- Most Effective Card Counting System Chart
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Gamblers have been fascinated by card counting ever since Edward Thorp shared his secrets through the 1962 book Beat the Dealer. This advantage-play technique has only gained further popularity over the years thanks to the MIT Blackjack Team’s efforts.
Card counting is an exciting prospect because you can win lots of money. Both Thorp and the MIT Blackjack Team are prime examples of this.
By doing this, these counts allow you to play without a ‘true count’ conversion which many people find to be the hardest part of balanced counting systems to learn. Yet, these are still quite effective in 4-, 6- or 8-deck games and the fact is, most. The trick to most card counting methods is categorizing the cards into two types. High cards; Low cards; The reason card counting works — or at least the biggest part of it — is the increased probability of being dealt a blackjack when the deck has lots of high cards left in it versus low cards. Counting Card Systems. Regardless of which system you use however, and how effective it is, proper implementation of blackjack card counting systems relies on the realization that the house will always have an advantage over the players in virtually every game at USA Casinos.With the proper use of blackjack card counting systems. Here are a few reasons why card counting is not dead. Card Counting Still Works in Live Casinos. Electronic shuffling machines. Changes to the games rules. All of these are measures taken by live casinos over the last thirty years to stop card counters, and some of them have been effective. In the Knockout Card Counting (KO Count) system, as explained in the book Knock Out Blackjack, all card values are the same as in the Hi Low system, except for the value of the 7. In this system, the seven is considered a low card and thus a positive value—unlike the Hi Low system where it is a neutral card.
But before you start earning big profits like these blackjack legends, you must first choose a counting system.
This is easier said than done, given that there are over one hundred card systems floating around. These strategies differ based on what kind of advantage they give you and how complicated they are.
Obviously, you don’t want to jump into the most difficult system if you’re new to card counting. Instead, a beginner-friendly strategy will help you learn this process with the minimum degree of difficulty.
Keep reading as I cover three of the easiest blackjack card counting systems for beginners. But first, let’s look at the basics behind counting cards.
What’s the General Basis Behind Card Counting?
Many gamblers like blackjack because it offers a chance to use extensive strategy to improve your winnings. Depending on the rules, you can lower the blackjack house edge to under 1% with good strategy.
But the key here is that the casino still has an advantage over those who use basic blackjack strategy. This is where card counting comes into play, because this strategy gives you the advantage and can lead to long-term profits.
The underlying goal of card counting is to find out when the shoe is rich in aces and tens. The reason is twofold:
1 – You have a better chance of getting a natural blackjack payout.
El rio casino. 2 – Your odds of quality double-down opportunities also improve.
Another positive product of card counting is that you can find out when the deck is high in low cards (2 – 6) and bet less.
Low cards improve the dealer’s odds of winning. The reason is because the dealer’s score must reach 17, and they have less chance of busting when there are more low cards available.
By keeping track of card values as they’re dealt, you can boost your chances of winning and potentially making big profits.
Of course, tracking cards in a bustling casino environment is easier said than done. This is especially the case when considering that modern blackjack games have six to eight decks in the shoe.
But just about anybody can successfully count cards with enough practice. And you can easily practice by using card counting trainers on websites.
Other ways to practice include dealing shoes to yourself while counting cards, or having a friend deal to you. I like the latter method because it simulates your friend being the dealer and you as the player.
Spreading Bets
Simply counting cards is only part of the equation to making money. You also have to bet more when the count is in your favor to reap profits.
This is referred to as “spreading bets” in card counting. The idea is to start at the table minimum, then increase your wager as the count goes in your favor.
The bet spread occurs between your smallest and largest bets.
Some systems have their own method for how you spread wagers during a favorable count. But the gist is that you must raise your wagers when the deck is in your favor, so you earn more money.
This requires a balancing act because wagering too much will attract the suspicion of casino staff members and potentially get you banned.
Experience and fully knowing your chosen card counting method will help you determine how to best spread bets when you have a favorable count.
3 Systems that Beginning Card Counters should Use
1 – OPP System
I begin with the OPP card counting system since it’s extremely easy to use. In fact, virtually any new blackjack player can quickly learn and understand this system.
The main thing you need to do with the OPP strategy is track low cards. You add one to your count whenever a low card is dealt and subtract one for every hand in play (including the dealer).
Low cards being dealt works to your advantage, because this means there are fewer cards that’ll help the dealer.
Pair of dice games. Here’s an example of how to use this strategy:
- You start the shoe with a +6 count.
- You subtract one (- 1) for every player dealt into the hand, including the dealer.
- You add one (+1) for every low card that’s dealt.
- The goal is to bet more when the count goes higher into the positives.
- You want to increase your wager when the count reaches +12 or +14.
Here’s an example of OPP in action:
- A new shoe is being dealt.
- Your count starts at +6.
- There are four players, plus the dealer (subtract 5 = count at +1).
- Four low cards come out during the hand (Add 4 = count at +5).
- Your next round will begin at +5 (minus number of players in the hand).
This is referred to as an “unbalanced” counting system because the count doesn’t end at zero when the shoe has been dealt. Going further, you don’t have to account for how many decks are in the shoe with an unbalanced system.
This differs from the Hi-Lo strategy (discussed next), where you must factor in the remaining decks to determine your “true count.”
Another great thing about the OPP system is that you don’t have to track high cards (A to 10) or neutral cards (7 to 9). Instead, you simply count low cards and subtract the number of players/dealer at the start of each hand.
The only downside to OPP’s simplicity is that it’s less accurate than the other systems I’m going to cover. Nevertheless, it can give you an edge on the casino.
2 – Knockout (KO) System
The KO system is more complicated than OPP because you also need to track high and neutral cards. Another difference is that the low card category includes 7.
Here are the different card groups and how you assign them values:
- Low cards (2 to 7) = +1
- Neutral cards (8 to 9) = 0
- High cards (A to 10) = – 1
You need to track every card with this system – not just the low ones like with OPP.
Another difference between KO and OPP is that there’s no preset starting count (+6) at the beginning of a shoe. Instead, your count begins as soon as the first card of a shoe is dealt.
Here’s an example of the KO in play:
- Ace is dealt (count at – 1).
- 2 is dealt (count at 0).
- 7 is dealt (count at +1).
- 8 is dealt (count at +1).
- 4 is dealt (count at +2).
- Jack is dealt (count at +1).
- Count = +1.
This is another unbalanced system because there are a greater number of low cards than high cards. Therefore, you don’t need to convert to a true count with KO.
The lack of a true count makes KO simpler than the Hi-Lo system that I’ll cover next.
Another benefit of KO is that it’s more accurate than OPP. This gives you the perfect blend of simplicity and accuracy.
But this also leads to downsides, including that KO is more complicated than OPP and less accurate than Hi-Lo.
3 – Hi-Lo System
This card counting strategy is similar to KO, because you need to track low, neutral, and high cards. But the two key differences are that 7 is neutral, and you need to differentiate between a running and true count.
Here’s how you assign values to each group of cards:
- Low cards (2 to 6) = +1
- Neutral cards (7 to 9) = 0
- High cards (A to 10) = – 1
The Hi-Lo is what’s known as a “balanced system,” because the count will always reach zero by the end of the shoe.
The reason why Hi-Lo is balanced and KO isn’t is due to the 7 being neutral. This means that an equal number of cards are high (5) and low (5) with the Hi-Lo strategy.
Given that Hi-Lo is balanced, you also have to account for the number of decks remaining in the shoe. Going further, you must convert your running count into a true count.
Here’s an example:
- Your running count is +8.
- There are four decks remaining in the shoe.
- This makes your true count +2 (8/2).
You use your true count to determine how much you’ll spread your bet by. Here are the guidelines for spreading your wagers with the Hi-Lo:
1 – Determine a unit size (e.g., $25).
2 – Figure out your true count (e.g., +4).
3 – Subtract one from the true count (4 – 1 = 3).
4 – Multiply this number by your unit size (25 x 3 = 75).
5 – Your bet should be three units, or $75.
The Hi-Lo is definitely tougher than KO and OPP due to the added steps. But from an overall perspective, Hi-Lo is relatively easy when compared to the dozens of other counting systems available.
Other Easy Card Counting Systems for Beginners
Ace/Five Count System
Ace/Five is a simple strategy that only requires keeping track of 5-value cards and aces. You add one for every 5 that’s dealt, and subtract one for every ace.
The goal is to get a positive count of +2 or higher. You double your bets at this point, while only wagering the table minimum when the count is +1 or lower.
Here’s an example:
- Ace is dealt (count at – 1).
- 2 is dealt (count at – 1).
- 5 is dealt (count at 0).
- 9 is dealt (count at 0).
- 5 is dealt (count at +1).
- Count = +1
Given that Ace/Five only requires you to track two card values, it’s similar to OPP in terms of simplicity. But like OPP, this strategy isn’t as effective as some of the other systems discussed here.
But if you’re just a casual blackjack player who wants to gain a bit more of an edge, then I recommend trying Ace/Five.
Red Seven System
Red Seven was developed by blackjack legend and card counter extraordinaire Arnold Snyder. This system works similar to KO and Hi-Lo, except that there’s a special distinction made for red and black 7s.
Here are the basics of Red Seven:
- 2 to 6 = +1
- Red 7 = +1
- Black 7 = 0
- 8 to 9 = 0
- A to 10 = – 1
You can actually switch the counts for the red and black seven – it makes no difference. But the key is that you do make a distinction between the colors.
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Snyder did this so he could create an imbalanced system that was easy to use with no true count involved. But he also wanted to make Red Seven more accurate than KO (black 7s being neutral).
Red Seven is great if you hate converting your running count to a true count, but still want the accuracy of a balanced system.
The downside to this strategy is that it’s almost as complicated as the Hi-Lo, yet you only get 80% of the same accuracy.
Ten Count System
Edward Thorp introduced the Ten Count System when he wrote Beat the Dealer in the sixties. Although not as accurate as modern strategies like Hi-Lo, the Ten Count gets the job done in certain situations.
The catch, though, is that Ten Count is designed specifically for single-deck blackjack games. And unfortunately, quality single-deck blackjack with 3:2 natural payouts are a rarity today.
Nevertheless, Ten Count is a good system to use when acclimating yourself to card counting. Here are the basics of this strategy:
- A to 9 = +4
- J to K = – 9
This is noticeably different from the three systems that I covered above. But Ten Count is still relatively easy for beginners to use.
Here’s an example of how you can implement the strategy:
- 5 is dealt (count at +4).
- 6 is dealt (count at +8).
- K is dealt (count at -1).
- 8 is dealt (count at +3).
- 3 is dealt (count at +7).
- Count = +7
Unlike some systems, Ten Count doesn’t have a defined amount where you begin increasing your bet by X amount. Instead, Thorp leaves it up to players to decide how much to increase or lower their bets by.
I suggest spreading your bets by five units or more when you have a favorable count of at least +2.
The advantage of Thorp’s system is that it’s easy. You only have to track two card groups and use two numbers for the count.
The downside is that this strategy is poor for multi-deck games.
All blackjack tables featured single-deck games in Thorp’s early blackjack days. Therefore, he didn’t account for the effect of removing aces from a six-deck shoe.
Lumping aces into the low card group is fine in single-deck blackjack because it doesn’t have as big of an impact. But this miscalculation plays a bigger role in the four-, six-, and eight-deck games of today.
Again, Ten Count is fine for practicing card counting. But it doesn’t apply to the modern blackjack world.
Is Card Counting Illegal?
A popular misconception is that card counting is illegal. This has been fueled by Hollywood movies like 21, where card counters act like their lives depend on not being detected by the casino.
The truth is that counting cards isn’t illegal. But casinos may ban you from their establishment if they think you’re a successful counter.
The easiest way for casinos to root out a card counter is by their betting patterns. For example, moving from a $10 minimum bet to $500 later in the shoe looks very suspicious.
Some players camouflage their counting efforts through the following ways:
- Make an occasional strategy mistake.
- Dress to blend in.
- Act like they increase and lower bets based on superstitions.
It also helps to research casinos to find out how tolerant they are towards card counters. Some casinos don’t sweat counters as badly as others.
Do You Have to Be a Genius to Count Cards?
The 1988 film Rain Man created the perception that you need to be a mathematical genius to successfully count cards. But as you may have gathered from these simple systems we covered above, this isn’t accurate.
Raymond Babbitt (Dustin Hoffman) kept track of every single card while counting in Rain Man. But you only need to keep a running tally of the card values to give yourself an edge.
As I mentioned earlier, nearly anybody can learn to count cards – especially with the systems covered above. Furthermore, you don’t need to be a genius to keep an accurate count.
Conclusion
The nice thing about card counting is that it’s not as difficult as most players think. You can quickly learn one of the systems that I discussed above and use it to give yourself an advantage.
How big of an edge you gain depends upon the exact strategy you choose. My favorite is the Hi-Lo, due to its combination of simplicity and accuracy.
But you may ultimately choose a system like OPP, KO, or Ace/Five because you just want an easy way to count cards.
Whatever the case may be, I highly suggest that you use one of the strategies covered here to give yourself an easy introduction to the card counting world.
Thunk
First off, the Martingale system does not work. I intend to prove to you, however, that by tweaking the strategy a bit, the 'optimum martingale' as I call it can be used to mask card-counting detectors employed by the casinos.
The Martingale Betting System- A failure by itself. It requires the player to double his/her bet every time she looses, covering previous loses incurred on the losing streak and returning to the player an amount equal to their lowest common bet. It is not efficient because when you inevitable hit a major loosing streak, you risk running your bankroll dry or reaching the maximum bet and not being able to double anymore, all for one measly lowest bet in return.
I documented over 1,000 hands using this technique, taking into consideration every variable, playing with basic strategy, shuffling after each hand, and purposely leaving out the variable of card counting to ensure there was only one variable. I ran the losing streaks out until I had either won, or ran my bankroll dry. Then, I went back and calculated what would have happened had I decided to cut my loses, reset my bet to the original, and continued playing after loosing 8 hands in a row, 7 hands in a row, 6 hands in a row, and so on until I was theoretically flat betting every hand. Most losing streaks did not exceed beyond 8 hands, but if they did, I calculated for that too.
I found that, beyond a shadow of a doubt, reseting your bet to the original low was most effective when you reset after a three-hand losing streak. Whereas reseting after any other number of lost hands either lost money in the scenario, or gained very little for the amount of time it took, reseting at three consistently wielded a positive average of roughly $41 per 70 hands played, using a $1 lowest common bet. At the same time, my bankroll never went more than $23 below it's original value, and steadily increased after that. After testing over 1,000 hands, this is quite definitely the optimum time to reset your bet using the martingale system.
This is a major bonus to Card-Counters, because it fools computer technology commonly employed to catch counters, and it also masks your efforts to the dealer (the most direct link between you and the pit-boss). Most card counters will flat-bet a small amount when the count is low, and then slam their bets up high when the count is in their favor. This is easily noticed by dealers and by computers, which use RFID sensors to keep track of the bets on the table, and another technology to keep count in the game using almost every count system imaginable. If your bet or cardplay matches what the computer has analyzed as close enough to consider counting, you got a one-way ticket to the next casino. If you employ the optimum martingale system instead of flat-betting when the count is low, it will mask your efforts to the dealer especially, and to an extent with the computers. It allows the counter to not risk much money, while also making the swings in his bets not as noticeable. I find it most effective to use the Optimum Martingale, even as the count climbs, but instead of reseting my bet at three, I will continue to climb my bets up, win or loose, until the count begins to decline. By sticking to the style of doubling your bets when the count is high, even if you win or lose, you stray from the average card counter which the computers are looking for while also retaining the ability to place large bets when the count is high and decrease them as it recedes.
I did this all by hand, using ledger paper, taking into consideration these variables: L.C.D. bet, starting bankroll, ending bankroll, starting time, ending time, Bank Roll amount, Hand number, Players Cards, Dealers Up Card, Suggested strategy action, actual action, win/loss/push/bust/dealer busts. If you have a computer to simulate this, with special attention to when to reset your bets on a losing streak, and would like to add on, please do! Otherwise, try it out! Even if you can't count cards it is a fun system and is slightly more effective than it's predecessor. However, I wouldn't play it for money if you intend on using it by itself. After all, betting strategies are not useless, but they're not reccomended by themselves.
The Martingale Betting System- A failure by itself. It requires the player to double his/her bet every time she looses, covering previous loses incurred on the losing streak and returning to the player an amount equal to their lowest common bet. It is not efficient because when you inevitable hit a major loosing streak, you risk running your bankroll dry or reaching the maximum bet and not being able to double anymore, all for one measly lowest bet in return.
I documented over 1,000 hands using this technique, taking into consideration every variable, playing with basic strategy, shuffling after each hand, and purposely leaving out the variable of card counting to ensure there was only one variable. I ran the losing streaks out until I had either won, or ran my bankroll dry. Then, I went back and calculated what would have happened had I decided to cut my loses, reset my bet to the original, and continued playing after loosing 8 hands in a row, 7 hands in a row, 6 hands in a row, and so on until I was theoretically flat betting every hand. Most losing streaks did not exceed beyond 8 hands, but if they did, I calculated for that too.
I found that, beyond a shadow of a doubt, reseting your bet to the original low was most effective when you reset after a three-hand losing streak. Whereas reseting after any other number of lost hands either lost money in the scenario, or gained very little for the amount of time it took, reseting at three consistently wielded a positive average of roughly $41 per 70 hands played, using a $1 lowest common bet. At the same time, my bankroll never went more than $23 below it's original value, and steadily increased after that. After testing over 1,000 hands, this is quite definitely the optimum time to reset your bet using the martingale system.
This is a major bonus to Card-Counters, because it fools computer technology commonly employed to catch counters, and it also masks your efforts to the dealer (the most direct link between you and the pit-boss). Most card counters will flat-bet a small amount when the count is low, and then slam their bets up high when the count is in their favor. This is easily noticed by dealers and by computers, which use RFID sensors to keep track of the bets on the table, and another technology to keep count in the game using almost every count system imaginable. If your bet or cardplay matches what the computer has analyzed as close enough to consider counting, you got a one-way ticket to the next casino. If you employ the optimum martingale system instead of flat-betting when the count is low, it will mask your efforts to the dealer especially, and to an extent with the computers. It allows the counter to not risk much money, while also making the swings in his bets not as noticeable. I find it most effective to use the Optimum Martingale, even as the count climbs, but instead of reseting my bet at three, I will continue to climb my bets up, win or loose, until the count begins to decline. By sticking to the style of doubling your bets when the count is high, even if you win or lose, you stray from the average card counter which the computers are looking for while also retaining the ability to place large bets when the count is high and decrease them as it recedes.
I did this all by hand, using ledger paper, taking into consideration these variables: L.C.D. bet, starting bankroll, ending bankroll, starting time, ending time, Bank Roll amount, Hand number, Players Cards, Dealers Up Card, Suggested strategy action, actual action, win/loss/push/bust/dealer busts. If you have a computer to simulate this, with special attention to when to reset your bets on a losing streak, and would like to add on, please do! Otherwise, try it out! Even if you can't count cards it is a fun system and is slightly more effective than it's predecessor. However, I wouldn't play it for money if you intend on using it by itself. After all, betting strategies are not useless, but they're not reccomended by themselves.
DeMango
Very interesting post - Thanks!When a rock is thrown into a pack of dogs, the one that yells the loudest is the one who got hit.
am19psu
One thousand hands in nowhere near a robust enough sample to draw the sweeping conclusions you are making. Hint: calculate your standard error.
FleaStiff
Most Effective Card Counting System Online
>This is easily noticed by dealers and by computers, which use RFID sensors to keep track of the bets on the table ..
I would think that extreme bet variation would indeed bring instant attention even before anyone in the casino started to verify the count when it was taking place.
I think those RFID tags inside the chips with sensors at the table's betting circles do actually exist but I doubt it exists in anywhere near as many casinos as people seem to assume. Its a bit pricey to have such systems and I rather doubt it catches all that much in the way of bet capping or card counting.
If you go from one green chip to three black chips, you are going to be noticed. If surveillance plays back the tape and counts down the deck to the time at which you suddenly started betting big they will be able to confirm their worst, but still foolish, fears: there is a card counter in their midst.
I don't see how any other aspects to the play are going to disabuse them of this notion. If you revert to a lower level of play after three losses, you are still a card counter who has come to their attention.
I would think that extreme bet variation would indeed bring instant attention even before anyone in the casino started to verify the count when it was taking place.
I think those RFID tags inside the chips with sensors at the table's betting circles do actually exist but I doubt it exists in anywhere near as many casinos as people seem to assume. Its a bit pricey to have such systems and I rather doubt it catches all that much in the way of bet capping or card counting.
If you go from one green chip to three black chips, you are going to be noticed. If surveillance plays back the tape and counts down the deck to the time at which you suddenly started betting big they will be able to confirm their worst, but still foolish, fears: there is a card counter in their midst.
I don't see how any other aspects to the play are going to disabuse them of this notion. If you revert to a lower level of play after three losses, you are still a card counter who has come to their attention.
Thunk
![System System](https://images-na.ssl-images-amazon.com/images/I/819O90p1kEL._AC_UL200_SR200,200_.jpg)
I agree about the chips, they are rare outside of Vegas. Also, not a lot of casinos keep track of card play electronically. It basically boils down to fooling the dealer. Think of it like you're an entire blackjack team and you're 'Wonging' your own table, the benefit being there is no obvious flat-betters keeping count or some 'big better' stepping in only when the count is high. Externally you appear to be relying on a betting system, in reality you are not.
As far as the 'reset' aspect, the three-loss rule doesn't use any information from the count; it's played using solely basic strategy while keeping track of the count, so you're still not playing your hands like a counter, just someone with a strategy chart. Only when the count is extremely high or low do you begin to change your gameplay according to the count, and double your bets even if you win. I didn't explain that very well :p
As far as the 'reset' aspect, the three-loss rule doesn't use any information from the count; it's played using solely basic strategy while keeping track of the count, so you're still not playing your hands like a counter, just someone with a strategy chart. Only when the count is extremely high or low do you begin to change your gameplay according to the count, and double your bets even if you win. I didn't explain that very well :p
Thunk
I used maximum likelihood to figure this out. Without knowing the true value of the standard deviation, which is impossible to predict, standard error is impossible to calculate and will only be an estimate, nothing I would take into consideration at the table. Standard Error in a game like blackjack, to me, is a fallacy.
I am a Statistical Analyst which is what got me into BlackJack in the first place, and I am very confident in my accuracy. I have taken this strategy to Biloxi on six occasions now and have banked $3,420 in those six trips.
I am a Statistical Analyst which is what got me into BlackJack in the first place, and I am very confident in my accuracy. I have taken this strategy to Biloxi on six occasions now and have banked $3,420 in those six trips.
pecogg
I used maximum likelihood to figure this out. Without knowing the true value of the standard deviation, which is impossible to predict, standard error is impossible to calculate and will only be an estimate, nothing I would take into consideration at the table. Standard Error in a game like blackjack, to me, is a fallacy.
I am a Statistical Analyst which is what got me into BlackJack in the first place, and I am very confident in my accuracy. I have taken this strategy to Biloxi on six occasions now and have banked $3,420 in those six trips.
I am a Statistical Analyst which is what got me into BlackJack in the first place, and I am very confident in my accuracy. I have taken this strategy to Biloxi on six occasions now and have banked $3,420 in those six trips.
I've always wondered, when using the Martingale (which I haven't before), what does one do when he has lost several hands in a row, has much more money out on the table, and then is faced with a double-down or split situation. In other words, after you've lost several hands and have doubled and then redoubled your bet accordingly, what is the proper action when faced with a double-down or split hand? Do you double-down or split per basic strategy and risk additional monies (and gains), or should you simply hit or remain with one hand?
Most Effective Card Counting System Definition
Thunk
This is a tricky question, and also why it is a good idea to stop at three. That way, you can never loose too much even if you do double down your third bet and lose again. As a rule of thumb, I don't deviate from basic strategy until the count is high or low enough to make a profound impact. However, if I am faced with a double down or split situation, and I have a lot of my bankroll on the table, I'll use information from the count to impact my decision. Don't do anything stupid, like not splitting eights against a six, or not doubling an eleven against a six, but for instance I would not double a 9 against an 8 if I was on my third loss, only on the first or second hand. There's simply not a high enough potential loss/potential gain ratio once you factor in the act of reseting your bets.
Remember: If you bet $10, lose, bet $20, then double and lose, you've lost $50 and your next bet has to be $60 to keep in pace. Some might prefer, once they get to that point, to just bet $50 and hope to merely cover loses before reseting.
Remember: If you bet $10, lose, bet $20, then double and lose, you've lost $50 and your next bet has to be $60 to keep in pace. Some might prefer, once they get to that point, to just bet $50 and hope to merely cover loses before reseting.
matilda
I used maximum likelihood to figure this out. Without knowing the true value of the standard deviation, which is impossible to predict, standard error is impossible to calculate and will only be an estimate, nothing I would take into consideration at the table. Standard Error in a game like blackjack, to me, is a fallacy.
I am a Statistical Analyst which is what got me into BlackJack in the first place, and I am very confident in my accuracy. I have taken this strategy to Biloxi on six occasions now and have banked $3,420 in those six trips.
I am a Statistical Analyst which is what got me into BlackJack in the first place, and I am very confident in my accuracy. I have taken this strategy to Biloxi on six occasions now and have banked $3,420 in those six trips.
Most Effective Card Counting System Based
1. You used maximum likiihood to figure what out? What are you estimating?2. Of course you would estimate the standard deviation, if you do not know it--this is basic statistical inference.
3. I do not wish to get too personal, but from you have written it is clear that you do not know basic, elementary statistics and yet you claim to be a 'statistical analyst'.
4. It appears that your conclusions are based on a sample of six and you have not used any statistical inference to reach your conclusions.
Thunk
I used maximum likelihood to figure out when to reset the losing streak, which is why I shuffled the deck after each hand to ensure an unbiased pool. The sample mean is of course the number of and values of the cards themselves, and is not an estimate. The estimate in this case was the sample variance like you said. I used this equation to determine maximum likelihood, only after I had proved it in principle to myself first. I chose not to use average log-likelihood and opted for the equation below, which is more geared towards statistic probabilities (statistics I had already gathered in my principle-proving session)
........................n.....
L(0|x1,..,xn)=f(x1,x2,..,xn|0)= II f(xi|0). (I apologize for my lack of accurate characters but you get the equation)
.......................i+1.....
If it appears there is no statistical inference, it's because the average blackjack player doesn't need to know all this and I don't really want to type it out. I don't feel the need to prove my understanding of statistics to anyone by confusing them into submission. This is a forum, not a classroom, and egos don't belong in mathematics. We're dorks.
........................n.....
L(0|x1,..,xn)=f(x1,x2,..,xn|0)= II f(xi|0). (I apologize for my lack of accurate characters but you get the equation)
.......................i+1.....
If it appears there is no statistical inference, it's because the average blackjack player doesn't need to know all this and I don't really want to type it out. I don't feel the need to prove my understanding of statistics to anyone by confusing them into submission. This is a forum, not a classroom, and egos don't belong in mathematics. We're dorks.