streaks

Just wondering what people thought of streaks. good or bad. Are streaks related to time or location? Or to individuals? If you are having a bad or good streak at one table, or machine, or casino, would your streak or luck change at the next table or machine? Is the streak attached to the individual? Or would it change at a different time? Ten minutes later? Or an hour or day later? Or does someone else or an object change your streak?

People often refer to having a lucky streak, or a bad streak, so I just wondered what people thought about this.

A lot depends upon what the streak meens in terms of future actions.

A popular betting action is to increase bets when on a hot streak. I do this myself. But when does the streak period end?

For example, if I'm on a hot streak at a BlackJack table, I may decide the strek ends when the shoe ends, and return to my base bet at that point.

On the flip side, if I'm betting an even money bet on Roulette, the streak refers to my accuracy and not the actual result. I.E. I may move my bet from black to red, or even from black to even. But as long as I guess correctly, the streak continues, and I continue to press it.

DJ--I agree with you. A streak is anytime I am winning, especially when I make a string of winning bets in baccarat (I switch between player and banker). But usually, I don't believe in "streaks." A streak can be anything, even something seemingly random like BBPPBPBPBPBPBPBBP. It's all in how you look at it.

A pit boss once admonished me for continuously betting Banker when Player kept showing up. He said, "Don't fight the streak." I said, "There's no such thing as a streak."

Of course streaks exist as part of the randomness of the game. Some people bet streaks according to their respective betting or money management system. I use streaks to control how much I bet in craps but that system is as stupid as any other system.

Streaks are ill-defined and can only be identified in hindsight. That is, for any series of independent random trials, it is impossible to predict streaks.

It is interesting to note that experiments have shown randomly generated series of outcomes exhibit more streakiness than human-generated series of outcomes. People asked to create random series do not put enough streaks.

So... you could argue that when people see random occurrences, like a series of wins and losses, they see more streaks than they expect! To me, this explains why people believe streaks occur for reasons other than pure randomness

Quote: inap

Are streaks related to time or location? Or to individuals? would your luck change at the next table or machine? People often refer to having a lucky streak, or a bad streak,

There is no such thing as hot hands or hot dice. An individual who has been winning will look favorably upon the situation and think he is on a lucky roll, but that next roll of the dice can be seven, that next spin of the wheel can be zero .
The annuciator showing the recent results of the roulette wheel or that form they give you at a baccarat table are just gimicks. No matter how lucky you've been recently, the casino knows your time is coming ... thats why they let you win all that money, they know it won't walk out the door.

I wrote an academic paper about the probability of streaks which the wizard posted on his column Ask the Wizard #232 . There is a graph and a .pdf file.
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For example consider the oft posted question about Martingale Strategy.
(1) If you are playing a game that permits up to 6 losses in a row [with no house edge] then you have to play exactly 89 times before you have a better than 50% probability that that you will have a loss streak of 6 or more. Your initial bankroll must be at least (2^6-1)*unit to begin this strategy (example $315 for a $5 minimum). It is extremely unlikely that in 89 plays you will have doubled your minimum bankroll.
(2) In general you have a 2:1 probability of hitting your losing streak before doubling your minimum required bankroll.
(3) With a game with a house edge, the number at which you reach 50% is lower than 89. How much lower depends on the house edge of the game in question.

Most people when discussing this problem are unaware of any quantitative analysis (like number of 89 plays associated with 50%). They tend to discuss Martingale in qualitative terms like coins, dice, and balls have no memory or Martingale works for a while, and then suddenly you lose everything or see the results of my computer simulation.
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Calculations of probabilities of streaks is fairly complicated mathematics, and usually depends on proper understanding of Markov transition matrices. Their are no algebraic formulas.
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I got some nice feedback on the paper after The Wizard posted it. Dr. Henk Tijms , Department of Econometric Vrije University De Boelelaan HV Amsterdam the Netherlands said, A marvellous paper. I wished I had hit upon the idea of including such a graph in my book Understanding Probability. As I said it is a very insightful graph.

Quote: pacomartin

I wrote an academic paper about the probability of streaks which the wizard posted on his column Ask the Wizard #232 .

Where was this article published?

Thanks,

--Dorothy

It was only published on the Wizard of Odds site. Most of the gambling publications have a stable of writers and they do not accept outside reports. Pure mathematics journals do accept publications about gaming, but it would have to be rewritten as a proper mathematics paper. I think it would be less interesting.

It has always bothered me that people always discuss Martingale theory in a non quantitative manner. Basically if there is no house edge at all after 89 plays there is a 50.3016% probability that you will have a loss of 6 in a row. If you add in a small house edge (like 51% that you will lose). The probability that you will lose 6 in a row is in only 80 plays is 50.046%.

As to how much money you will win in those 80 or 89 plays it is also subject to another probability distribution. But it is relatively unlikely that you will have doubled your bankroll in 80 to 89 games.

Even for no house edge, the odds are roughly 2:1 that you will hit your losing streak before you double your bankroll.

The curves also basically parallel in a logarithmic scale. Other games may let you lose 7,8 or even 9 times in a row before you hit your maximum. But in those cases your minimum bankroll will be 2,4 or 8 times as large to cover those loses. Basically you get the same result. Even for no house edge, the odds are roughly 2:1 that you will hit your losing streak before you double your bankroll.

Dorothy, there is a discussion of Markov Chains in Wikipedia and Stochastic processes. In general an expression that can be written as a Markov chain, can also be written as series of recursive rules. However, the solution is not algebraic. Most people are not familiar with non-algebraic rules. If you write computer simulations you will converge on similar results.

Quote: pacomartin

Dorothy, there is a discussion of Markov Chains in Wikipedia and Stochastic processes. In general an expression that can be written as a Markov chain, can also be written as series of recursive rules. However, the solution is not algebraic. Most people are not familiar with non-algebraic rules. If you write computer simulations you will converge on similar results.

Many recursive processes have a closed form solution. Binet's formula is a perfect example for n-term linear recurrences. If you like, "algerbraic" in that the general solution involves roots and multiplicities for the characteristice equation of the recursion. Solving recurrences is critical to getting big-O estimates for various algorithms. For example proving that sorting is O(nlogn) in the general case. Many discrete recursions can be directly correlated with a pde or ode and simple numerical techniques apply. I'm sure this isn't news to you.

Kind regards,

--Dorothy

I know that some recursive relationships can also be expressed in closed form (like Binet number and fibonacci sequence), but not everyone can be expressed that way. There is a

The solution to the problem of what is the probability that you can roll N times in a pass line bet in craps can be done as Markov transition matrices or as a recursive relationship. Time magazine incorrectly reported the odds as 1 in 1.56 trillion which is (36/30)^154. It is the wrong answer since 7's are permitted on come out rolls.

thank you everyone for your input. i kind of suspected an explination for streaks from a mathematical perspective. but what about streaks of a more human, supernatural nature? for example, the person who always seems to win when they go to vegas. or the one who never seems to win. or is there such a thing as 'good luck' charms, or your girlfriend or wife comes next to you and your 'luck' suddenly changes. or superstitious rituals, or objects, etc.

i know there are people on both sides so i don't mean to start a bar fight, but just wondered what experiences people had. i know this is an unexplainable which i would like to try to explain. but what the heck :). this is just a part of gambling which is hard to ignore.

Psychologists have observed that people tend to think that streaks are much rarer than they actually are predicted to be. The supernatural or the superstitious belief in streaks is deeply rooted the human psyche.

that the curves kind of have an S shape is interesting, but I guess I see why.

is an S shaped curve and a recursive curve the same thing?

Well I did the curve twice. For 1 to 100 games I used a normal scale, but for 1 to 1000 games I used a proportional (or logarithmic scale). The S shape is more because of the logarithmic scale.

Stochastic processes are the kind that only depend on the current state and some rules of transition. Recursive formulas are ones that describe the current quality only as some expression of previous states. Markov transition matrices are ways of describing how to go from one state to another state.

Let me give you an example from craps. The odds that you won't get a 7 in N rolls is expressed by a simple algebraic equation (36/30)^N . But the odds the won't 7-out in N rolls depends partly on how often you have a come out roll, and the probability that you 7,11 or hit craps. To do this calculation you need a series of recursive relationships (or alternatively as transition matrices). The wizard worked this out in detail in one of his Ask the Wizard Column Craps . Because recursive formulas are more familiar than matrix algebra to most people he used columns of recursive relationships to represent the various states.

A lot of people felt that you need to know how many times the woman hit her point in order to be able to calculate the probability of rolling the dice 154 times. It isn't necessary, because returning to a come out is perceived as one of several possible states. Each state has a formula that depends on the probability of the previous state.

Take a look at his answer. This is not high school math (or frequently not even undergraduate math).

Just received a book on gambling from Inter Library Loan.
The typeface is going to be a real struggle but the very first page sets the tone:

If by saying that a man has had good luck, nothing more was meant than that he has been generally a gainer at play, the expression might be allowed as being very proper in a short way of speaking: But if the word good luck be understood to signify a certain predominant quality, so inherent in a man that he must win whenever he plays or at least win oftener than lose, it may be denied that there is any such thing in nature.
....The Doctrine of Chances 1716.

You can't win if you don't play the game.
You can't lose if you don't play the game.

From the poet Sumner A.Ingmark:

A gambling streak's good fortune,you win again and again,

The math predicts how often,but nothing can tell you when.

Quote: pacomartin

I wrote an academic paper about the probability of streaks which the wizard posted on his column Ask the Wizard #232 . There is a graph and a .pdf file.

Great work on the math and graphs.

I had made the math tables and graphs years ago (and have lost them since)
but just had only streaks of heads.
(edited 8/Friday the 13th)
From what I remember, for just heads only, as opposed to yours for either heads or tails, just add 1 to n=3 for example you have curve n=4, the curve for just 3 or more heads only.
Example: streak of 5 or more heads only in 20 trials.=.2499(rounded)or exactly(1-(786568/1048576))and that can be seen at label n=6

Quote: pacomartin

I got some nice feedback on the paper after The Wizard posted it. Dr. Henk Tijms , Department of Econometric Vrije University De Boelelaan HV Amsterdam the Netherlands said, A marvellous paper. I wished I had hit upon the idea of including such a graph in my book Understanding Probability. As I said it is a very insightful graph.

One of the best beginning books on prob and stats for the average person! at least in part one!

I just finished reading the book: Understanding Probability by Henk Tijms

a quote from the beginning of the book:
"where the informal Part One motivates probabilistic thinking through many fascinating
examples and problems from the real world"

The real world is the key!
I think one can preview the book in google books.
I downloaded the book in pdf form.