Sessions, or No Sessions???...
  • SSR Quote 1,
    "in the game of blackjack there are no "sessions".
    Just one long series of hands,
    stretching for as long as you play the game.
    Sessions are meaningless"...

    SSR Quote 2,
    "I have always played by the rule "one hour per session max, at a given pit."

    SSR, can you "clarify" this for us?
  • Certainly...

    From an EV point of view, you play one long (lifetime) session in BJ. Your final win/loss result is determined by the result of that long session. You can't win by quitting when ahead and quitting when behind, and using the logic "most of my playing sessions end up with me winning some small amount so this is the way to beat the game."

    The other type of "session" has nothing to do with EV. It has to do with longevity in a casino. I never play more than one hour with the same "crew" (pit, shift, etc.) I never play across a shift change (a common strategy). And I will sometimes have a "session bankroll" to prevent me from busting out in the middle of a long trip when I am out playing for fun with my family. Example: I take $2000 with me and we are going to play for 5 days. I set a daily loss limit of $400. If I "tap out" I just don't play any more that day, so that I am sure to have money to play tomorrow. None of this has anything to do with improving my EV, or winning more "sessions" than I lose, etc.

    Bottom line: A "session" is a time management, or longevity management, or "don't run out of money too soon" strategy only. It has absolutely nothing to do with how much I will win or lose while actually playing the game.

    Hope that helps. I use the term "session" to mean "the period of time from when I buy in until I cash out." It has nothing to do with a strategy to help me "win"...
  • Question...if you set a daily loss limit at a fixed value (e.g. $400), but no limit for gains, does this practice increase your overall expected value?
  • Not one single penny. All it does is guarantee me that I will have money to play for 5 consecutive days, even if I bust out each and every day and lose my entire session bankroll each time.

    Doesn't influence your EV whatsoever... It is critical that you understand why that is true, if you really want to take on the casinos and leave _really_ winning, rather than "pseudo-winning"...
  • All I will say is my "pseudo-winning" strategy has helped me raise my permanet bankroll quite nicely.

    Assuming one divides his BR into four equal parts to assure they are able to play all four days,shouldn't they
    then divde their BR on day two into thirds,and on day two into halves.

    As all things tend to revert towards the mean,and even world class advantage players have only a two percent edge,if all my winning X amount on a given day means in the long run that I will lose X money back in my "lifelong session",I can live with that.
    Perhaps you should think of it as a reverse IRA. I'm deducting now and will pay later. If later ever comes.
    Will days come when I will get absolutely hammered? Without a doubt. But if I set a goal for today,and reach it and quit,if nothing else,I've postponed the inevitable.In the meantime,my "psuedo-winnings" are invested in T-Bills,drawing real interest.
    Good old fashioned Voodoo economics.
    I'm not realy sure what is so difficult to grasp in that concept.
  • Some common sense- If you play against a house edge, that which is a
    certainity reduces to only probable in the short-term. Luck will play a role
    in the outcome, but the effect is minor. This fact is due to bad and good
    luck cancelation. If you play 100 short sessions, you are the underdog
    for every session, 1 to 100. Thus, you will lose in the short-term, mid-term
    and, of course, the long-term.

    If you don't believe the above reality, how can you believe basic strategy?
    How can the casinos stay in business? How come insurance companies own
    half the shopping centers in the US,etc?
  • There are _many_ good reasons to divide and sub-divide a bankroll. I gave one, which guarantees that I will play every day. If you prefer to play 3 sessions per day guaranteed, then subdivide the daily bankroll into three equal parts. Etc.

    The one reason to _not_ think "session" has to do with EV. Your EV is your EV, period. Sessions have _nothing_ to do with that. And I do mean absolutely nothing.

    Best way to "beat the house" without counting, is to walk in and bet the house on one hand. The variance is so high you have a reasonable chance of winning. Play a lot of blackjack, playing pure BS, and you are going to lose, period. No matter what "session rules" you use, no matter what kind of money management (progression), etc.
  • How do casinos stay in business?
    By offering their clients value for their dollar.
    Have you noticed the trend towards first class dining establishments,world class shows,ect,ect.
    Have you seen the trend towards other table games that
    have a higher house edge and a faster pace than BJ?
    Notice the growth of single deck 6/5 games,and how crowded they are? Surelyyou have seen the growth in slot machines,and the absolute proliferation of penny and nickel machines that have house edges many times that of a real BJ game.
    Why? Because most people who go to casinos go to be entertained,and accept that the cost of their entertainment will be leaving a chunk of their cash
    behind when they depart.
    A good SD or DD game in Las Vegas,played by anyone that knows BS,and can CC enough to know when to use a few variations, and when to take insurance is damn close to a 50-50 game.
    Even if the house has a minute edge,the player is the one that determines when a certain session ends,not the house.
    If I am determined to win only one unit in the session,and am willing to play until I am up one unit and quit-no matter how long it takes to get up that one unit,one hand,ten hands,1,000 hands-how does the house have an edge?
    What edge does a casino have in a martingale betting system? None. Thats why they institute table limits,because the limits are the only thing the house has in its favor.
    In BJ,the biggest,perhaps only advantage it has is the fact that it goes last.If we tie on 21,we push. If we tie on 22,I lose.
    The advantage the player has is he can quit anytime he chooses,no matter if he is ahead,even or behind. The house MUST deal as long as the player puts his money in the circle.
    Anyone with an open mind will agree that this is a factor in the game,yet I've never seen anyone try to quantify it.
  • If you,SSR,believe the best way to beat the house is on a single hand,how does that square with your "there are no sessions" mantra. Your advice sounds a lot closer to my "set a goal,achieve it and quit,paying the minimum amount of hands needed",except I am depending on my knowledge and skills to achieve my goal. You are calling for a one shot all or nothing.
    Would you risk your life,your health or even your entire BR on a single hand of BJ?
  • A couple of points.

    1. The casinos stay in business, not because they offer us some sort of entertainment, they offer us "hope". Hope that we can join the pictures on the wall that won a million dollar progressive slot jackpot, or whatever. It is about hope. Nothing more, nothing less. They offer attractive stuff to try to lure us into _their_ casino rather than our visiting another casino. Hence the mega-resorts like MGM, Mandalay, etc... But _nobody_ goes to those places to lose money. They _all_ (except for the APs of the world) go there _hoping_ to be that one in a hundred or one in a million that actually wins. APs go there knowing they will win long-term. Would I risk _my_ entire bankroll on one hand? No. By counting cards, I don't play against the "house edge". I play with my own edge, and there I depend on the long-term to zero in on my advantage, rather than relying on one hand which is still a 43 out of 100 long-shot. An AP doesn't "gamble". He plays a sure-thing long enough to let the long-run smooth out variance to reach a target EV.

    2. My play one hand is _totally_ square with the no session idea. I don't want to turn this into a math class, but the idea is this.

    (a) you play BS for 20,000 hands. You are going to lose .5% of each bet made. And there is no room to play with. You will _absolutely_ lose in the long-term.

    (b) you play BS for 1 hand, the house edge is still .5%, but the variance for a single hand is _very_ high. For example, assume you win 43% of your hands, so you almost have a 50-50 chance of winning one hand, and doubling your bankroll. But njotice I am playing _one_ hand and then either quitting because I am broke, or quitting because I doubled my bank. There is no long-term as I won't play ever again. So I take the short-term, with its very high variance, and live with the result. You have a 43 out of 100 chance of doubling your bankroll on a single hand. You have absolutely no chance of doubling your bankroll (using BS) over 20,000 hands. That is the difference. Not that 43/100 is good odds, but it is better than 0 out of 1,000,000 for long-term prospects of winning..

    Again, if you don't understand that simple idea, there's not much that I can add to the discussion. It is a basic fact of sampling theory. If you know a good probability/stat person, ask him. You will get the _same_ answer you are getting from me (and others like Ray) here.

    Your question "how does the house have an edge" is simple to answer. You are _not_ going to win $5 every time you play. That's what you are overlooking. There are times you will play until you are broke. And the more of these "mini-sessions" you play, the closer you get to the "long term" which is an absolutely losing proposition for a pure BS player.

    But if you believe you can pull that off, I'm all for freedom of choice. Feel free to either listen to those that understand the math, or those that deliver incantations and voodoo.

    But, for the record, the math _works_ here without fail... Just look at the Vegas strip. Who do you think pays for all that? The tooth fairy? Or the non-AP 100% losers?
  • For the pure basic strategy player, one hand is about it as far as his best
    chance. When you play two hands the chance decreases and the same
    for all hands that follow. This defeats all claims of goal setting, reach it,
    and quit.
  • Ray said:
    For the pure basic strategy player, one hand is about it as far as his best
    chance. When you play two hands the chance decreases and the same
    for all hands that follow. This defeats all claims of goal setting, reach it,
    and quit.

    Why would the second hand be any different for a pure BS player than the first? or the third,or the 10,000th? Since he is not counting cards and is using the exact same strategy on every hand,how does his chance of winning decrease?Even if he is not changing his bet due to the count,he may be betting in to a huge positive count,which would increase his odds. Suppose I get 5,3,5,5 and beat the dealers 2,5,7,4- Do you really think my chances of beating the dealer next hand are less?
    than they were the first hand?
    SSR says you have a .5 negative EV on each and every hand,yet you say your chances are best on the first one and decrease every hand you play?

    Anyways,I'm off to bed. Off to Vegas via Jet Blue in the AM.
  • True, you have the same expectation each hand, but with each hand played
    luck continues to vanish as a factor. This in a nut shell is why theory and
    reality join hands (become one and the same) out in the future.
  • Here's something I have never really gotten about statistics despite taking many higher math classes.

    To make things simple, let's assume we have an even game. If you bet $1 over 1,000,0000 hands, you would expect to receive at the end of the game $1,000,000.

    Let's say you play 1,000,000 hands, but due to variance, you are actually up $100,000 (10%).

    Now, on the same even game, if you predict your performance for the rest of your life, you would predict that you would simply get back the money you spent. However, you are already up that initial $100,000. Thus, over your life time, you are actually +$100,000. Now, as n goes toward infinity, that $100,000 means less and less, but you would still expect to always be positive, which is not what you should be from the beginning.

    And before someone says, yes, but for everytime you are up $100,000, you are going to be down $100,000, you're missing my question. You're already up the 100K. You are now predicting your performance for the rest of your life. Past events don't matter except that they do add to your overall bankroll at the end of your life.

    Anyone have this problem? It always bugs me.
  • Funky:

    First, you have a misconception. If you play 1,000,000 rounds of a perfectly equal game, say a coin toss, you do _not_ expect to get 500,000 heads. In fact, that is a very unlikely outcome. To explain, lets play 16 tosses rather than a million.

    Now you can enumerate all 16 possible outcomes of three flips:


    Now to break even exactly, you need two H's and two T's. How many ways can you get that from the above? I see only 46 That is 3/8 of the time if you flip a coin 4 times, you are going to get 50%. What about 3H and 1T or 3T and 1H? 8 times. So you are twice as likely to get 3-1 as you are to get 2-2. Notice that 4-0 happens only twice, total.

    So if you flip the coin enough, which is most likely? 3-1 happens 8 of 16 times while 2-2 only happens 6/16 times.

    That's "lesson #1" here. Now if you flip the coin a million times, you can easily compute the probability of coming up 500,000-500,000. But it is not as likely as 499,999-500,001. But notice that either is _very_ close to 50%, one being exact, one being off in the 4th decimel or whatever.

    Now, for your being up $10K example. This is all under a bell-curve, with a mean u, and std deviation S. When you reach the "up $10K point" you are still "under the curve" but you are to the right of the mean, in the + side of the curve. There is a distinct probability this will happen. But over time, it is equally probable that another "session" in the future will end up in the -$10K. It isn't guaranteed, as there is nothing that says you can't win the lottery once and be ahead for the rest of your life. But you are _way_ out on the right-hand "tail" of the bell curve, which happens in very rare cases. If you are a BS player, with a -.005 expectation, even though you are up $10K today, if you keep playing, you are going to steadily lose at your normal expectation. Sometimes worse, sometimes you win, but overall you are heading toward your actual expectation over the long run. As a BS player, you can expect to see that $10K slowly drain away at the -.005 rate, and after enough hands, you will be "very close" to your -.005 expectation, even though at some point you could have been well above or well below that number.

    To understand this further requires a good understanding of "the long run". That's the reason I said the BS player's best hope of winning is to play one hand, all or nothing, and walk away. There he has an almost 50% chance of ending _way_ out on the right end of the bell curve. Take the coin toss game. Heads you win, tails you lose. With one round, you have a 1/2 probability of doubling your bank, 1/2 probability of losing it all. Play two hands and you have 1/4 chance of quadrupling your bank, 3/4 chance of going bust. Play 3 hands and it is 1/8 of ending up with 8X, 7/8 chance of ending up with zero. As you can see, each additional flip doubles your chances of losing it all. So just play one, cut and run.

    Also remember "EV" is not winning, it is "expectation". A pure BS player, playing an infinite number of hands, will lose all the money in the universe.

    win_amount = EV * bet_size * number of hands.

    EV is negative, so no matter what bet size is, -EV times infinity = -infinity, or lose everything.

    That's why AP's want to play fast. Quicker to reach the "long run" and overcome the up/down swings that naturally occur... Give me the game where I play the most possible hands per hour, no other players, fast dealer, etc... if "N0" (the long run for the specific game I am playing) is 20,000 rounds, I'd rather play 200 hours at 100 hands per hour than 600 hours at 33 hands per hour.

    Hope that helps. Forget about being ahead or behind at any "point" in your play. Remember that you are tending toward the "long run" the more you play, whatever that particular expectation for you is (everyone has a different EV, some blow parts of BS, some are superstitious and won't double in certain cases, some won't split 8's against a dealer 10 up, etc, all of which lower the EV). It is theoretically possible for a +.01 EV AP to lose everything. It would be rare, assuming he reached N0, but winning is not _guaranteed_, just "expected". Any single player can end up _anywhere_ under the EV bell-curve. But most are going to end up clustered around the mean EV. A few will be out in 10-sigma territory. A _very_ few...
  • Chicken-You will be well-off and ready for the big,big time. As for the bi-nom
    calc to determine the probability that you will win exactly 600k times out of the million trials, why bother? Based on Mr. M's law, if it can happen, it will happen.
  • Rat,

    Thanks for your comprehensive message. Its appreciated. You are right in that I mispoke about expecting even money.

    However, I don't really feel you hit my question on the head, but maybe it was due to me not explaining it well. If you are already up $10,000, history means nothing for future probability predictions. If you are predicting your next inifinit number of hands at even odds, the greatest single number of observations under the curve will be even money (I undersand the area under the curve of +-1 percentage point is greater than the middle of the curve, but the middle of the curve is the highest point and thus the greatest number of observations). Thus, after you have already won the $10,000, if you had to predict how much you would be up to infinity from then on (again with even odds), it seems to me that you would predict $10,000 as your ending balance. To do otherwise, would be to fabriacte that your past performance somehow affects your future performance.

    And yet, we say that if you are up $10,000, that amount will go towards the expected value over time. I don't think that's accurate. Once you are up the $10,000, your expected performance from that point forward is what the EV is regardless of your past performance. Is that not basic probability theory?

    I understand what you are saying, trust me. I've just always had this theoretical problem with the entire field and have never gotten a good answer to my question (although perhaps I am not explaining it well).
  • SSR- I think Chicken is correct in his example. If by whatever method you
    win 100K in an even game, it is history. Then if you project your remaining
    life in the same even game, you end up getting all future bets back and keep
    the 100K profit. The only real question is how did you get so lucky in the first

    It would be a different story if you were playing against a HA and had a
    variance that large in your favor. You may not equal/null the 100k for a
    very long time, but eventually you would.
  • I thought I addressed that, perhaps indirectly. I mentioned that there is no "trend" that will drag you back down. But the point is this:

    If you play long enough, even with that one big win, you are going to have more big losses to go along with it. And while those losses are not there to offset that big win, they are going to happen. Because the sum of all your "trials" is going to end up very close to your EV. The more trials, the closer you ought to get (and of course, with very few trials, you can end up way to the right or left of the EV just as easily, but over time "averaging" drags you back "home"...

    I've had one of those "huge wins". 10K in one session. I've also had a losing week where I lost half of that much right back to them.

    Some might think "OK, huge win, I am simply ahead and expect to stay there." I think "OK huge win. That will offset one of these huge losses that are on the horizon somewhere."

    As far as variance goes, 21 certainly has more than enough. :) It is the most painful part of this game.. I'd love to play for a flat $X per hour, rather than the existing $X +/- $Y per hour where $Y is _far_ bigger than $X....

    For example, my favorite DD game on the coast (now gone of coures) was DD, S17, LS, 75%-80% pen. Spreading $5-$40 my hourly win rate according to CVCX is almost exactly $20 per hour. But the standard deviation for that is $175 per hour (that is, about 68% of the time I will win $20 +/- $175 every hour I play. That is a remarkable variation to the base win rate.
  • SSR- I have changed my mind based on Murphy's law. If you can win 100K
    in an even game you can also lose 100K in an even game. You may not be
    able to see it in a lifetime, but see you will.
  • I'm becomming more firm in my stance. Although we seemingly agree on probability, Rat, you are still making statements that seem to indicate that past performance somehow changes future performance such as "If you play long enough, even with that one big win, you are going to have more big losses to go along with it." While creating that bell curve means that you will have big losses in the future, you will also have other big wins in the future. Once you are up $10,000, you are up $10,000 and the casinos can't do anything about it. For every $10K you might lose in the future, there is the same chance you will win another $10K in the future. Once you are up, you are up. Once you are down, you are down.

    The only reason you get dragged back to the mean is because after an infinite number of trials the one $10K win isn't as significant as it is when you are starting out because you've risked infinitely (literally) more than that.

    So, I'm going to continue to combat statements unless you can prove me wrong that you shouldn't stop when you have a big win because you are going to have big losses in the future. While that is true before you get the win, that is not true after you get the win. I know its a fine point and one that is used incorrectly to promote progression and other types of betting strategies. The difference is that the progressive player believes a $10K win in the future won't be offset. I'm just saying a $10K win in the past won't be offset (although it will become less significant over time).
  • "If you play long enough, even with that one big win, you are going to have more big losses to go along with it."

    ...which goes back to my original question of whether setting loss limits will affect EV (e.g. setting loss limits to thereby avoid the big losses). I understand the statistics behing the answer. I think I knew the answer before I posed the question. It just seems that the answer to the question of setting loss or even win limits lies in the risk the player is willing to assume based on total bankroll, entertainment value of playing everyday on a trip, many other factors, etc. SSR even admitted that he set loss limits to ensure that he had some $$$ to play everyday rather than risk the unlikely event of losing his bankroll in one day.

    "I'm going to continue to combat statements unless you can prove me wrong that you shouldn't stop when you have a big win because you are going to have big losses in the future."

    FC...I agree that past winnings won't affect future winnings, but what SSR is saying is that over the long run, the winnings (or losses for the BS player) will tend to go to the EV of the game you're playing simply due to the mathematics of the game. The decision to quit when way ahead or behind depends on risk a player is willing to assume or in some cases past experience with the dissonance of not quitting when way ahead or way behind.
  • Funky:

    think about this:

    Let's say you are a pure BS player. With a -.005 EV. OK so far?

    Now, today you go out and play, and end up _way_ on the right-hand side of the bell-curve, and win $10K where your expectation was to lose $1000. So you are actually $13K ahead of where you are supposed to be. Consider this one of "those" events where you flip a coin 8 times and it comes up 8 heads. Rare, but no outcome is impossible.

    Now, you are up. But you continue playing over time. What do you _expect_ to happen?

    I expect you to lose at your normal rate of $1000 per day on average. On some days you will win, on more you will lose. And on average, you are going to get that $1k loss per day. I'm not sure where we disagree. If you think you can "keep" that $10K, in a -EV game, sorry but the only way to do that is to stop playing forever. We are now at the example I gave where you played just one hand, and won, and doubled your B/R. If you quit, you are ahead. If you do not quit, you are going to lose, and slowly that $10K is going to be eroded.

    Remember, it is _exactly_ as probable that you will have a $10K losing session, as it was for you to have a $10K winning session. The "once you are up you are up" is simply wrong. Because you are not "up" if you continue to play.

    One example is to go to Eliot's web site ( and look at the graph of his B/R he has posted there. Always trending up, but with _lots_ of dips. Would it surprise you to know that as an AP, you are playing at a point where you are _below_ your peak bankroll 99+ percent of the time. You make a new all-time high, and immediately drop off. And eventually you re-reach that point and sooner or later you go a little higher (an AP is playing with a +EV remember)...

    If you believe you can "stop while you are ahead" and somehow "keep those winnings" for all time, you are simply badly mistaken. Again, you are walking right into the common misconception about "sessions". You have losing streaks, winning streaks, but you can't tell which until _after_ the streak has ended. How do you know your 10K win won't be followed by a $10K loss where you break even?

    This entire concept is simply wrong, based on a concept that is not accepted in any sort of probability theory. If you don't believe in the central limit theorem, then there's no hope you will accept how this works. If you do understand and believe in the central limit theorem (and it is 100% accepted and proven in the real world btw) then we wouldn't be having this conversation in the first place.

    What happens to the person that goes out and loses big his first session? Is he stuck with that big loss? Or do future wins pull him back up, eventually to his expectation?

    Short-term, anything can happen. Long-term, your expectation is going to happen. Nothing else is possible.

    Just don't forget that "your expectation" is a probability distribution. That is, you _can_ end up to the right or left of the mean, although the farther from the mean, the lower the probability that will happen.

    But first, you have to win that $10K. The probability of that happening is so low... Because out at 5 sigma or 10 sigma things can be very good, or very bad, but also _very_ unlikely to happen. :)

    Finally you say "won't be offset". But let me remind you about sampling theory here. This is a normal distribution, and there are a _bunch_ of data points in the sample space. Some +10K, some -10K, and everywhere in between. And just because today you saw the +10K _first_ does _not_ mean you won't see the -10K tomorrow. These samples are taken randomly from the normal distribution. They have a known mean, and with blackjack, a known standard deviation. So you probably _will_ see that -10K in the future, with a probability equal to the probability of seeing the +10K sample today. So while "mother nature" is not counting random events and guaranteeing that for every tit there is a corresponding tat, probability theory suggests that for each big win, there will be a corresponding big loss, given a large enough sample size. Since all the samples, summed and averaged, must end up at the mean, with error limited by standard deviation. The more samples you take, the smaller the standard deviation becomes... When you finally get to an infinite number of samples, the standard deviation is zero.
  • I don't think we are off at all basically, I just think I'm just picking up on an inprecise way that you are speaking sometimes.

    First, I agree with you that in a -EV game, your $10,000 win will slowly go down (or quickly). My hypothetical was a even EV game.

    What you say about sampling theory is true -- but only if you look at the events before they occurred. If I'm talking about tomorrow, the chance of winning $10K or losing $10K is the same in an even game. However, once I have won that $10K -- the chance of winning or losing $10K the next day is still even. In a manner of speaking you are always up that initial $10K once it has occurred. That's the point I'm arguing about. Once you've won it, the fact that you have won it does not in any way affect future events.

    You are talking about going back in time to a certain degree. Yes, you expect at the beginning to sometimes win $10K and sometimes lose $10K -- and in an even game the chances both will happen are the same. But once one has happened its a different story.

    The reason you will drift back to the EV is not because once you have won $10K, it is more likely you will lose $10K in the future to offset that; but that $10K that you won becomes less significant over time.

    I think we are on the same page -- I think I'm just being picky about wording; and again, I have always been speaking about an even game (which Basic Strategy is not). And yes, I agree that the initial $10K win is unlikely. I'm just pointing out that you should feel lucky if you make that initial win, and if you were playing an even game, there is no reason to feel that for that $10K win, the chances of getting a $10K loss in the future are any greater than before you won that $10K.

    But Emperor, seting limits will not in any way effect your EV. Any type of progression play or limit play is based on the future. You can't change the EV in the future with these methods. You can extend your playing time or your fun factor, but you can't change your ultimate outcome.
  • Here is what you are overlooking:

    In a truly even game, the probability of any sample being above the mean (you win) is exactly the same as the probability of any sample being below the mean (you lose).

    If you win big on your first session (very unlikely) there is an exactly equal probability that you will lose equally as big later on. Whether they will offset or not is not really that important. But the more you play, the more likely you are going to see those significant departures from the mean in your samples.

    If you are very lucky in an even game, and win early, you might be a "winner for life". This happens in lotteries every week, and it is very unlikely someone is going to lose 200M after winning that much. Of course, we know the probability that is going to happen is incredibly close to zero. But not _exactly_ zero. So you _can_ win an even game. Or a very uneven game like the lottery. Once in a zillion times. But guess what happens over the long run with enough samples? All the _rest_ of us lose way more than that 200M you happened to win.

    BS BJ is not an even game. The lottery is not an even game. Suppose you enter the lottery and win $200. You are now ahead. Do you quit? Or do you continue to play hoping for a bigger win, say $1000 or more?

    Again, I'll remind you all this fits under the normal distribution. The + and - tails reach off into +/- infinity. It is _possible_ (remotely) that a pure BS player can win every dollar the casino has available. Or, in theory, he could win every dollar on the planet. But the further to the right (or left) you go, out into those "tails" of the normal curve, the lower the probability that you will ever get there. There is an element of chance. Losers can win. Winners can lose. There is no _guarantee_ that an AP is going to win long-term. There is a high probability he will.

    Just remember that the usual betting ramp has a 13.5% RoR. That means that just under one of every 8 players using that ramp with their counting skills are going to go bankrupt. one of every eight. Is that you? Or me? If you cut your RoR to a vanishingly small 1%, that means that one of every 100 players is going to go bankrupt, even though they are playing a winning game by counting or whatever. So nothing is _certain_. "likely" is another thing entirely. It is _likely_ that a competent card counter is going to make a profit. But absolutely not guaranteed. The more you play, the closer you get to that guarantee. After an infinite number of trials you are guaranteed to be at "the mean" but you can't play that long. For BJ, with its fairly modest S.D., 20K hands gets you pretty close to "infinity"...

    On our BS player, however, things are different. Because he just had a big $10K win. But the remainder of his wins/losses are going to be centered around the _mean_. And the mean is fixed at -.005 EV. Which means that he is most definitely going to lose that $10K and more. In fact, he is going to lose everything he has if he doesn't stop playing, because this is a -EV game from the start. There is _no_ way to protect that $10K win, in a -EV game, with one clear exception: stop playing forever. Then you can't lose it back.


    loss limits don't do anything at all for your EV. Suppose you set a sesson loss limit of $200. And you quit when you lose $200. What says that your losing streak won't continue the next time you sit down? Just because you get up from the table for a while doesn't change anything at all, except provide you a break. That's the key point here. You can set loss/win limit to $5, and all that will do is make you play _lots_ of very short sessions (one round average at a $5 table). You can set loss/win to $100 and play longer sessions, but fewer total sessions, with probably more hands played overall due to not losing so much time moving around. But your EV is exactly the same for either style of play, although your hourly win rate will go way down with tiny loss/win limits...

    There is no way to profit by stopping play at arbitrary points. The "session" spans those stop points and you are going to keep winning or losing as the odds predict, regardless of how many playing sessions (and how long) they really are...
  • I think we are talking around ourselves to a certain degree. I'd just make one slight correction to the above:

    "If you win big on your first session (very unlikely) there is an exactly equal probability that you will lose equally as big later on."

    That's not precisely right. If you win big on your first session, the probability that you won big on your first session is 100%. Before either has occurred, the chances of winning big or losing big on your first session are the same. That's the only thing I'm saying. Once you've won or lost, you have won or lost. Probability can only tell you what is likely to happen in the future and it is not based on what has happened in the past. I think we agree -- I'm just being picky about your words.
  • I've never said "past history effects future results" when dealing with probabilities. But the one and only point is, no matter _how_ you do on your first session, there is a very high probability that you are going to end up _exactly_ on the mean EV for this game, long-term.

    If you look at the bell curve, the sides "squeeze in" as the number of samples increases. By the time you get out to an infinite number of samples, the bell curve turns into a single point at exactly the mean of that infinite number of samples. We won't ever get there of course. But we can play to the point where the bell curve is very "thin" in the center, even though those "tails" will always go off to +/- infinity. And the more we play, the closer we will come to our true EV. That $10K sounds good over 1000 hands. winning 10 bucks a hand is pretty good. play 100,000 hands and that $10K is pretty meaningless, turning into a dime per hand.

    Anyone playing this game thinking there is a "guarantee" they will win is simply mistaken. _badly_ mistaken. Flipping a coin is not a pure 50-50 game either. It is remotely possible that the coin ends up on its edge... So nothing is truely certain. All we can do is shift the mean of the normal distribution left or right. Counting moves it right to the .01 (1%) point, but there is a lot of the curve far farther to the right, and plenty back to the left on the - side of the EV X axis as well.

    This is still gambling, but gambling with an edge on your side. The casinos see huge losses at BJ tables regularly. But those are also offset by huge gains over time, with the final result being just what they expect, they win more than they lose... Just not every day on every table in every pit. However they very nearly play an infinite number of hands/rounds, and they end up right where they expect to be, time after time...

    as will we, if we play enough. Stop before "N0" and your results depend mainly on luck. Get to "N0" and the luck factor is dimished (but never eliminated)..

    "And yet, we say that if you are up $10,000, that amount will go towards the expected value over time. I don't think that's accurate. Once you are up the $10,000, your expected performance from that point forward is what the EV is regardless of your past performance. Is that not basic probability theory?"

    Not quite. Probability theory is based on "long term" and in that concept, how you did today is meaningless. If you play enough hands, you _must_ end up at the mean, or the basis for probability theory and statistics (central limit theorem) is wrong and none of this means a thing. But again, since you can't get to "infinity" the bell curve is never a single point, which means you always have a chance of ending up left or right of the mean. The more you play, the closer you get, the less you play the farther out you can be without being a really exceptional case...

    Don't think of EV as a single value. It is a single value (mean) with a modifier (standard deviation). SD shrinks with more hands played, or can be very big for a single hand played...

    The way to analyze this is to ask the question "what is the probability that I will end up ahead 10K dollars after playing 1000 hands?" That can be directly answered. And it won't be 1.0 or 0.0, but somewhere in between, much closer to 0 than 1 of course, but not exactly either. If you think of "EV" as a "single value" then you are thinking about it wrong, and I believe that is where this discussion is dancing around a bit, because I am thinking of the normal distribution _every time_ I use the term EV, since the EV _is_ a normal distribution, not a single value...
  • Again, I think we're agreeing and talking past each other so I'll leave it at that.

    BTW, I just noticed you are a "senior member" -- is that an official title? or perhaps based on the number of posts?
  • I believe it has to do with how long you have been a member of the forum. That's all I can guess. I've neither asked for, nor been given any sort of "special status" that I know of.

    It might be related to number of posts, or number of months a member, or phase of the moon. :)

    At least I hope we are agreeing that the concept of "session management" has absolutely no effect on one's overall EV? That you either play the game with an advantage and have a good chance of coming out ahead, or you play with a disadvantage and have a good chance of coming out broke.
  • I agree that session management has no effect on one's overall EV. Assuming you are ever going to play blackjack again, sessions are meaningless from an EV standpoint (although are significant from a getting tired/number of mistakes standpoint).
  • If you flip a coin a million times there is a small probability that heads will occur every time and equally so for tails. No matter how small that probability
    is, given enough time, it will occur.

    If you play against the HA in BJ and win $1000 betting a flat $10, you have done the exceptional and the probability of doing that is low. However, the
    probability that you will lose that 1000 and then some is higher. The house
    wins more hands, his streaks are longer and more frequent than yours and
    for that reason setting win goals is an illusion. When you stop at 1000, how
    do you know that is all you could have won? Say 1500 or maybe even 2000.
  • FC:

    Of course sessions make sense for a lot of different reasons. The classic I gave to make sure you don't lose all your bankroll the first day of a week trip, assuming we are talking a "pleasure trip" rather than a "business trip". Or if you get tired. Or hungry. Or your wife wants to see the desert, or Hoover Dam, or Oatman, or Route 66, or Lake Las Vegas, or ...

    Just not to limit losses and maximize winning sessions, however, as some have suggested...
  • Ray said:
    If you flip a coin a million times there is a small probability that heads will occur every time and equally so for tails. No matter how small that probability
    is, given enough time, it will occur.

    If you play against the HA in BJ and win $1000 betting a flat $10, you have done the exceptional and the probability of doing that is low. However, the
    probability that you will lose that 1000 and then some is higher. The house
    wins more hands, his streaks are longer and more frequent than yours and
    for that reason setting win goals is an illusion. When you stop at 1000, how
    do you know that is all you could have won? Say 1500 or maybe even 2000.

    Who cares what you could have won?. What counts what you did win.If you buy in for $500,and double that to $1,000,you are ahead of the curve.Stopping play then insures you have made a $500 profit.
    When I buy a stock,I set sell prices. If it goes to that price,I sell. If I buy for $20 and sell for $50,who cares if it goes to $75 next week.I certainly don't.
    Walking away from the table when I've reached my immediate goal for the day insures that I leave wit the money I wanted to leave with.Why worry about some hypothetical "coulda". Its just as likely that I will lose money as make money in the immediate short term,so I walk away happy,and enjoy the rest of my day. Now,if my favorite thing in the world was to sit in a loud,smokey casino and talk to strangers,I'd stay. But cards are a means to an end,not the end.
  • I've always liked the Stock Market analogy to gambling in general. But I remind the players, that analogy only holds true for OPTIONS, as there is a time vigorish to be paid... sort of a "house edge" if you will.

    Buying and selling STOCKS is not the same... but is the same as far as buy/sell (enter/quit) is concerned. No house edge in buying/selling stocks... but education and timing are factors.
  • Investors- I compare the serious blackjack player to the individual who
    invests for the long-run. This individual has history on his side and can look
    to the future with confidence. He understands that bulls, bears and other
    factors are to be expected. Your 401K is just one example out of many.

    The serious blackjack player does not allow the feel good situations to affect
    his thinking. He knows full well that his results is a function of time and num.
    of hands played. How else could an average edge of .75 produce an expected
    profit? The mystics would have you believe that you can in some way alter
    or enhance the results via goals, limits, schedules, etc. I think not........

    Frequent traders have their advantages/disadvantages, but IMHO those
    methods do not compare, in any way, to the ever changing relations in BJ.
  • Ray,
    One one hand you saythat quitting when you've reached a specfic number is stupid because you might have won more money by playing more,yet then you say that the longer one plays,the more the house will win.
    You harp on the fact that if I continue playing after I've reached a goal that I might win even more.Yet the reality of it is that if I continue playing,the chances that I will lose are higher than that I will win.
    If I walk away from today a $500 winner,next time I sit down I have the exact same odds of winning as if I had walked away a $500 loser,don't I?Except that I'm $1,000 richer.

    What I don't understand is how YOU decide when to walk away from a table. You don't have set win limits. Do you set loss limits? Time limits? Or is it just seat of your pants,I quit when I quit or go broke?If you set a three hour time limit,couldn't you argue that you are giving up all the profits you might have made in hour four?
    I find setting achieve short term goals,in life and in BJ helps me accomplish them.
  • Let's understand the specifics. The longer you play as a basic strategy
    player, the greater your chance to lose. Quite the opposite for a counter.
    I quit when I have a time constraint. I quit when I'm tired enough to where
    it affects judgment. That's about it.

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