Blackjack Series: The Winning Move - Caleb Jones

Blackjack is one of my favorite hobbies. In an effort many years ago to monetize all of my hobbies, blackjack is also a source of net income for me, albeit a small one. I track my results on spreadsheets, and since figuring out a regular system, I win at blackjack more often than I lose. I don’t win much more often than I lose, but my winnings are a net positive over the losses, over time.

This is the first of many blog posts where I will talk about what I do, what I don’t do, why 99% of people lose at blackjack in the long run, including the computer models.

I’m looking at my current blackjack spreadsheet right now, and since the start of this month, I’ve played blackjack four times with these results:

Feb 1st
Starting Pot: $500
Base Bet: $25
Time played: 32 minutes
Ending Pot: $725
Result: Won $225

Feb 5th
Starting Pot: $500
Base Bet: $25
Time played: 27 minutes
Ending Pot: $800
Result: Won $300

Feb 11th
Starting Pot: $500
Base Bet: $25
Time played: 28 minutes
Ending Pot: $605
Result: Won $105

Feb 18th
Starting Pot: $500
Base Bet: $25
Time played: 55 minutes
Ending Pot: $263
Result: Lost $237

If you do the math, I’ve made a net income of $393 from playing blackjack this month so far. Not many just-for-fun hobbies make a guy $393, thus my love of playing this game.

You might be asking, “That’s fine for February, but what about all of your wins and losses for years before that?” I will repeat that since developing a system for playing this game back in late 2008, if you add up everything I’ve done (the wins, losses, and break evens) I’ve won more money at blackjack than I’ve lost. The only thing I’m not counting towards this total is when I purposely deviate from my system because I’m with friends and screwing around while playing blackjack just for shits and giggles with no intention of actually winning. But when I’m on-system, and I almost always am, I win more than I lose, though not by much.

February, so far anyway, has been pretty typical of my results. A few wins, some big some small, and one big loss, all of which still equals a small but nice net profit.

Why Do I Win?

There are several reasons I’m able to do this and all of them are important, but I’ll give you what I think is the most important reason, the “winning move.” It’s simply this: As soon as you start winning, stop playing, cash in your chips, and go home. 

That’s really it. When I start with a pot of $500, and my balance starts shooting up a little past that, like to $700 or $800, I start paying very close attention to any losing hands. Once I’m up, if I lose two hands in a row, I immediately stop, cash in my chips, leave the building, get in my car, and go home.

Quitting as soon as you start winning requires a decent amount of emotional control, something most people don’t have. I have seen thousands of blackjack players over the years and virtually no one does this. They either play completely wrong, immediately start losing, and keep playing until their balance is zero (this is the most common scenario), or they start winning, get really excited, keep playing (often greatly raising their bets when they shouldn’t), and eventually lose their winnings and stop playing when they’re below the balance they started with.

If you sit down and play blackjack for a long time, you will lose. That’s how the odds work, and that’s why casinos make so much money. (I would love to own one.) Therefore, if you want to win, the goal is to NOT play blackjack for a very long time, and buzz out of there as soon as you start winning a little. Do that every time you play, and assuming you play correctly, you’ll win more often than you lose (edited addendum: …assuming you play exactly the way I play, which involves very careful casino and table selection along with some limited card counting, all of which I will describe in later posts). You’ll notice that I often play for just 30 minutes. This is why. You’ll also notice that my longest February playing session resulted in a loss instead of a win. That’s not a coincidence.

This explains why mathematical or computer models always show that it’s “impossible” to win at blackjack over time. Correct, it’s not. The computer under these models plays and plays and plays until the odds grind it into powder. Fortunately I’m not a computer, so I don’t do this. Unlike the computer, I play for a very short period of time, and as soon as I start winning, I stop and buzz out of the casino a winner.

As I said, this all assumes you’re playing blackjack correctly, and about 95% of people I watch do it incorrectly. I’ll be discussing exactly how I play in future blog posts.

Category: Fun

34 Comments on “Blackjack Series: The Winning Move

  1. No, at least not Hi-Low. I only do ace counting. And I only play single or double deck, which makes this easier. Even then I sometimes screw it up though.

    I know how to count cards, but it’s extremely difficult (more so than people think) unless you’re constantly practicing all the time or have a naturally superhuman memory. And since I keep winning I haven’t bothered to focus on it.

    That being said, this year I’m going to attend a few bootcamps where they drill the card counting into you. We’ll see how that goes.

  2. Very good stuff BD. I’ll be interested to learn what sort of system you implement to increase your odds of winning.

    What other hobbies have you tried to monetize?

  3. I’ll be interested to learn what sort of system you implement to increase your odds of winning.

    There’s a lot of pieces to it. I’ll be blogging about it all (over time).

    What other hobbies have you tried to monetize?

    – Fantasy fiction writing (putting a business twist on it and using it to market my consulting). The best example of this is Sampson and the Wizard, available for free here.

    – Travel, including international travel (doing seminars, consulting, or coaching in any city I decide to visit for fun).

    – Movies (selling used DVDs and Blu-rays).

    – When I was younger: computers (many ways) and martial arts (selling energy drinks at tournaments and practices).

    There’s a few others I’m forgetting too. There’s no reason your hobbies can’t make you at least a little money.

  4. “This explains why mathematical or computer models always show that it’s “impossible” to win at blackjack over time. Correct, it’s not. The computer under these models plays and plays and plays until the odds grind it into powder. Fortunately I’m not a computer, so I don’t do this. Unlike the computer, I play for a very short period of time, and as soon as I start winning, I stop and buzz out of the casino a winner.”

    The computer can be easily programmed to stop when it’s ahead. Do you think the average results would change?

    How does the number of hands played influence the results of the system? The computer shows that using the best mathematical system you lose a small percent of the starting bet on each hand played, on average. It really does not matter how you distribute the number of hands played. It doesn’t matter if you play 50 hands now and 50 a day later, a week later, or immediately afterwards. The computer can be programmed to make the best decision each hand, it does not tire. Since you are making a profit, you either act on more information than a computer can (using a better system) or you have not played enough for your results to be average (unlikely).

    What you are describing here is basically the gambler’s fallacy:

    “The gambler’s fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the mistaken belief that, if something happens more frequently than normal during some period, it will happen less frequently in the future, or that, if something happens less frequently than normal during some period, it will happen more frequently in the future (presumably as a means of balancing nature). ”

    http://en.wikipedia.org/wiki/Gambler%27s_fallacy

    There is no reason you should lose after winning unless you stop making the same decisions. Yes if you get emotional or tired you will make errors that will cost you even more than the best mathematical system.

    However, results are not to be argued over so I’m very interested in this series.

  5. The computer can be easily programmed to stop when it’s ahead. Do you think the average results would change?

    Yes, I do, based not only on my experience but on that of professional blackjack players who play blackjack for a living as a primary income source. Granted some of those these guys count cards, but many of them don’t, or don’t all the time, because if they did they’d get more easily banned from casinos and thus would lose their livelihoods.

    The computer shows that using the best mathematical system you lose a small percent of the starting bet on each hand played, on average.

    And that’s exactly why relying on these mathematical computer models doesn’t always work, because what you describe is precisely NOT how it works in the real world when you stop playing 100% of the time you’re ahead. As I mentioned in the post, that model you’re talking about is a computer playing hundreds if not thousands of hands, usually regardless of its running balance, and taking an average of all that. Mathematically it’s 100% correct, but in terms of reflecting what a person actually does in real life (assuming he does what I do) it paints a misleading picture.

    What you are describing here is basically the gambler’s fallacy

    No I’m not. I’m not stating one will consistently and/or statistically receive X results if he plays for 10 minutes and Y results if he plays for 2 hours (though I realize it sounds like I’m saying exactly that).

    Rather, I’m saying if you behave in ways the computer does not, you’ll receive different results than the computer is predicting. It’s that simple.

    Bottom line, there are only four possibilities here:

    1. I am playing differently than these computers play, thus getting (slightly) different results.

    or

    2. The computer/mathematical models are wrong in that they do not reflect the reality of how shuffled cards work in the physical world.

    or

    3. I’m lying about all of this and I actually lose at blackjack all the time but keep playing anyway because I’m stupid or insane.

    or

    4. For some magical reason I am the luckiest man on planet Earth. (As are the other men I know who do this on a regular basis, more frequently than me.)

    Number 3 isn’t true, and I don’t believe in number 4 or 2 (though I admit there’s a nonzero chance number 2 might be possible; this has been postulated by others but I don’t know how one proves or disproves this).

    That leaves number 1, unless you can think of another possibility I haven’t come up with.

  6. Wow. Greg is correct.

    The fact that you stop when you’re up doesn’t change anything. It doesn’t change the streak of cards you will get the next time you sit down.

    Mathematically speaking “sessions” don’t exist. Nothing is “reset” when you quit. Whether you leave the table or not have absolutely no impact on your win rate over the next X number of hands. The chances of you winning money on your next hand is 42%, whether you play that hand right now or you play it next saturday. And the same goes for the next hand. And the next. And the next.

    So 1) is not the case, I’m sorry.

    2) is very unlikely, and in either case this has nothing to do with your model. If this is the cause of you winning then it’s all because of luck. If you were to present a theory about how IRL shuffling is different from completely randomized shuffling, and explain how you exploit this at the table, that would be interesting. But again, that has nothing to do with the system you are presenting.

    3 is out the question as well, IMO.

    What you are missing when it comes to 4) is that even though the house always has an edge, the winnings and losses are distributed across a huge number of players, over a long period of time. Some players will have lost money and some will have won. That’s the nature of chance. Card counting aside, 42% of players will walk away from a session as winners. 49% will walk away as losers. (The remaining 7% broke even.)

    Taking this further, 7.5% of players will win money three sessions in a row, just like you did. So no, you are not the luckiest guy on earth. You were lucky, but not extremely so. Not as lucky as the 3% of players who have won money in 3 out of their last 4 sessions. (Which is of course not remotely close to being luckiest on earth”

    Also, even assuming you were alone at the table, speeding up the number of hands dealt per hour significantly, you’ve played at the most 500 hands of black jack. Do you realize how small that sample size is?

    I’m struggling to see how you don’t understand this. 🙂

  7. Go back and re-read my comment above. Slowly. Especially when I say:

    I’m not stating one will consistently and/or statistically receive X results if he plays for 10 minutes and Y results if he plays for 2 hours (though I realize it sounds like I’m saying exactly that).

    Rather, I’m saying if you behave in ways the computer does not, you’ll receive different results than the computer is predicting.

    Greg is indeed right, but I’m not saying what he (or you) says I’m saying.

  8. I did read that. In which way are you not behaving like a computer, that has an actual effect on the chances of coming out of a session on top?

    You can only win, lose or push on a given hand. The math dictate how often you will do either of them. You deciding when to take a break in between one hand and the next has no effect whatsoever on the likelihood of either outcome happening.

    If you play the very next hand instead of quitting, the chance that you will win that hand is 42% (or whatever).

    If you go to the toilet and come back, the chance that you will win the next hand is 42% (or whatever).

    If you choose to take a break from blackjack for a year, the chance that you will win the next hand you play is 42% (or whatever).

    And that’s equally true whether you are up or down at that very moment (session-wise or in total), or whether you won or lost the last hand you played.

    The only reason that you are up so far is because of luck. I’m sorry.

  9. You can only win, lose or push on a given hand.

    Wrong. That’s where your entire analysis is getting screwed up.

    There is more involved than the results of an individual hand. What you’re not factoring in at all is your actions after the hand. You can:

    1. Keep playing at the same bet.

    2. Keep playing at a lower bet.

    3. Keep playing at a higher bet.

    4. Stop playing, take your money, and go home.

    You can base this decision on:

    1. Your current balance of winnings (or losses).

    2. The makeup of the cards you know are left over in the shoe.

    See? There’s so much more involved than just the mathematical results of a single hand, which is all you want to focus on.

    Moreover, no computer model I have ever seen accounts for the above factors, and adjusts based on those factors. All they do, as I said in the blog post, is just grind and grind forever, regardless of those factors, until it loses.

  10. Caleb is right about the computer models. They’re not intelligent. Even the ones that are programmed to vary their bets don’t play the way a human being would. Its a good mathematical analysis but not necessarily reflective of the real world.

  11. What happens if every blackjack player in the world adopts this strategy? The casinos go broke in a game they have a mathematical edge in…?

    I’ll make it simple as possible.

    Let’s say you and I meet up every Friday night to flip a coin.

    There are only two rules. The first rule is that you decide how much we bet on each flip. The second rule is that you decide when we are done for the evening.

    You are saying that this would tilt the odds in your favour.

    Think about it.

  12. Let’s say you and I meet up every Friday night to flip a coin.

    There are only two rules. The first rule is that you decide how much we bet on each flip. The second rule is that you decide when we are done for the evening.

    That is in no way representative of the factors involved in blackjack, and I can tell you’re not really considering what I’m saying in my comments. So I think we’re done here. If you want to think I’m full of magic and am the luckiest man in the world, that’s wonderful.

  13. “You can base this decision on:
    1. Your current balance of winnings (or losses).
    2. The makeup of the cards you know are left over in the shoe.”

    This is the key of the issue. Assuming a big enough number of games, you should not be ahead if you blindly followed the mathematical model. Since there has been a sufficient number of games and you are ahead, the logical conclusion is that you are doing something differently.

    Where I disagree with you is that you attribute this result to quitting while ahead. I say it makes no difference when you quit or how much you bet on each hand in the long run while taking the best mathematical decisions you can during the game.

    I attribute this result to 2 while minimizing the importance of 1. I expect the reason to be a (probably subconscious) process that strays you from the mathematical model at key points, and the information that you process (that a computer does not) could be intuitive card counting, or maybe some reactions of the dealer.

    Quitting while ahead by itself does not influence anything in the long run, barring tiredness or emotional decisions.

  14. It is the same thing. I think you don’t understand the mathematics involved.

    Your assumption is that in some way you can tweak the odds in your favor for (some) individual bets. If you aren’t, then there is no way you can beat the house edge.

    For each individual bet you are an underdog to win. It doesn’t matter what you did before that bet, or what you are going to do after it, or when you think is a good time to go home. The cards don’t know that you left or that you came back again. No matter what trick or strategy you apply (card counting aside, which is not what you suggest), you can’t change the odds of any specific hand into your favour by adjusting the betting amount, and definitely not by deciding to postpone the next hand for X number of days. And if you can’t do that, you can’t beat the house edge.

    Take a look at what the Gambler’s Fallacy is. Wikipedia has some pretty extensive information. The only cases in which that fallacy does not apply is if the system has a memory. I.e. one Ace is already gone from the deck so that affects the probability of another Ace coming. That’s what card counting is based on, as I’m sure you know. If you don’t count cards (which you say is not what your system is based on), or if you play blackjack online (where the deck is reshuffled after each hand and card counting has virtually no effect) the Gambler’s Fallacy absolutely applies.

    You can also check out http://pokerdope.com/poker-variance-calculator/. It’s for poker but if you put -0.5 as winrate and standard deviation somewhere between 10 and 20 it will be accurate enough for blackjack to use as an example. I will generously assume that you have played 25.000 hands or so since 2008. Click “Calculate” and you will see a bunch of lines. The blue line is “the luckiest guy in the world” (not really, just the luckiest out of 1000 players), and you will see that ~35% of players will be profitable over this number of hands, using optimal strategy and no card counting. You happen to be in that group. That’s absolutely not even close to being super lucky. A few poor fellows will have been losing since the very first hand, and never even gotten the chance to quit while ahead.

    This is the type of simulation you want to look at. Not some sort of model of a single computer playing forever, until it busts. Yes, the expected value (the black line) is negative, everyone knows that, and you don’t need a computer model to figure that out. It doesn’t mean that everyone who plays eventually loses. No human plays to infinity.

    You seem to believe that anyone, human or computer, who plays a large enough number of hands will be at or close to the black line, and since you’re not it must be because of your strategy. It’s not. Note the difference between the red and the blue line.

    Just for kicks, type in a million hands at SD 20 and see how a small % of players will still be winning (again using optimal strategy and no card counting). It means that there will be people out there winning in blackjack in the “long term”, without counting cards, probably thinking they have some secret method that is working for them, when it is pure and simple mathematical variance.

    Look, I’m not trying to bullshit you in order to spite you or something. I used to play online blackjack (profitably because of the generous bonuses involved back then) and I also played poker professionally (profitably because you play against other players and not the house – a game I can recommend by the way if you want to make money from a hobby while spending time in the casino). I then went on to work in the business for several years. You are not the first person to come up with something like this. The industry makes money off of people who think the way you do. Trust me.

    From what I’ve read before I consider you a very intelligent person. I stumbled onto this blog from one of your other blogs and this was the first post I saw. Frankly, it surprised the bejesus out of me. But I think you are right in that this discussion leads nowhere, which I guess should have been clear to me from your original post anyway.

  15. “Quitting while ahead by itself does not influence anything in the long run, barring tiredness or emotional decisions.”

    This. Gary is much less long-winded that me. 🙂

  16. “You can base this decision on:
    1. Your current balance of winnings (or losses).
    2. The makeup of the cards you know are left over in the shoe.”

    This is the key of the issue….

    ….I attribute this result to 2 while minimizing the importance of 1.

    That’s fair, and you may be right. We don’t really disagree much on that, in that it’s a combination of several different factors all working in tandem instead of just one variable (which is something NoMathWiz doesn’t want to hear).

  17. I’ll be interested to see your future posts, because I have done simulations similar to this, and the results are very clear. Unless you count cards, it is impossible to make money in the long run. The short explanation why is because even as you accumulate a small surplus most of the times you go out, eventually you’ll go on a long enough losing streak that it will wipe out all your winnings. Even if you stop playing when you get down too much, that streak will continue across sessions and the only way to stop it is to stop playing all together.

    The simulations I did were very sophisticated and most times would not only win, but win big. However, you would still lose in the long run.

    But if you insist that your method would work in the long run, I would be more than happy to write a simulation program to your exact specifications. Since the topic is gambling, I would love to put a wager on it. If the simulations show that you would lose in the long run, I get all of your Blackdragon materials, including the SMIC program, for free. If you’re right and it comes out ahead in the long run, I will donate $5,000 to the charity of your choice.

  18. Unless you count cards, it is impossible to make money in the long run.

    I do count, just not hi-low which is the standard system people are referring to when they say “counting cards.” I count aces. Sometimes I do an ace/five count. I’ve been slowly experimenting with other counting systems that aren’t as difficult as hi-low.

    But if you insist that your method would work in the long run, I would be more than happy to write a simulation program to your exact specifications. Since the topic is gambling, I would love to put a wager on it. If the simulations show that you would lose in the long run, I get all of your Blackdragon materials, including the SMIC program, for free. If you’re right and it comes out ahead in the long run, I will donate $5,000 to the charity of your choice.

    FUCK YES. I’ll take that bet. You’re going to have to account for exactly how I play, how I count, the type of tables I play at, and the liberal blackjack rules at the casinos I play in (single/double deck only, double on anything allowed, surrender allowed, etc). But I will provide you all of that information in detail.

    Let me make a few more posts here on blackjack to describe everything I do first. Then when I’ve covered the basics, I’ll lay out the specific parameters, and if you’re still willing to publicly take that bet (and do so under your real name, no internet aliases allowed), we’ll do it!

  19. Way to go Tony! This way we should get to the crux of the issue, and maybe Blackdragon will learn a little more math, though I wouldn’t bet on it 😉

    Have you made simulations that include for counting cards? I’d love to know what percentage of each hand do you win with perfect card counting abilities.

  20. “If you sit down and play blackjack for a long time, you will lose. That’s how the odds work, and that’s why casinos make so much money. (I would love to own one.) Therefore, if you want to win, the goal is to NOT play blackjack for a very long time, and buzz out of there as soon as you start winning a little.”

    Taken on its merits, this shows a complete lack of understanding of basic statistics. The length of time playing any one session has no effect on long-run expectation.

    If you post the details of your system, it should be relatively easy to calculate your EV. If it’s negative, I’d be very interested in betting against you over any number of hands you choose. 🙂

  21. Taken on its merits, this shows a complete lack of understanding of basic statistics.

    Then you’re ignoring the last part you quoted, where I said:

    buzz out of there as soon as you start winning a little

    If you leave while winning a little instead of leaving while you’re losing, or keep playing while you’re winning, then you’re more likely to go home with money. True or false? That’s all I’m saying.

  22. Really the only thing that matters is if the expected value for a single hand is less than zero. If you count cards you can get it above zero and make money, but without counting cards it should be impossible. And with an expected value less than zero you’ll lose in the long run no matter what you do.

    I didn’t make simulations for counting cards. My simulation was technically not blackjack at all. I was testing the strategy of double your bet every time you lost (which will guarantee that you make your money back when you win as long as you don’t run out of money), and doing some variations on it (for example, I’d multiply by 10 for the first loss, 7 the second, etc. down to 2) to make more money.

  23. Really the only thing that matters is if the expected value for a single hand is less than zero.

    Not if you’re already up well over your starting pot at the point of that hand (and thus have the option of ending play).

    Also, not if you modify your approach based on the makeup of the cards left in the shoe. But you just admitted as much (sort of).

    As I keep repeating, and as some of you either don’t understand or don’t want to admit, you math-freaks are acting as if each hand is played in 100% isolation from all other hands prior to it, and that’s simply not the case in real life. It’s much of the equation, I’ll grant you that, but not all of it.

    As you play, two variables change: A) the value of your current pot, and B) the makeup of the remaining cards left in the shoe. These two variables do indeed have an influence over your odds of success (based on you doing the correct things of course, based on these two changing variables).

    My simulation was technically not blackjack at all. I was testing the strategy of double your bet every time you lost

    Well…yeah. That’s a horrible real-life strategy that I would never employ. Of course your simulation didn’t work.

    I’m definitely getting more excited about taking your bet. 🙂

  24. What us math-freaks understand is that without using the information of “B) the makeup of the remaining cards left in the shoe”, there is no way to win money in the long run. It does not matter how much you play for or when, when you statistically lose a couple percent of “A) the value of your current pot” each game. Which is what you seem not to grasp when you say

    “if you want to win, the goal is to NOT play blackjack for a very long time, and buzz out of there as soon as you start winning a little. Do that every time you play, and assuming you play correctly, you’ll win more often than you lose.”

    You may want to take a look at “Innumeracy” by John Allen Paulos to see just how unintuitive statistics is to the untrained brain.

  25. What us math-freaks understand is that without using the information of “B) the makeup of the remaining cards left in the shoe”, there is no way to win money in the long run.

    I’m not disputing that. Nor have I ever said otherwise. You’re trying to argue with statements I never made.

    I’m saying:

    A) There are more variables involved in your blackjack success rates than just the statistical results of a single hand. This is fact.

    B) If you are winning (at a positive net balance from your starting balance), your odds of winning are higher (i.e. 100%) if you stop immediately and go home than if you keep playing. This is also fact.

    In fairness, I have added an addendum onto the sentence you quoted in the above post, just to make it more clear to my more mathematically anal readers. 🙂

  26. “This explains why mathematical or computer models always show that it’s “impossible” to win at blackjack over time. Correct, it’s not.[?!] The computer under these models plays and plays and plays until the odds grind it into powder. Fortunately I’m not a computer, so I don’t do this. Unlike the computer, I play for a very short period of time, and as soon as I start winning, I stop and buzz out of the casino a winner.”

    This implies that you think a computer that is programmed to play blackjack without counting cards and stop as soon as it’s ahead will come out winning in the long run. It seems like you think what’s missing for the computer to win long-term is just a way of stopping (for whatever while) when it is ahead, then start again in a different session. That is what I disagree with.

    Your system as I understand it now:

    Choose casinos with the best blackjack rules.
    Use a method of counting cards. [these 2 rules insure you are making money when playing]
    Quit while ahead to avoid mistakes. [this is just a reminder not to deviate from the winning system. if you have the discipline to use the same method without making more mistakes you can just keep going and win more. also, you can increase the bet and win more]

    “B) If you are winning (at a positive net balance from your starting balance), your odds of winning are higher (i.e. 100%) if you stop immediately and go home than if you keep playing. This is also fact.”

    I agree with this statement but I don’t see the value of it, because we want to win in the long run. Winning a little in one session is not indicative of long term winnings. For example winning 10 dollars for 5 sessions then losing 60 dollars the next session does not mean you are winning.

  27. @Greg, @Tony, @NoMathWiz: it’s obviously pointless continuing to discuss this right now. Either there’s some kind of bizarre reverse-trolling exercise going on here or he’s just not capable of understanding. Let’s just run the simulations when he posts more details of his system.

    @Greg: the best card-counting system I’ve come across has an EV ~ +2%. Much better off playing poker against bad players instead like NoMathWiz!

  28. Michael, read my most recent two comments. I don’t think we’re disagreeing as much as you think. I think were just all micro-focused on different areas of the argument.

  29. You obviously know nothing about and have not studied statistics and probability enough to follow some half-baked strategy like that.

Leave a Reply

To leave a comment, enter your comment below. PLEASE make sure to read the commenting rules before commenting, since failure to follow these rules means your comment may be deleted. Also please do not use the username “Anonymous” or “Anon” or any variation thereof (makes things too confusing).

Off-topic comments are allowed, but Caleb will ignore those.

Caleb responds to comments in person, but he only does so on the two most current blog articles.

Related Posts

Begin typing your search term above and press enter to search.