Quote:weaselmanIf a hundred thousand players make a hundred thousand bets, that's your "long run".

What you are missing is that your "long run" does not have to be constructed only of bets, made by you. If that large devastating loss is supposed to happen "in the long run" when you use martingale, there is no reason it won't happen to you on your very first bet.

What you are missing is that I am talking about individual players. As I said, the casinos and the players, taken as aggregates, play in the "long run"; individual players do not. I am not advocating progress-on-a-loss betting, by any means. And I have pointed out exactly that same fact -- that the big loss can occur at any time.

Quote:weaselmanA given player may get lucky for some period of time. Or he may get unlucky. There is no way to tell for sure which way your luck will swing, but because it is a -EV game, the distribution is shifted to the left, meaning it is more likely, that you'll get unlucky than that you'll get lucky.

That's not true -- a player is just as likely to experience positive variance as negative variance; it's just that the mean of the distribution is on the losing side of the zero point. So, for any given degree of variance, the losses are greater than the wins.

Quote:weaselmanThe simple truth is that, long run or not, you are more likely to lose than to win, and the longer you play the more likely you are to lose, and the larger bets you are making, the more is the amount you are likely to lose.

That's the simple truth, all right, but it is too simple for my tastes. It needs to be supplemented with more information about likely outcomes. What I have been objecting to is mkl's repeated incorrect statements that "the more you bet, the more you WILL lose" (emphasis mine).

There is no specific definition of "long run", but we can define different degrees of likelihood that a player will be ahead after different numbers of bets. I did a post a while back about where the ev equals the standard deviation, which means a player needs to have experienced one standard deviation's worth of positive variance in order to offset the expected loss. The probability of this is about .16. When enough bets have been made that the SD is half the ev in magnitude, then the probability of a player breaking even or better is down to less than .03. However, let's take your 100,000 players; at the point where |ev| = 2 SD, we'd still expect over 2000 of them to be even or ahead.

Cheers,

Alan Shank

Woodland, CA

Quote:weaselmanNot that it matters much for anything, but it's not assymptotic. It fluctuates around the expected value, crossing it many times back and forth. As the number of experiments grows, the amplitude of fluctuations becomes lower.

As an absolute number, I meant, since whether it is positive or negative in relation to the mean at any one point is irrelevant.

Quote:mkl654321Oddly enough, YOU seem to have blinders on when I talk about the "long term", even though I'm sure you understand the term. Long term does not mean a billion billion outcomes. It means enough outcomes to smooth out the effects of variance, with the goal of approaching expected value.

For craps players, approaching expected value is certainly not a "goal". You claim to be a +EV player, presumably not in craps; that is a different story entirely, since the ev is on the plus side. Most craps players do not play enough over their lifetimes to "smooth out the effects of variance" to the extent of having almost no chance of being even or ahead.

Quote:mkl654321For me, that may mean 1000 hours, or 800,000 hands, of video poker. When I say I regard only the long term as meaningful, it means I will NOT stop and assess my results before I reach that long term perspective--I will not Singerize, and stop and assess my results every 400 hands.

Why not? How would that hurt you? Your results for the first 400 hands are "in the books"; the expectation going forward for the next 799,600 hands does not change, unless you believe, as many do, in the "cosmic rubber band" pulling your results back toward the mean. Here again, you seem to assume that if someone assesses his/her results, that means he/she doesn't understand what they mean and don't mean. If I plan to flip a coin 1000 times, and the first 10 flips are all heads, those ten heads are "in the bank", and my expectation for the entire 1000 is now 505 total heads, not 500.

Quote:mkl654321

I'm sure there's a mathematical expression of the long term, in that an increasing number of trials causes results to converge on the mean to such an extent that the mean is, for all intents and purposes, reached--it's not unlike the sum of an infinite series approaching 1. Of course I understand that those results are virtually certain to not fall ON the mean, but as a practical matter, for casinos and APs, close is good enough.

I am not talking about casinos and APs, as I have pointed out several times. "Long term" as far as I'm aware does not have any specific definition, mathematical or not, but a degree of "long termness" can be defined by the ratio of the ev to the standard deviation, as I have suggested on this or another thread.

Cheers,

Alan Shank

Woodland, CA

Quote:goatcabinI am not advocating progress-on-a-loss betting, by any means. And I have pointed out exactly that same fact -- that the big loss can occur at any time.

What's your point then?

Quote:That's not true -- a player is just as likely to experience positive variance as negative variance; it's just that the mean of the distribution is on the losing side of the zero point. So, for any given degree of variance, the losses are greater than the wins.

What's "not true"? You said the same thing I did.

A small correction is that the losses are not only greater than the wins, but also more frequent, since you are correct that "positive variance" is as likely as "negative variance", but some of the former is still a loss, because EV is negative.

Quote:

That's the simple truth, all right, but it is too simple for my tastes. It needs to be supplemented with more information about likely outcomes.

Well, the EV of the game gives you that information, yet you keep objecting to it being looked at.

Quote:There is no specific definition of "long run", but we can define different degrees of likelihood that a player will be ahead after different numbers of bets.

Yes, and the more bets you make, the less that likelihood is. That's exactly mkl's point.

Once again, you seem to be making a point, and disputing it at the same time.

Quote:weaselmanWhat's your point then?

I am objecting to mkl's assertion that "you will lose". Here is his statement: "The more you bet, the more you will lose (odds bets excluded)."

That is clearly incorrect.

Quote:weaselmanWhat's "not true"? You said the same thing I did.

A small correction is that the losses are not only greater than the wins, but also more frequent, since you are correct that "positive variance" is as likely as "negative variance", but some of the former is still a loss, because EV is negative.

No, I didn't say the same thing. Again, quoting will clarify: "There is no way to tell for sure which way your luck will swing, but because it is a -EV game, the distribution is shifted to the left, meaning it is more likely, that you'll get unlucky than that you'll get lucky."

You now say yourself that positive variance is just as likely as negative variance, and that was my point. I equate "getting lucky" with "experiencing positive variance", not necessarily with being ahead.

Quote:weaselmanWell, the EV of the game gives you that information, yet you keep objecting to it being looked at.

Not at all. It is an important piece of information, but it is not the only one. The variance (standard deviation) is equally important in determining what chance a player has of coming out ahead for any given number of bets. It's the ratio of ev/SD that tells you how lucky you have to be (i.e. what degree of positive variance you have to experience) in order to overcome the expected loss. I have NEVER objected to the ev "being looked at".

Quote:weaselmanYes, and the more bets you make, the less that likelihood is. That's exactly mkl's point..

No, it is not. Read his post again, please. It's an absolute statement "you will lose", not couched in terms like "the longer you play, the higher the probability you will lose". That is what I have been objecting to, on this and other threads.

Cheers,

Alan Shank

Woodland, CA

That just might be a key point of disagreement. Do you often hear people say, " I was really lucky in the casino today; I (a) lost money, (b) lost less than I expected to, (c) lost less than I did yesterday." I suspect most people would describe that session as just not being as unlucky as it might have been.Quote:goatcabin... I equate "getting lucky" with "experiencing positive variance", not necessarily with being ahead..

I tend to agree that positive deviation from expectation is an indication of better than normal luck, even if a loss is involved, but I think this may be a point of disagreement in many cases.

As a side matter, I see that you use an expression that I formerly used and decided was incorrect: "experiencing positive variance". Isn't variance by definition a positive number? I now try to refer to positive deviation -- is there an issue of correctness here? I'm not really sure.

Quote:DocThat just might be a key point of disagreement. Do you often hear people say, " I was really lucky in the casino today; I (a) lost money, (b) lost less than I expected to, (c) lost less than I did yesterday." I suspect most people would describe that session as just not being as unlucky as it might have been.

I tend to agree that positive deviation from expectation is an indication of better than normal luck, even if a loss is involved, but I think this may be a point of disagreement in many cases.

As a side matter, I see that you use an expression that I formerly used and decided was incorrect: "experiencing positive variance". Isn't variance by definition a positive number? I now try to refer to positive deviation -- is there an issue of correctness here? I'm not really sure.

By "positive" I mean in the direction advantageous to the player. Yes, variance is always positive in the mathematical sense, since the differences are all squared, which is just a way to get an absolute value, or magnitude, of differences from the mean. Also, I often use the term "variance" not in its formal meaning but as a general term for a degree of volatility. "Positive deviation" sounds good, too -- less chance of confusion. Thanks.

Cheers,

Alan Shank

Woodland, CA

Quote:goatcabinI am objecting to mkl's assertion that "you will lose". Here is his statement: "The more you bet, the more you will lose (odds bets excluded)."

That is clearly incorrect.

If he added "likely" after will, would that be all?

Quote:

No, I didn't say the same thing. Again, quoting will clarify: "There is no way to tell for sure which way your luck will swing, but because it is a -EV game, the distribution is shifted to the left, meaning it is more likely, that you'll get unlucky than that you'll get lucky."

You now say yourself that positive variance is just as likely as negative variance, and that was my point. I equate "getting lucky" with "experiencing positive variance", not necessarily with being ahead.

So, that's where we disagree then.

Not at all. It is an important piece of information, but it is not the only one. The variance (standard deviation) is equally important in determining what chance a player has of coming out ahead for any given number of bets. It's the ratio of ev/SD that tells you how lucky you have to be (i.e. what degree of positive variance you have to experience) in order to overcome the expected loss. I have NEVER objected to the ev "being looked at".

No, it is not. Read his post again, please. It's an absolute statement "you will lose", not couched in terms like "the longer you play, the higher the probability you will lose". That is what I have been objecting to, on this and other threads.

Cheers,

Alan Shank

Woodland, CA

Quote:mkl654321As an absolute number, I meant, since whether it is positive or negative in relation to the mean at any one point is irrelevant.

it's still not asymptotic by the meaning of the word.

Quote:goatcabinI am objecting to mkl's assertion that "you will lose". Here is his statement: "The more you bet, the more you will lose (odds bets excluded)."

That is clearly incorrect.

so, if he added "likely" after "will", you would agree then?

Quote:

No, I didn't say the same thing. Again, quoting will clarify "There is no way to tell for sure which way your luck will swing, but because it is a -EV game, the distribution is shifted to the left, meaning it is more likely, that you'll get unlucky than that you'll get lucky."

You now say yourself that positive variance is just as likely as negative variance, and that was my point. I equate "getting lucky" with "experiencing positive variance", not necessarily with being ahead.

That's simple misunderstanding then. I used "get lucky" as a synonym to "win". If I lose, I don't consider myself lucky even if I lost less than EV.

With this correction, do you agree that we are saying the same thing now?

Quote:Not at all. It is an important piece of information, but it is not the only one. The variance (standard deviation) is equally important in determining what chance a player has of coming out ahead for any given number of bets.

Not really. If the distribution is symmetric, increasing SD raises your chances of winning as much (actually, slightly less) as your chances of loosing. Yes with a huge SD you can win a lot, but you can lose a lot as well, so on average, it's the same.

Quote:It's the ratio of ev/SD that tells you how lucky you have to be (i.e. what degree of positive variance you have to experience) in order to overcome the expected loss.

It's misleading though for the reason I mentioned above. If SD is large, you may not need as much "luck" to win, but at the same time it doesn't take much "lack of luck" to go bankrupt either. If you consider both possibilities, you'll have to conclude that you need about the same total amount of luck.

Put it another way, consider a single bet with extremely large SD. You can win a lot with relatively higher probability, that's correct. But at the same time, you can lose even more with even higher probability. And, if that happens, you are going to need to make many more subsequent bets to dig you out of the hole (again, risking to lose even more on each of them). You may need only a little bit of luck to win one bet, but overall you need a lot of it to come out ahead.