Among emails I receive, a fairly common question is something like this:

Can you tell me the odds of losing six hands in a row at blackjack?

Sometimes it is 5 hands, sometimes 8, sometimes more. No matter, I cringe whenever I get this question.

To me, it’s like an airship designer asking a chemist: “Does hydrogen weigh only half as much as helium?” We all know how THAT turned out.

In either case, there is nothing wrong with the matter-of-fact question being asked, but it is apparent to the recipient that the question is likely a clue to dangerous thinking, whether it be the Hindenburg or the Martingale progression.

I’ll get back to that in a moment. But first, let me respond to the question, very carefully…

The first thing I want to do is change the wording of the question from “*What are the odds*” to “*What is the probability*“. Most people asking this question want an answer that is a single number or percentage, representing how likely the event is to occur. “Odds” means something slightly different, although the two are often used interchangeably. If you want to understand the difference, Google it.

There is a crucial piece of information missing from your question. How do you plan to play?

Let’s say you sit down next to me at a blackjack table, and I look over and tell you: “This is unbelievable! I’m on the most horrible losing streak. My luck is so bad, I bet you $100 that I lose the next six hands in a row.” If you were foolish enough to bet me, I would quickly demonstrate how the probability of losing six in a row can be 100%!

But for the sake of your question, let’s assume the player will use accurate basic strategy on the game. I cannot resist the temptation of pointing out that virtually no player who asks this question will know a completely accurate basic strategy! But I’ll play along anyway.

There is another picky detail to consider. I assume you are not asking for the probability of losing exactly six hands in a row, which implies that the seventh hand cannot be a loss. Instead, you want to know the probability of losing six **or more** hands in a row. We can easily sidestep that complication, if we simply say that you want to know the probability of losing the **next** six hands of blackjack.

For a typical shoe game, a basic strategy player will win 43.3% of hands, lose 48.0%, and push the other 8.7%.

If I answer the revised and improved question…

*What is the probability of losing the next six hands at blackjack, using basic strategy?*

Since each hand has a 48.0% chance of being a loss, the answer is 0.48 ^ 6 = 0.012 = 1.2%.

But wait a minute…

That probably isn’t what you meant either. What if you lose the first hand, push the second hand, and lose the next five hands in a row? You would probably want to call that losing six in a row. We should just ignore pushes altogether, and only count hands that end in a win or a loss. Of non-push hands, players win 47.4% and lose 52.6%.

Finally an answer that may satisfy you:

*What is the probability of losing the next six hands at blackjack, using basic strategy, ignoring pushes?*

The answer is 0.526 ^ 6 = 0.021 = **2.1%**.

That is roughly 1 in 47 attempts.

Just because this is a convenient place to do so, I’ll publish the numbers for other lengths of losing streaks.

Probability of losing n hands in a row, ignoring pushes. | ||
---|---|---|

n | Probability | One in |

1 loss | 52.6% | 1.9 |

2 losses | 27.7% | 3.6 |

3 losses | 14.6% | 6.9 |

4 losses | 7.7% | 13 |

5 losses | 4.0% | 25 |

6 losses | 2.1% | 47 |

7 losses | 1.1% | 90 |

8 losses | 0.59% | 170 |

9 losses | 0.31% | 323 |

10 losses | 0.16% | 614 |

11 losses | 0.08% | 1168 |

12 losses | 0.04% | 2219 |

13 losses | 0.02% | 4217 |

When players ask questions about how likely it is to lose hands in a streak, it usually means that they are considering a negative progression betting system that would fail if they encounter a certain number of losing hands in a row. Most commonly, they have rediscovered the infamous Martingale system, where you double up after any losing hands to catch up.

The Martingale is the simplest of the negative progression betting systems. The idea is simple. If you lose one hand, just double your bet on the next hand. Eventually, you will win a hand, and make back all of your losses plus a profit of the initial bet. Indeed, this seems to work very reliably, until it doesn’t. The problem is that most people underestimate how likely those “unlikely” streaks of losses really are. Check the table above. The probabilities get small, but not nearly small enough.

If you think the Martingale is a good idea, you are badly mistaken. Yes, it gives you a high percentage chance of winning a small amount, but it does not take long to run out of luck. For a $10 bettor who wants to be able to handle up to 7 losses in a row, he needs to have a bankroll of $2550, and be willing to bet $1280 on the eighth hand. All this, for a $10 win each time.

And he will run into that fatal eighth loss once every 170 trials on average. You can think of that as making $1700 in profit before you eventually lose $2550. (Yes, I am oversimplifying because doubles and splits make the math very messy. The real numbers still make this a very bad idea.)

On top of that, blackjack is a terrible choice for the Martingale system. With the necessary doubles and splits, sometimes both on the same hand, you will actually need a far larger bankroll to play correct basic strategy. If you choose to ignore basic strategy doubles and splits, you can get by with “just” the $2550, but at a substantially increased loss rate on all your bets.

**Any progressive betting system is doomed to fail**. Any series of negative expectation bets is guaranteed to create a negative expectation overall. If you are just playing for fun, you will lose less money by flat-betting. If you are playing for profit, you need to find a true way to get an edge, such as counting cards.

Hopefully you are reading this before you learn the hard way. After all, we don’t fly airships full of hydrogen any more either.

The chance you loose 6 in a row is 2.1%. The article then states this will occur 1/47 times. The 1 occurrence is a loss of 6 hands, meaning the other 46 times 6 hands were also played and you won at least 1 time those 6 hands. Meaning a total of 282 total hands of blackjack were played here and six losses in a row occurred 1 time. Giving you the odds 1/47. Now if you use a modified martingale and cap your self at 6 losses in a row with an original bet of 10 your 6th bet will be 320. Your min bank roll would have to be 710. Based on these odds you plan on loosing 710 dollars per ever 282 hands of blackjack you play. However In that 282 you will also win a lot. The min amount of times you can win in 282 is 46. 46×10=$410 $410-710=Net of -300 dollars. However the theoretical amount of times you win in 282 hands based off having 43.3% chance of winning each hand is $1,221. Net profit of 1,221-710= $511. In theory you should alway net more money in 282 hands even when you loose 6 in a row one time.

I always wanted to ask this question. I have been playing at home with a 2 deck shoe. I have been playing for several years at home. I use a negative betting strategy. I play on a 100 table with 10k max stand on soft 17. I bet 100 100 300 600. After I lose 4 hands in a row I bet 100 100 1k 2k when I win either the 1k or 2k I go back and bet my original strategy of 100 100 300 600 until I lose and start it all over again. I used to start with 10k then switched to 7k start because I noticed starting with 10k did get me more wins in the long run. After 2 years I’m up at home 1 million bucks of fake money. I started with 50k and never went broke. I never lost more than 5 times in a row making the lose 35k. How was I able to do this and why won’t it work at the casino. I realize I’m playing at a table with just me. What are the odds of replicating this at the casino ?

It looks like the house edge for these calculations is 5.2%. What are the odds of losing 10 in a row with a blackjack game with rtp of 99.91%, or 0.09% house edge? I played a game with 99.91% rtp and lost 8 in a row after only playing 7 hands. I made $2 and lost $256. Is that statistically uncommon?

Furthermore, is the probability impacted if a player plays to win $1 on 100 different blackjack games, rather then playing to win $100 on one blackjack game.

I’m not a mathematician here; help me out: When you say the probability of the 6-consecutive losing streak is 1 in 47, you don’t mean every 47 hands you get a 6-hand losing streak. You mean each segment of six is multiplied by 47, right? That’s a 6-hand losing streak per 282 hands of play. And the 7-hand losing streak is 1 in 90, or a 7-consecutive loss per 630 hands of play. Is that correct?

I mostly play poker 1/2 Texas holdem I asked a dealer about the automatic shuffler; does it know if there 51 or 53 cards in the deck? He said yes it counts to make sure there are 52, and it can even put them back in order

A123…JQK.

If it can put them in starting order, it can put them in any order, for blackjack all the 10’s together in the front or in the back

Taking into account a player will cut the cards in the middle somewhere, the high cards would still be all together

is this really true? How would a dealer know this information? maybe a pit boss, but a dealer? Where did this happen? (just curious). I will not be playing there. Also, was it a continuous shuffler or automatic shuffler?

Listen i been study bj awhile and basic strategy just seem to conservative so i design combined positive and neg progression system on the computer playing 200 dollar bank roll and a modified playing strategy where i used the marginegale and 1-2-3 unit betting count on a win and on 7of10 100 hand 5 doller betting system i profit over 500 dollars before ive played a tota of 40 hands

Hey William, I’d love to connect with you and talk about your strategy. I myself have been trying different strategies and would love to share them with you. Send me an email to [email protected] or request me on IG: gaintheadvantage21

Okay, I’ll risk sounding like an idiot here just to make a point. The Martingale system loses because the player runs out of real estate (betting room) and the reason for this question is obvious–but necessary. How many times will you lose X hands before you WIN Y hands. I have done thousands of simulations using basic strategy and I do NOT get the same rate of losses to wins as the chart above–true odds or not. Take it for what it’s worth but the short term (Martingale)–and that’s the KEY–short term, produces consistent wins for me. I’m getting closer to the 6 loss percentage only going to five bets. I’m having to take a stop/loss (limit) about every 47 hands which keeps me in profits. Now before you call me an A**hole–try it yourself and see if it works.

I lost thirty hands in a row today – but it was online. Is that .526 to the power 30? 447 million to 1?

Out of curiosity, what site was this with? Is it just me, or do you feel like some versions of blackjack are not being inspected properly? For example, I feel that versions like Virgin Games/Monopoly Casino/Gamesys brand are really true to rtp%, while there’s some sport bookmaker’s casinos feel very off sometimes.

I agree. Somehow they find a way to win 30 hands in a row. Its bs

How the hell did you lose 30 in a row are you not playing by the book perfect strategy. I made over 1500 in 6 hrs doing 5-15-35-70-140-280-560-1120 . I basically do 10 games per set and 5 sets which would be 50 games it got scary I got to hand 6 a few times $280 . I guess sooner or later you will lose 8 in a row . I just wonder if it is better to use maybe 5-6 hand losing streaks for martingale . Then start over because if you lost 8 in a row all your profits are gone. I guess if you were rich you would never lose double forever lol

Woah. I woulda went and grabbed a padded suit and locked myself in a completely accident free zone for at least a week of that happened to me. LOL couldn’t imagine losing 30 hands in a row. I’d be fighting somebody.

this guy is crazy with the money you need to progress. If I played at a $25 dollar table, I would need $800 to be able to lose 6 times. On the 6th loss I would be broke. If you do this martingale, and only have a goal of $150 profit, you can fairly easy get up 6 hands and leave. And the system I am talking about is the exact same, except lose $25 and then bet $25 again to break even. Every double win you get your $25 profit and $25 profit for every consecutive win after that. $2550 for a $10 bet starting? How many damn hands do you plan on losing in a row????? And if i get up $150 a day and end up losing my bankroll on one visit every 47 times like the losing 6 hands says, then I will lose 800 compared to the 46×150 which is $6900, still coming out $6100 profit. Now I know you can lose more than 1 in 47 attempts and I know shit happens. But getting up only 6 hands with this system is not that staggering of a goal. Stick to your limit/goal and it could be way better than this guy makes it out to be. When minimum wage is $8.00/hr, bringing home $750.00 a week isn’t bad for getting up 6 hands, 5 days a week.

Ya feel DUMB bucking the odds. But sometimes it’s NOT so crazy. I have experienced similar results while doing thousands of (non computer) real play hands. My loss percentage is smaller than the true odds would indicate–leaving room for consistent profits.FACT: you’re going to take your share of losses so be prepared. Have the proper banks and a solid betting plan in place. Know basic strategy. Be patient and play like a machine. Set your stop/loss limit. You should absolutely WIN in the end.

Get over yourself, someone else can answer the question then

I realize this post is old, but the most common thing that happens to me Is if I draw a 12. I almost always, no exaggeration, I hit, and 8 out of 10 times I draw a face card. Dealers make hands on 12 like it their job…wait, it is.

In online blackjack, I played 10,000 hands and of all the 12’s I hit on, 83.8% gave a ten. I asked the casino why this was and they told me I had bad luck

Same here it’s bs

Wow. First of all, this article addressed the losing nature of reverse progression as related to BlackJack (almost). It was simplified to large degree. However, the author is corrects in two major points. First being that in and of itself, Martingale will fail at BlackJack over the long run. Second is that a vast majority of players will not make the optimum decisions each and every time to increase their odds given ANY particular strategy. If someone does not understand the math, have the discipline and bankroll to try any system to it’s strictest mathematical constraints, and have a willingness to lose, he has no business experimenting. Most people searching this sot of thing (As the author suggests) are looking for a simple, quick way to beat the house. And thy will fail.

Most striking among the replies are the liberal doses of perceptual bias. ANYONE who makes a claim based on observed results is suspect. The human mind is not capable of correctly interpreting complex statistics from it’s observations. This is a fact. Make no mistake, your 9 or 38 or 21342345 trips to the blackjack table to try a system, and your recollection of results is skewed. Humans remember the extreme examples better than the more average examples. This has been proven time and time again. It is why math, specifically linear progression, is necessary to bear out the validity of any given system. One then has to have a mature and reasonable viewpoint to assess any practical application.

As far as playing any BJ game with reduced odds, or where you cannot see the shuffle, don’t. 6/5 is for tourists who don’t know better or care if they lose. Casinos who cannot or will not show a shuffle simply deserve to lose your business. This is a moral, not a mathematical response. As far as a mathematical response, it is ridiculous. There is no possible stack of a deck that can ensure victory over an unknown number of players. The deck could be juiced, meaning that the ratio of small cards to 10’s and/or aces is illegally modified. But any casino trying this is risking their license. You might see that in the Caribbean or some such place, but not in Vegas.

The article failed to mention caveats to overall strategy, and objective.

I’ll run a negative progression at times. Never by itself of course. That’s stupid. There are ways to MAKE the Casino THINK you’re running negative progression, and actually hide it in something else (No, I’m not giving away everything here).

Regardless, as with any mathematical game, you have to take into account strategy, and objective. Of course, this is taking into account that the individual is not a degen, and is actually going to “work” when they walk into the casino.

You run counting cards, and the rest of your strategy, and you’re up your target amount, plus a little spill over your target. Here … I’ll give you one for free.

Take that SPILL ONLY (and sometimes, if you want every dealer to be in love with you until the end of time, the tip amount) and run your strategy on a strict Martingale. You’ve already made your money. So just run the spill, down to a predetermined kill arena, but run strict negative progression until you hit the new target, or your kill spot is hit.

You __ MUST TAKE INTO ACCOUNT STRATEGY SPECIFICS __ before throwing around “never’s” and “Dont event think about” ‘s

Blackjack is actually a simple game to beat, with even a rudimentary understanding of differential mathematics; which in my opinion, they should be teaching to 9 year olds.

Just got back from Ceasers Palance. Tested my suspicions again.

1) New Deck

2) Deck Spread out

3) Deck placed in shoe and never shuffled in front of me

4) EMPTY TABLE – I was the only player at the table

IMMEDIATLY LOST 7 HANDS IN A ROW STRAIGHT !!!! Per this website – odds of this are 1.1% or 1 in 90 !!!!!

My suspicion has again been confirmed. However I have NO EVIDENCE other than circumstance. So I need to know if anyone else has experienced this.

I’m wondering if the casinos are setting up the new decks in a mathmatically predetermined way which give the dealer an edge if they are not shuffled good enough.

Anyone comment on this? I don’t want to hear oh your an idiot. ALLOT of math research goes into Casinos and they have BILLIONS at thier disposal – basically infinate money to see if there is a way to get a new deck in a preset way that mathmatically give them a huge edge.

IF you have the time and money to test this – give it a try on 5 sessions and see if 3-4 lose money. AGAIN this is how you do it:

1) Empty Table – Table must be EMPTY

2) Cards spread out on table

3) New Deck (if the cards are spread out on the table it means IT IS A NEW DECK)

4) YOU NEVER SEE DEALER SHUFFLE THE CARDS. THEY SIMPLY PUT THE CARDS IN THE SHOE AND START DEALING.

Follow these steps as an experiment (if you have the time, money and are interested) and record your results. Most of you probably won’t do this but if I’m wrong – you have no reason not to.

I am suspicious because the odds of this happening WITH the same environmental variables I just listed must be very, very low.

I am wondering, if the casinos are engaged in a legal conspiracy to “legally defruad” players based on the above.

If I’m the only one – fine. However I’ve been talking to other people and they have noticed the same thing.

Again – I’m not willing to say anything for sure – at this point is an ongoing experiment. I’m going to go to other casinos and try this AGAIN and record my results under the same conditions.

I agree, their shuffling machine reads the card, so I am suspicious if that in between lines in laws there is a loop hole that they can some how shuffle, that bunch of smalll numbers comes out, so it ruins all your doubles and splits!

Also, Golden nugget that hand shuffle, they change their cards every two hours, I think the way the shuffle, there is a same math to it, and as soon as cards gets shuffle we’ll, two hours cards change comes!

I think they do. I have witnessed 10 small cards come out in a row and dealers don’t bust. I have also witnessed every player having 20 including the dealer. I think this is due to lack of shuffling. No wonder they allow basic strategy charts. Cards are not coming out random as they should to make the game fair.

No. It’s the basic gamblers fallacy in hitting a losing streak (for any number of reasons, which could be they simply did not play basic strategy correctly; Hitting at 15 when the dealer stands at 6 for example. Or it could be a simple mathematical deviation). Regardless … your theory falls apart on your own premise. NO ONE ELSE MUST BE AT THE TABLE, per your own words.

That’s not something the Casino controls, or can control. It’s what we refer to in Mathematics, as Non-Linear Complexity variables.

Per your own statement, if anyone else walks up to the table during the above statement, the entire necessity of the Casino “arranging the cards” (which in actuality, they’d be allowed to do) falls apart.

Regardless, Blackjack is so stupidly simple to beat if you have the correct math … even using negative progression as part of your overall strategy (and where the above article falls apart … is the author doesn’t account for other strategy specifics … see the comment below)

Yes! I know dealer and confirms shufflers stack deck against card counters, but I have ran into the problems you have mentioned. Once they realize what you are doing you will lose.

I have played live online blackjack and after 4 days I kept losing, so to confirm my theory I joined with another name and same thing after 4 days I kept losing.

Their cheating isn’t limited to the circumstances you describe. And yes, it’s ostensibly idiocy for them to risk their licenses but they get away with it so apparently that is an insufficient deterrent or the gaming commission is such that the casinos aren’t actually taking a risk… and you’re seven consecutive losses at Blackjack is nothing compared to my 22 consecutive losses at Baccarat… 3 am… I was alone staring down about four pit people

I’ve noticed the same thing as Benjamin. The cards are coming “pre packed”. Can’t help but wonder if there is a certain mathematically proven way to stack the deck. When you arrive to the tables in Vegas the cards are splayed out in a “display” kind of way.

Pay attention now: YOU NEVER SEE THEM GET SHUFFLED IN FRONT OF YOU ON A NEW DECK.

I walked up to an empty table at MANDALAY BAY , cashed 2 grand in chips , asked the dealer or to shuffle the cards in front of me. The nasty little Vietnamese bitch refused got major rude attitude and yelled the cards were shuffled already why you want shuffle again i no unda stand nobody ask that why you saying shuffle …. On and on and on … I called over pit boss and told him my play isn’t starting until I see the cards are shuffled.

Pit boss sided with dealer and said she already shuffled them she doesn’t have to show you she shuffled.

I said NO and left they demanded i color out my chips (change green 25s to black 100s) I said i don’t HAVE to color up and stormed out.

I only play large sports betting or tiny roulette amounts now – or video black jack. I will not play reg blackjack on strip unless it’s only for a small stop loss or there is a hot single girl sitting alone. I strongly suspect the casinos are pre shuffling the decks or doing something nefarious – because the difference in losses between the strip and downtown is night and day.

It’s COMMON for me lose 4, 5 , 10 hands in a row at MGM and Ceasers properties – COMMON … I will literally sit down and lose money AND i always look for tables with nobody there so there always a new deck and i always lose ….. It’s not probable and other people are saying the same thing. I’m not a card counter i just really hate playing with other people (strangers) since I’m not there for the fake social hour hello goodbye I’ll never see you again in my life kind if thing – I’m there to win money. Again:

1) Strip Properties Only

2) MGM and Caesars Only

3) Brand new deck only

I didn’t realize they were not shuffling in front of me until I noticed the cards were all splayed out on the tables for display.

rarely has this happened downtown. Whenever i play Cortez it’s always ups and downs and cortez ALWAYS shuffles in front of you by hand with the original blackjack rules.

I 100% agree with Benjamin something is not right with Black Jack on the strip

And another thing .. Fuck these dealers. Most of them are “nice” enough but cannot even speak correct English !! Vegas is importing cheap labor to cut out the job market and profit on the backs for poor 3rd world and developing H1B1s who are in a new country far from home and Scared to speak up.

That’s how these people like Sheldon Alsdale and Wynn – want the world to be. Remember the song from the famous goth band Nine Inch Nails:

“god money I’ll do anything for you … god money just tell me what you want me too ….. god money dances on the backs of the bruised … god moneys not one to choose”

NONE of the old timers can tell me hey have not noticed these huge and obvious changes over the past 50 years which has ruined the entire Vegas experience. everything from the class of employees, imported dealers , rude pit bosses , asshole security staff , sky high prices and the worst – a non stop roller coaster of nickel and diming .

.. I will take Vegas 50 years ago over Vegas today any day.

Tell me i am making this up .

I know this is an old post. Ive read some of these and am curious. Through observation and the probability somehow favoring the dealer. And I don’t mean by percent alone as in the amount of decks and the hitting or standing on soft 17. I mean it’s like those casinos have a special witch doctor looming behind the scenes. The spread of cards sometimes seems astronomically improbable, such as last night where the dealer gets 4 aces in a row with kings. Now this is a reputable casino of course. I digress. So my question is. I’ve read the charts and such for increasing win percentages by using accurate basic strategy. But wait. What planet did those stats come from? If I stand on a dealers up card of 2-6 with a 14, 15, 16 for example, I almost always lose and dealer won’t bust. And he beats me with some ridiculous number either just one more or by far. So when sometimes I hit on a 13 and a 5 or 6 up card I’m of course much heckled and chastised by the players who think they know how to really play (but they all bet like random bobbleheads). And FYI off topic I despise not many things but hindsight strategists I call them.

“shoulda hit 3 rounds ago… ” I say.. “Shoulda told me what card I had then coming next and what card I have coming now.” lol But for the most part. Not trusting the dealers cards. I’ve won. My problem is too my lack of patience and maintaining and ultimately betting more than I think not commanding my brain to think of the next dealer streak. But I also play two hands as it seems more safe , until a loss streak. I’m new mostly and don’t mean to discount anything of this or any post and or anyone’s skill, knowledge and professionalism of the game. I simply just can’t get down counting because it’s just too fast (even though I play piano lightning fast) and with the HiLo numbers and running and true count, I’ll just say I couldn’t add dived and solve for X like that. Especially quick dealers. Maybe I’ll find a slow one. Lol Any additional advice at this point would be helpful. Mostly just want to bet more safely and practically. I understand your post above about the 2500. I did read it lol I’m just more asking for anyones advice on what they might use personally and what works and hasn’t worked. . Forgive the long post. Thank you all.

Benjamin CA

You have a 1/20 prob. of being dealt a blackjack w only a 1/25 chance (assuming 8-deck shoe) of having your blackjack pushed. Suppose you are playing a 13 loss Martingale, then that means you will have 200 strings that end with you getting a blackjack and making $10 plus your bet on the string. Simply counting $10 profit on every string ending in a loss and multiplying by the number of times you can expect to win and then subtracting by the total lost win you do run through the string is incorrect. Perhaps, you can figure the math using martingale relative to expected losses while figuring in the mathematics of a 3/2 payoff on the probability of each length string ended by a blackjack?

You’re right. I ignored blackjacks in this simplified comparison, just like I ignored doubles and splits. The math gets quite a bit messier, although I suppose it would fairly easy to account for only the blackjacks. The conclusion is however unavoidable. In blackjack, your expected loss is the total of your bets times the house edge, unless you vary your bets based on the deck composition instead of some scheme based on a string of wins or losses. No progression can change that fact. Feel free to work it out in laborious detail if that interests you. It doesn’t interest me.

You also didn’t factor in the 3/2 payoff on a blackjack that can be the streak ender. If you bet, say $640 after your 6th loss in a row and hit a blackjack, you make $330, not $10. Also, since double-downs and most splits are in your favor, while you certainly need a much bigger bankroll for the possibility that you’ll get deal an 11 when the dealer has a 6, those hands also put the odds in your favor when you have the most money on the table.

Question and Observation regarding raising your bet when the count is a negative 7 to 13 true negative of 4′ Has anyone run simulations on this.

So far , 100 hands only, it works almost as well as a true positive count of 4′. If Simulation agree, Why?

And when bets are only the true count 1 or greater than 1?

Positive true counts don’t affect the win percentage as much as you probably think and hope. See this: https://www.blackjackincolor.com/truecount5.htm