Sorry about the threadjack SenorBeef!
Or, continuing along this line, think of it this way. You say that it should even out, but at what pace? If you insist that 300 straight tails will even out after 1000 flips, you’re implying a different set of result than saying it will even out over 700 – but how could the arbitrary plan for the number of flips that you have in your head affect the results of the next 300 or 400 flips?
The truth is that it will even out, if you give it enough time; that is, if you execute trillions upon trillions of flips. Sooner or later, there will be a comparable run of heads, but you need the trillions and trillions of flips before the incredibly unlikely start will probably have been counterbalanced by an incredibly unlikely opposite result. Does that make sense to you?
Getting back to this for a moment, I just finished testing the hypothesis I laid out in (2), above; i.e. that I should be measuring the results after two or more losses against a 5-9 record instead of a 5-11 record. To test it, I looked at the record of every 9-7 team since 1978 in games following two or more wins. If (2) is correct, then instead of performing like you’d expect a 9-7 team to perform in that set of games (with a .563 W%), they would actually have be slightly below .500 following two or more wins – .500 because we would expect them to perform like a 7-7 team, and slightly below because they’d be somewhat more likely to have a road game following two or more straight wins. If the effect was identical, in fact, we should expect the 9-7 teams to have a W% of .475 in these games (take the percentage difference between a 5-9 record and the performance of 5-11 teams following two or more losses, and apply it to a .500 record (7-7)).
As it happens, their winning percentage in these games is .474. 
In my mind, this settles it. Teams on a losing streak are no more likely to win their next game then they would otherwise be expected to given their record.
I know this isn’t a very thorough explanation, so I expect to answer some questions about it tomorrow.
Ok, Esoteric, I want to take one more try, because I noticed that your location is Las Vegas, and I want to make sure you don’t take your theory to the blackjack tables.
Probability goes forward, not backwards. After the first of 1,000 flips, you’re no longer measuring the likelihood that the coin will land heads x number of times in 1,000 flips; you’re measuring the the likelihood that the coin will land heads x number of times in 999 flips. The likelihood of a given result over 1,000 flips is now irrelevant, because it can’t help you.
Or, answer this: By what physical process do the first 300 flips affect the next 700? If 500 out of 700 flips are going to turn up heads and it’s not a fluke, then how is the coin manipulated into landing heads so often? Very important question.
Also, answer this: If what you say about probability is true, why haven’t you the world’s richest blackjack player? The dealer will only hit a 20 or 21 a certain percentage of the time – say, for the sake of argument, 10 times out of every 25. If he happens to hit a 20 or 21 10 times in a row, and if what you say is true, shouldn’t you bet the max the next 15 hands, and expect to win much more than your fair share?
Or, if for some reason you can’t stomach that example because it doesn’t have a “set, defined probability” (not that I agree that that matters), then switch to roulette. Every number on the wheel should come up 1 time out of 38. By your logic, the numbers that hit repeatedly in a short span are now very unlikely to hit for the next 76, or 114, or 142 spins, because the wheel needs to even out. By taking note of which numbers are unlikely to hit for this reason and avoiding them, you could easily tip the odds in your favor and make millions of dollars if you put in enough hours. Why don’t people do this?
I really don’t mean to pester you, and I hope I haven’t come off as rude or combative. It’s just that it’s so rare to come across a disagreement in which I know the right answer and the other guy doesn’t. If I can’t convince you of this, I may not be able to convince anyone of anything.
Wow, this thread has been busy since I was last here.
I’ve never heard of a bookmaker ever factoring that sort of thing to evaluate the expected value of games. Not saying it doesn’t happen - I don’t know any handicappers, but it seems somewhat unlikely.
The reason is that there’s no “true line” for the game, as you say. You can’t objectively calculate the probability of a certain team winning on a certain weekend. There are far too many unpredictable factors. So, while in, say, roulette, you can objectively say “okay, we pay 36:1 on a 38:1 shot, so each bet is +5.26% EV for us”, you can’t do the same for football. You can take your best guess, but there are no true odds.
Sports books balancing the action isn’t just about reducing variance - it’s the ideal situation for them. Trying to predict a “true line” for a game could blow up in their faces and cause them to offer bets that are actually -EV for them. By balancing the action, they’re no longer attempting to set odds to the inherently unpredictable in terms of their own EV - they’re essentially just charging a service fee on each bet.
I disagree - we’re not talking about a random, independent event. We’re talking about a competition wherein human psychological factors play a large role. I’m not saying I agree with the guy, but what he says isn’t absurd. Having a win or loss streak can affect the mental state of the players, which can certainly affect the games.
We may be in fundamental disagreement, or I may not fully understand you. You seem to be saying that the handicappers think Ari will win, and the det +1 line will get all of the idiots to bet that. But like I said - it’s generally bad for the book if the action all goes one way, so they wouldn’t want to set a line that would encourage one-way betting, even if was in the personal view of the handicapper the wrong bet. Handicappers don’t attempt to predict the games - they attempt to predict the public’s reaction to the line. Often those things correlate - if some team’s star player is injured, it both makes them less likely to win, and also makes the public less likely to bet on them, so the line adjusts. But the line adjusts because of the public perception, not the actual changing odds of the team winning the game in the bookie’s view.
To put it another way, even if the handicappers personally thought Detroit would completely stomp Arizona, but there was a legion of millions of Arizonans who reliably bet on their team no matter what, then the line would shift and give Detroit even more points, even though the handicappers thought Detroit would win. Because they’re attempting to find the point where all action goes halfway, and the hordes of Ari homer bettors would drive the line in Detroit’s favor to encourage action on that side.
This perplexes me. Are you suggesting that our current understanding of probability is fundamentally wrong, and that there’s something else at work that we’re incapable of understanding?
Anyway, I’m sorry Esoteric, but Varlos has been entirely correct. You confuse me because in one statement you seem to acknowledge the nature of random, independent events and then in the next statement you contradict it.
I won’t explain entirely where you’re going wrong, as Varlos is doing a good job, but I will ask a few questions.
What force exactly interacts with the coin to ensure that it complies with your sense of probability? If a coin is flipped 10 times and comes up heads, and therefore in your view is more likely to come up tails to balance it out, something must actually interact and influence the coin to enforce this result. What, exactly?
When you say if you flip a coin 1000 times, and the first 300 come up one way, that it’s more likely that the other 700 come up the other way - specifically, you said, in roughly a 200-500 ratio - how does the coin know that your trial is 1000 flips? What happens if you have 300 flips one way, and then decided that instead it would only be a 500 flip trial? Now it’s impossible for the coin to make up the ground. Your explanation seems to require the coin to know how many times it will be flipped.
Let’s say you have a coin flipping machine that strums along and flips a coin every 5 seconds 24/7. You observe the machine after it’s been running unattended. You notice 20 heads in a row. That’s odd, you think - it will have to come up tails some soon. But what if, before you started observing it, it had flipped tails 100 times in a row? Now you have a streak of 100 tails followed by 20 heads. Since you started observing at the point that the heads streak started, you view it as having tails due. But since tails was just flipped 100 times, unbeknownst to you, there are a whole lot more heads needed to balance it out. What, now, dictates which side is due? Your observations, or the unattended streak?
Doesn’t seem so important to me. We’re talking about statistical anomalies, which, I think we’re both in agreement, are bound to correct themselves over a larger sample size, given the defined probability. The problem is, and I think a far more effective argument against my position than the ones you’ve given, is that the larger the sample size, the more inconsequential, mathematically, the difference between heads and tails. A 52/48 split is absolutely plausible, and if we flipped a coin 100000 times, that would result in 52000 heads and 48000 tails. That means that even if the first 200 were all heads, over the next flips you STILL flipped more heads than tails, and yet the trend reversed itself. I don’t know, did you say that? That’s an argument I absolutely can’t counter. End of fanciful, devil’s-advocate-style theory.
You have to know the answer to this, right? I’ve never played blackjack, so maybe I’m wrong, but isn’t it the same as other card games where drawn cards aren’t immediately recycled into the deck? Doesn’t that mean that every card drawn changes the probability of other cards being drawn from the same deck? Afterall, there are only 4 of each card, so drawing one affects the chances of drawing another, right?
Isn’t this is EXACTLY how you “count” cards in blackjack (proven to foster an amazing advantage in blackjack)? You bet low until you have a statistical advantage over the house, and then up your bets and rake in the dough. Or am I wrong about that? Either way, the reason I don’t do it is because I don’t want to risk a beating or jail time, casinos don’t generally like this stuff. Not exactly a good counterpoint on your part.
[QUOTE=VarlosZ]
Or, if for some reason you can’t stomach that example because it doesn’t have a “set, defined probability” (not that I agree that that matters), then switch to roulette. Every number on the wheel should come up 1 time out of 38. By your logic, the numbers that hit repeatedly in a short span are now very unlikely to hit for the next 76, or 114, or 142 spins, because the wheel needs to even out. By taking note of which numbers are unlikely to hit for this reason and avoiding them, you could easily tip the odds in your favor and make millions of dollars if you put in enough hours. Why don’t people do this?
Because in this scenario, much like dice, you can be right and still lose. If I know 23 won’t come up as often and start betting around it, I may start betting on 12, which hasn’t come up at all, but still lose because 29 came up, which also hasn’t come up often. If someone rolls a die five times and gets 6, 6, 3, 6, 6, I may think 6 won’t likely come up as often anymore and bet on 2, but be wrong because 4 came up. Right, and yet I lose my money anyway. The reason I singled out coins is because if I’m right, I’m right.
I know how probability works. This isn’t because I “don’t know the answer.” I can’t remember, have I actually said that anything you or Ellis said was wrong? I see myself arguing against a very simple and common mathematical truth and exploring some possible counter mechanism to probability. It isn’t that I don’t know that coin flips are independent of one another, I know this (I said as much to prevent this sort of extended discourse). I was stipulating that at some point, you have to step back and say, “Wow, he just flipped heads nine times in a row. It’s 1 in 1024 that someone flips a coin heads ten times in a row, pretty unlikely!” I think there might be something to that. Even if the next flip is still 50/50. And I think every single person here does this, whether they know it’s stupid or they don’t.
But really, the whole pseudo-altruism thing is a little condescending. I can’t imagine you much care for my betting habits or my likelihood to blow my money on a foolish and unfounded theory about probability affecting itself. I was willing to stay and play around with a theory that goes against what is absolutely mathematically true, but come on, this is going a little far! I mean, I picked the 0-8 Rams to cover against one of the hottest teams in football, and this is more shocking than that? Really?
This is a lot like that cat in that box, isn’t it? Wait, I know the answer to this, hold on.
Actually in this case, tI would take the tails as the 21st flip for the reasons I said before, mathematically correct or not. A .0000005% chance to flip 21 heads in a row, very unlikely. Just like I would probably pick heads from about the 8th flip of the 100 on. I can’t imagine a normal person seeing someone (not cheating, mind) flip 20 heads in a row, wouldn’t pick tails. Maybe I’m completely insane, I wouldn’t pick tails.
My latest reply to VarlosZ got a little mangled at the end, and one of my replies to his questions was caught in the quote box. I missed my edit timer, sorry if that becomes confusing.
I’ve heard from several sources, including people who have worked for Vegas sports books, that balanced action is not always the goal. From here:
Not the most authoritative site, I know, but it’s just meant as an example of what I’ve heard elsewhere.
Well, theoretically there is (i.e., there is always a line that will be covered by the favorite exactly 50% of the time), it’s just that you can never be sure where it lies. And even though the books might pick wrong when they favor one side over another, they are much better informed than the general betting public, and tend to have a much better idea about the probability of a given team covering a given line.
Don’t be so sure (see posts #37 and #43). Besides, I got the impression that he was saying basically the same thing as EsotericEnigma – i.e., that a team is unlikely to lose that 4th straight game, specifically, because a four game losing streak is rare.
Heh, I see we’re thinking along the same lines – I asked him those same questions.
Ok, but this isn’t what you’ve been saying. You did mention something about knowing that coin flip results are independent of each other, but every other thing you’ve said here contradicted that statement. Are you just playing devil’s advocate? It’s fine if you are, but it’s better if you say so up front.
If not, then saying that coin flips are independent is completely inconsistent with this:
It’s impossible that both of those statements are true. Could you explain how the statements are consistent? Alternately, could you say which statement you agree with?
I was joking about your hitting the blackjack tables. I’m sorry that I didn’t make that clear.
I’m sorry, but it is an important question, and you didn’t address it directly. If the coin is more likely to come up one side than the other over a set number of tosses, there must be some physical (not abstract) process that causes it to do so. What is the physical force that acts on the coin to make it come up tails?
I don’t agree that your objection to my blackjack analogy makes it invalid, but that’s fine. I don’t think your objection could apply to my roulette question; could you explain how that is meaningfully different from coin flipping?
Yeah, you did. I phrased them a little differently and put them all out by themselves to encourage him to ask them to himself.
It’s actually rather common for people to have a bad intuitive grasp of probability. It seems like it’s a rather small group of people who can intuitively understand what random, independent events are.
Edit: I don’t mean this condescendingly. I genuinely posed those questions trying to get Esoteric to evaluate his views. There’s something about the human brain that makes people intuitively grasp at gambler’s fallcy type stuff.
Anyway… back to further helping me blow my money, does anyone have any opinion on the Phi @ Was (-3) game? I don’t know a whole lot about the NFC East. Neither Philly nor Washington has looked good recently. The reason I ask is that the cost of picking Washington across the spread has been going down steadily because everyone is betting Philly. It was -110, then -105, then even, and now it’s +105 to bet Washington -3. If it keeps going like this I’m tempted to take it.
Like I said, I could map which five numbers come up the most and bet away from those numbers. I could be right 100% of the time on my next few bets (that those mapped numbers won’t come up) and still lose because I picked the wrong number. This is why it wouldn’t work. It’s like my die example, which I think was pretty clear. If I’m positive that a number won’t come up, I won’t bet that number. But I could be right that it won’t come up and lose because a different number than the one I picked came up. Unlike in coin flipping, where if I’m certain that a heads won’t come up, if I’m right, I’m right. There’s only two options. It’s vastly more difficult to play probabilities when you have even 6 options, or 38, or 1.5 million.
As far as blackjack goes, that analogy was absolutely, completely invalid. I know I’ve been grasping for straws from the beginning with some of the arguments I’ve made, but you absolutely can’t compare blackjack to coin flipping. The simple mechanics of the probabilities are different. I mean, that is if the decks aren’t reshuffled after every hand. There have been well documented examples of people (MIT grads) who have used card counting in blackjack to make fortunes, and to my knowledge, card counting works by tracking which cards have been played and varying your bets based on a statistical advantage over the dealer. Casinos don’t allow this, which is why I wouldn’t consider doing it.
I never, ever even implied that what I was arguing about coins even remotely transferred to the NFL, or sports betting. In fact, I know of at least once where I said the exact opposite. I thought I was really careful not to get the two confused, how could you possibly say this? As far as I’m concerned, there is no such thing as probability in the NFL, and if there is, it can’t possibly be mathematically explained. There are too many variables, many of which aren’t ever known to the general public.
If you just placed one bet, sure you could lose. But if knew which numbers to avoid, started with a large enough bankroll (a few hundred dollars at the low-limit tables), and, most importantly, you kept on betting, you would be guaranteed to make a profit. There would be no more risk for you than there is for the casino. So why wouldn’t you do it?
I wasn’t saying that you were talking about football, I said that the person I was referring to seemed to be making the same kind of mistake as you with regard to probability.
I’m still very curious about your answers to the other questions in my last post:
God… the Dope can’t get away from its pet arguments, can it?
While Varloz isabsolutely right, theoretically, if you flipped a coin 50 times and it cames up heads every singletime, I’d definitely toss money down on it coming up Heads again. There’s no such thing as a result being ‘due’, but there sure are funny coins out there.
Heh, my system says that’s a head-scratcher. The line is 3, and it’s spit out a line of 3.1.
According to this, Washington is the pick of the mass public. OTOH, this indicates that you’re right about the line moves favoring the Skins. One way to look at these two pieces of information: the mouth-breathers are all over Philly, while the sharp bettors are backing Washington. I don’t know if that’s true or not, but that’s what the information suggests to me. Maybe.
If the coin came up heads 50 times in a row, I think the smart move is not to bet, since there’s a good chance that the game is rigged and you can’t win. If you’re not worried about that, though, yeah, definitely heads.
YES! I can’t wait for the Boys to thrash the Giants and crush their hollow win streak.
Whenever I hear arguing over consecutive coin flips I think of Rosencrantz & Guildenstern Are Dead.
… if The Boys can do like they did last week in Philly and play the way they’re capable of. Don’t be doin’ any more of that Monday Night in Buffalo, inept, dinkin’ around. Btw, how long’s it been since you’ve seen an NFL stadium (Philly) that empty near game’s end?
The Giants, while much improved since Dallas beat them in their first meeting, are still I think #2 in the NFC East. I hate that Dallas makes the long trip up two weeks in a row, but am still looking for another W to notch.
Heads!