.
link to original post

Have you informed Norm and DShless about it and the implications? Or you fear they might as well ban you again or forever? I am banned overthere. They have shown several times sims that always won for every counting system. CAC is the latest. All sims win after some billions of rounds. No ruin, not even losses.

It would be interesting to see their take. debates are always healthy.

I haven’t been able to talk to them. They sell things, sometimes by over exaggerating simulation results.

“over exaggerating” is just LYING. you cant over lie. A lie is a lie is a lie. Sorry if they banish you thinkin they ban me again.