winning and losing streaks

[bigboydan]

we have just recently seen alot of these streaks in the past week or so. i personaly can't bet against a hot or cold streak myself.

my question to you guys is this... at what point do you start betting against a streak, if at all 4,5,6,7,8,???

[Dark Horse]

Even if you could flip a coin at 70% heads, it would still be hard to do so ten times in a row: 0.7x0.7x0.7x0.7x0.7x0.7x0.7x0.7x0.7x0.7 = 0.028. In other words, it would work only 1 in about 36 streaks for someone with a 70% winning percentage. So, at least mathematically, there is definitely something to say for betting against streaks. Especially if you make it a chase.

What you need to know is the person's (or system's) winning percentage. If it is 60%, the chance of five straight wins is bigger than of five straight losses: 0.6x0.6x0.6x0.6x0.6 = 0.078. The chance of a 6th straight win is not 60%, but 0.6x0.078 = 0.047. So about 1 in 22 streaks will reach 6 straight wins for a 60% bettor. The next win is 0.6x0.047 = 0.028. That is, 1 in 36 streaks will reach 7 wins in a row.

By the way, I could be missing something. lol. But it sure is an interesting subject for gamblers.

What is the chance of a 75% system to lose 3 in a row? 0.25x0.25x0.25 = 0.016. A chance of 1 in 64. No wonder we sometimes feel dejected. But it would be best to increase the bet size, because the chance of losing four in a row is 1 in 256. This would only work if you had very solid systems.

[slacker00]

BBD, I think you need to clarify you definition of "streak" a little bit. Are you talking about a capper picking ATS, or a team covering a spread in consecutive games, or what exactly?

But I agree with Dark Horse in the coin flipping example. If you've flipped heads 10 times in a row, the odds are still the same on the 11th flip, no reason to put an inordinate bet on heads for the 11th flip, all else being equal. Maybe we need to page Ganchrow for an elaborate mathematical explanation!

[bigboydan]

BBD, I think you need to clarify you definition of "streak" a little bit. Are you talking about a capper picking ATS, or a team covering a spread in consecutive games, or what exactly?

just a straight up wager aka a money line type wager.

[slacker00]

just a straight up wager aka a money line type wager.

Man, (duh, me) it's 4 am here. So you're just talking about a particular team's W/L streak.

I'd be inclined to bet against a team's winning streak actually. Seems like the pressure of thre streak gets to be too much, plus the lines start to get bloated as the team becomes "overrated". My example would be the Colts last year when they started getting into double digit wins in a row. The burden of the streak was a major distraction, IMO, and the lines got bloated as well. I'm mainly talking about high profile sports though. My theory kinda breaks down in some league like the WNBA where nobody really knows or cares if the Comets (or whoever) are on a 12 game winning streak or whatever.

Losing streaks are trickier. There is pressure on a team to break a losing streak, which can be a distraction. But, a team also becomes underrated because of the streak sometimes. Sometimes a losing streak can be due to factors such as injuries or whatever, that a team is going to continue to have. In total, a losing streak has to be examined moreclosely to understand the nature of the streak, then bet accordingly.

In the end, I don't know if streaks should be a huge factor in one's wagers, but certainly something to consider. I'd be more prone to examine the underlying reasons for a streak and use that information rather than only looking at the streak itself.

[Ganchrow]

If you've flipped heads 10 times in a row, the odds are still the same on the 11th flip, no reason to put an inordinate bet on heads for the 11th flip, all else being equal. Maybe we need to page Ganchrow for an elaborate mathematical explanation!

You said it just fine without me.

[Ganchrow]

Even if you could flip a coin at 70% heads, it would still be hard to do so ten times in a row: 0.7x0.7x0.7x0.7x0.7x0.7x0.7x0.7x0.7x0.7 = 0.028. In other words, it would work only 1 in about 36 streaks for someone with a 70% winning percentage. So, at least mathematically, there is definitely something to say for betting against streaks. Especially if you make it a chase.

What you need to know is the person's (or system's) winning percentage. If it is 60%, the chance of five straight wins is bigger than of five straight losses: 0.6x0.6x0.6x0.6x0.6 = 0.078. The chance of a 6th straight win is not 60%, but 0.6x0.078 = 0.047. So about 1 in 22 streaks will reach 6 straight wins for a 60% bettor. The next win is 0.6x0.047 = 0.028. That is, 1 in 36 streaks will reach 7 wins in a row.

You're confusing ex-ante (prior to the start of the streak) and ex-post (after the streak has begun) expectations. Indeed the probability of winning 6 straight games if the probability of winning a single game is 40% and all games are independent is 60%^6 ≈ 4.7%. However, just as slacker says, the probability of winning 6 straight independent trials given that you've already won 5 is still that very same 60%. The key is of course the assumption of independence.

What is the chance of a 75% system to lose 3 in a row? 0.25x0.25x0.25 = 0.016. ... But it would be best to increase the bet size, because the chance of losing four in a row is 1 in 256.

Again, this does not stand to reason mathematically. Probability has no memory. There's no such thing as being "due" a win when it comes to independent events. Of course you may well argue that unlike tosses of a coin or spin of a roulette wheel, the outcomes of a single team's consecutive games are NOT independent.

[slacker00]

But I agree with Dark Horse in the coin flipping example.

I change my mind. After reading Ganchrow's explanation, I see Dark Horse is incorrect in his post. I think I read Dark Horse's post too quick at 4am, without realizing that I was actually disagreeing with what was actually written. Mathematically, there's not enough information inherent in the streak itself to justify raising or lowering a bet size. It's probably a corrollary of why the Martingale system doesn't work.

[BuddyBear]

BBD, I think you need to clarify you definition of "streak" a little bit. Are you talking about a capper picking ATS, or a team covering a spread in consecutive games, or what exactly?

But I agree with Dark Horse in the coin flipping example. If you've flipped heads 10 times in a row, the odds are still the same on the 11th flip, no reason to put an inordinate bet on heads for the 11th flip, all else being equal. Maybe we need to page Ganchrow for an elaborate mathematical explanation!

umm...there is what is known as a validity issue here. Flipping a coin and baseball games (picking winners) are not even remotely the same thing so the comparison is of little value.

Slacker you are 100% right about the coin example but the thing that you fail to mention is that flipping a coin is what in statistical jargon is known as an "independent event" Basically it means that the outcome of the previous event has absolutely no influence on the outcome of the subsequent event. So flipping a coin--assuming it is not weighted--is an independent event.

Baseball games are not independent events in the sense that we as gamblers should not operate under the assumption that the outcome of the previous game(s) has no influence on the game....it does...the degree of the impact is debatale but you shouldn't make the comparison between coin flipping and baseball games outcome...

Now point spreads and coin flippping may be a different issue as I am more torn on that but I would lean that covering a point spread is NOT an independent event but someone would have to provide some justification as to why they are independent....

[Dark Horse]

You're confusing ex-ante (prior to the start of the streak) and ex-post (after the streak has begun) expectations. Indeed the probability of winning 6 straight games if the probability of winning a single game is 40% and all games are independent is 60%^6 ≈ 4.7%. However, just as slacker says, the probability of winning 6 straight independent trials given that you've already won 5 is still that very same 60%. The key is of course the assumption of independence.

Again, this does not stand to reason mathematically. Probability has no memory. There's no such thing as being "due" a win when it comes to independent events. Of course you may well argue that unlike tosses of a coin or spin of a roulette wheel, the outcomes of a single team's consecutive games are NOT independent.

As example I mentioned a 75% system. Maybe I should have added 'time proven'. The outcome in the long run will have to conform to the 75%. In that case, it becomes increasinly 'difficult' for losses to continue, and therefore increasingly better to up the stake.

For an independent coin flip the outcome is 50%, but for a 75% system the odds change in the bettor's favor. Each independent coin flip is 50/50, even after ten tails, but the chance at eleven straight tails is very much smaller. (I edited this out later, Slacker, so you weren't dreaming at 4AM).

What I'm saying, and I realize this goes against 'conventional' mathematical wisdom, is that in gambling the game is NOT independent from previous games. Why not? Because WE are part of the experiment. We have a memory of the past results, and that memory will, in some way or another, affect our picks. We are the link between our picks. Therefore the picks are connected. Streaks are real. And based on the long term percentage of the player or the system one should be able to calculate the point where betting against the streak becomes wise.

[Ganchrow]

Baseball games are not independent events in the sense that we as gamblers should not operate under the assumption that the outcome of the previous game(s) has no influence on the game....it does...the degree of the impact is debatale but you shouldn't make the comparison between coin flipping and baseball games outcome...

While I certainly agree with you on this in principle, I'm not yet prepared to take it on axiomatic faith that this is true in reality. It certainly may well be (and conventional wisdom seems to hold so) but that would have to be proven to me.

The big warning light I see flashing is that while most gamblers do think that prior game outcomes impact future results, no one seems to be in agreement even as to whether we're dealing with positive or negative correlation.

My theory would be that there's probably short term autoregression due to player injuries (with an additional slightly longer period for starting pitchers) but not to an extent that isn't already recognized in the prevailing money lines.

[Ganchrow]

As example I mentioned a 75% system. Maybe I should have added 'time proven'. The outcome in the long run will have to conform to the 75%. In that case, it becomes increasinly 'difficult' for losses to continue, and therefore increasingly better to up the stake.

For an independent coin flip the outcome is 50%, but for a 75% system the odds change in the bettor's favor. Each independent coin flip is 50/50, even after ten tails, but the chance at eleven straight tails is very much smaller. (I edited this out later, Slacker, so you weren't dreaming at 4AM).

What I'm saying, and I realize this goes against 'conventional' mathematical wisdom, is that in gambling the game is NOT independent from previous games. Why not? Because WE are part of the experiment. We have a memory of the past results, and that memory will, in some way or another, affect our picks. We are the link between our picks. Therefore the picks are connected. Streaks are real. And based on the long term percentage of the player or the system one should be able to calculate the point where betting against the streak becomes wise.

You're getting in to dangerous territory here. This is what's known as the gambler's fallacy. As I mentioned to BuddyBear, prior outcomes may well be indicative of a change in a team microstructure, and that change may well revert to the long term mean; but that in no way implies that we'd be able to determine when a streak is likely to come to an end in excess of current money lines.

The Wizard of Odds talks about the Gambler's fallacy here.

[BuddyBear]

ganchrow are you a professional gambler?

[Dark Horse]

If I have a system that produces 75% winners, I will be more inclined to increase my wager size after three losses, than to lower it. Such a 'chase' is only dangerous if you're talking about percentages close to 50%.

This doesn't mean I'm doubling up to quickly make up for losses. It's just another way to play the percentages.

[tacomax]

If I have a system that produces 75% winners, I will be more inclined to increase my wager size after three losses, than to lower it.

Because surely you're more likely to get a winner after 3 losses, right?

And that's the gambler's fallacy.

[Ganchrow]

ganchrow are you a professional gambler?

More of a professional statistical arbitrageur.

[Ganchrow]

If I have a system that produces 75% winners, I will be more inclined to increase my wager size after three losses, than to lower it. Such a 'chase' is only dangerous if you're talking about percentages close to 50%.

This doesn't mean I'm doubling up to quickly make up for losses. It's just another way to play the percentages.

Let's say you roll a die and I agree to pay you $1 every time a 2,3,4,5, or 6 shows up and you agree to pay me $6 every time a 1 shows up. You certainly do expect to win that bet 83 1/3% of the time and clearly your expectation is about -$0.1667.

Now let's say you make this bet only after observing 5 consecutive rolls of a 6.

Guess what? Your expectation is still -$0.16667 and your chances of winning are still 83 1/3%

[Terris]

well pros ignore streaks, cause they know it will even up in the end. Also id say many here are scalpers or bonus hunters, and they dont care anyway

[BuddyBear]

well pros ignore streaks, cause they know it will even up in the end. Also id say many here are scalpers or bonus hunters, and they dont care anyway

not necessarily....sure if you take every game played an entire season and bet on it, it will get close to 50/50...but with individual teams it rarely ends up 50/50. Pros don't ignore streaks...there is a lot of gaming theory out there about this issue and ignoring streak can be costly...look at the As a couple years ago they won 20 games in a row...

[Dark Horse]

What I'm saying is that there is a law of averages, and that every streak will ultimately gravitate towards it. That law is 50% for a coin. It is 75% for a 75% system.

I understand that conventional science insists on isolating events from their natural surroundings. Easier to study them. But modern developments in science have broken out of that box. Not isolation, but connectedness is the direction now. 'Chaos' theory to the old garde.

I strongly believe that flipping a coin is not an isolated event. And you can write that on my tomb stone. Meanwhile, I'll take it to the bank.

[totobernal]

well I'd put $$ against the streak (money line) after the 4th. If I don't win, i'd put in the next game the double of the previous one, until I win, or till i'm out of money!

[Dark Horse]

Chasers often go four deep. So they put a predetermined stop on it. Seems to work for a lot of them. All depends on the quality (percentage) of their system.

[Ganchrow]

I understand that conventional science insists on isolating events from their natural surroundings. Easier to study them. But modern developments in science have broken out of that box. Not isolation, but connectedness is the direction now. 'Chaos' theory to the old garde.

I strongly believe that flipping a coin is not an isolated event. And you can write that on my tomb stone. Meanwhile, I'll take it to the bank.

Any "science" that tells you that the outcome of a previous coin flip impacts the outcome of future coin flips can only be termed "pseudoscience".

Still, if that remains your mantra then all I can say is best of luck to you.

[BuddyBear]

I strongly believe that flipping a coin is not an isolated event. And you can write that on my tomb stone. Meanwhile, I'll take it to the bank.

woah...sorry dark horse you are a good guy and i enjoy your posts and avitar but this is 100% inaccurate. flipping a coin is and always will be an isolated (independent) event from now till the end of time. An introductory stats text book will use this example regularly to make this point....

[Ganchrow]

well I'd put $$ against the streak (money line) after the 4th. If I don't win, i'd put in the next game the double of the previous one, until I win, or till i'm out of money!

Employing this strategy you're going to win most of the time. The only problem is the black swan. Every once in a while it will appear and you'll lose many orders of magnitude more than you ever won.

That will be a bad day.

[Dark Horse]

I know. Going out on a limb. lol
But doing so with open eyes.

What I'm really saying is that NOTHING is isolated.
That is not pseudo-science. That is the Butterfly Effect.

[BuddyBear]

well I'd put $$ against the streak (money line) after the 4th. If I don't win, i'd put in the next game the double of the previous one, until I win, or till i'm out of money!

this is a great way to go broke...

[Ganchrow]

.

this is a great way to go broke...

Yep. Afraid so ...

[Dark Horse]

All we need to know is the difference between risk and danger.

Fear has no place in that.

[Ganchrow]

What I'm really saying is that NOTHING is isolated.
That is not pseudo-science. That is the Butterfly Effect.

Which is certainly of relevance in chaotic systems.

But of absolutely no relevance in the present context.

[bigboydan]

ok guys... heres one for you.

after a big steak is finaly broken (win or lose). i've noticed that some teams seem to lose a game or two more after that.

do you just chalk that upto the let down factor, or what ?

[Dark Horse]

Gangrow, my understanding is that this is true for dynamic systems. Chaos theory is uncovering hidden (very subtle, previously considered pseudo-science) patterns.

Why would that not apply to gambling? What attracted me to gambling is the very possibility of uncovering hidden patterns. There's a whole group of people out there that would consider that impossible. Only those who leap into the unknown can find new things. So excuse me for not paying too much tribute to what is 'definitely' known.

[Ganchrow]

Gangrow, my understanding is that this is true for dynamic systems.

It certainly is true for dynamic systems. Chaotic ones.

Chaos theory is uncovering hidden (very subtle, previously considered pseudo-science) patterns.

I am unaware of a single example of this.

Only those who leap into the unknown can find new things.

True enough. But the gambler's fallacy is hardly the unknown and hardly new. It's an extraordinarily simple phenomenon (no less a part of reality than 2+2 equaling 4,) which left countless many gamblers before you utterly devastated by its wake.

[slacker00]

Dark Horse,

I still disagree that there's any reason to vary your bet size in your "75% system" no matter how many wins/losses you might string together.

I do agree that even two flips of the coin can be viewed as connected events, but their "connectedness" is beyond anything that any mortal can comprehend, much less allow for. I imagine if you had a supercomputer which could use lasers to measure the velocity, spin, ground texture and 100 other variables, you might be able to call a coinflip in the air with 55% accuracy. Unfortunately, it would probably cost millions to build such a coin flipping analyzer. Plus, we are examining coin flips in there here and now, not at some future date when a coinflip analyzer is available.

My point is that we've got to deal with limited abilities and resources to try to decide what to do. Sure, chaos theory may open some doors in the future, but good old fashioned basic math is much more useful here and now.

ok guys... heres one for you.

after a big steak is finaly broken (win or lose). i've noticed that some teams seem to lose a game or two more after that.

do you just chalk that upto the let down factor, or what ?

This seems like an easy question to answer, for someone with access to a large sports database. Does anyone have experience analyzing sports databases against questions like this? I'd love to start doing analysis like this. First I need a database and software.

[Dark Horse]

Hidden patterns? Number 4.669 appear to be one.

http://www.imho.com/grae/chaos/chaos.html

I study harmonic patterns pretty extensively. Not in relation to sports betting though. Maybe the strange water wheel motion has made it into my method of keeping records, but that's about it.

Logically, I have no argument with the gambler's fallacy. But intuitively, I know there is something missing there. Hard to explain. It's like there has to be an intersecting point where the graph of isolated events (flips) meets that of 'stringed' events. Both are happening. An event is isolated, but it is also part of a string. Probably makes no sense, but that's where I'm going. To insanity and beyond! lol.