Mathematics and Probability as it relates to pool

What is the probability that a player during a match is calculating his/her probability of running out? What is the probability of knowing your runout probability during a match has any significant value?

I see at as a risk/reward analysis, which makes it much easier. And most good players take the risk/reward factor in almost unconsciously. You do not usually shoot shots that are very high risk and that have a very low probability of reward.


Braden<---------"probably" won't run out!
 
Let's not get confused here. An example other than pool to explain the math is to use the flipping of a coin so that human error does not interfere.

The probability of getting a 'head' is .50. That is the same for each flip. But if you bet on 9 heads in a row the bet becomes basically a parlay. The probability of 9 heads in a row is .002 (.50 to the 9th power). That's long odds.

But let's flip one more time. The probability of that one next flip being a head, by itself, is .50. A lot of money is lost by making the intuitive bet on the next event being "Tails' because it's, " due."

That's also why the old, "double or nothing," bet is a loser's gamble.
 
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There is a large body of neuroscience research that says that humans are excellent at instinctively calculating and being aware of probabilities. It is also part of a larger framework that suggests that the information the brain is acting on and encoding is actually probabilities of different occurrences in the environment.

The point being that even if you don't sit there and do the calculations on every shot, at any one point you intuitively have a pretty good idea of what your probability of the intended outcome is.
 
12310bch said:
That's also why the old, "double or nothing," bet is a loser's gamble.
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No it's not, provided you have deep enough pockets and the other party always accepts subsequent "double or nothing" bets. Given the those conditions, double or nothing is actually a "cannot lose" gamble (also provided you have a non-zero probability of actually winning each time). This is the primary reason why there are max betting limits on blackjack and craps tables.

But anyway, that's besides the point of this thread. :D
 
WhatsTheSpot said:
Over the years I have observed that very few people have a clear concept on probability, and especially so when it relates to pool.

I want to give you a mathematical problem. You can easily solve it with a calculator, but just take a guess first before calculating.

Here is the scenario.....

The game is 9-ball. The player has made 1 ball on the break, so there are 8 balls remaining.

For each of the remaining shots, this player has a 90% chance of pocketing the ball, and a 90% chance of getting position on the next ball.

For the 9-ball, he has a 90% chance of pocketing it, and a 90% chance of avoiding a scratch.

What is the mathematical probability that he runs out?
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That is 90% each for pocketing and position, or 0.9^16=0.185302019, or 18.53% chance to get out. That must be one tough table, or you just suck. Or I suck at math! [fixed]
 
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JB Cases said:
90%?

I don't know how to solve it easily with a calculator. But if the player has a 90% chance of getting shape and the resulting shot is also 90% then I say getting out is 90% certain.
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The odds are 90% for each shot, and 90% for each position. This is the same probability as rolling a 10-sided die 16 times and never rolling a 10. How often will that happen? about 18.53% of the time.
 
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Aaron_S said:
The way I read it, pocketing the ball doesn't imply automatic position, which is why the position probability was explicitly stated. I'm sticking with .9^16 (or .81^8 if you prefer). :smile:

I do agree that a good player will get out more often than .185 if there is a 90% probability of obtaining position on each ball, which implies that the balls are open, but I attribute that to the fact that a good player will make more than 90% of shots that he/she has ideal position on. If we give them a 95% chance of making each shot they have ideal position on, which I think is more realistic for a good player, their odds of getting out jump up to about 30%, which I also think is more realistic.

Aaron
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what he said....
 
Aaron_S said:
The way I read it, pocketing the ball doesn't imply automatic position, which is why the position probability was explicitly stated. I'm sticking with .9^16 (or .81^8 if you prefer). :smile:

I do agree that a good player will get out more often than .185 if there is a 90% probability of obtaining position on each ball, which implies that the balls are open, but I attribute that to the fact that a good player will make more than 90% of shots that he/she has ideal position on. If we give them a 95% chance of making each shot they have ideal position on, which I think is more realistic for a good player, their odds of getting out jump up to about 30%, which I also think is more realistic.

Aaron
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95% to make each ball and 90% to get position: 0.285580742 or 28.6%
95% to make each ball and 95% to get position: 0.440126669 or 44.0%
 
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jsp said:
No it's not, provided you have deep enough pockets and the other party always accepts subsequent "double or nothing" bets. Given the those conditions, double or nothing is actually a "cannot lose" gamble (also provided you have a non-zero probability of actually winning each time). This is the primary reason why there are max betting limits on blackjack and craps tables.

But anyway, that's besides the point of this thread. :D
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This is true because there is a system that relies on doubling the bet each time you lose. If there is no limit and you have enough money then you will always beat the house and walk away with more money than you start with as long as you apply the system diligently.

Say you start with a $50 bet. Bet only 50 and only double if you lose a hand. Keep doubling until you win a hand and then go back to 50. This can NEVER lose in a no limit game.

And if you play blackjack then it's certain that you will hit black jacks occasionally on the times you have doubled the bet thus increasing your profit.

Limits kill this system because you can lose more hands in a row than the doubling allows for.

I have made money using this system on a $5 min $2000 limit table but it's certainly making your heart skip a beat when you are trying to grind out some money and the doubles take you to $500ish on one hand. At the end of the day it's a losing system with limit tables.

And THAT is the limit of what I know about it. I like to play it on the video machines. Sometimes I have made good scores and sometimes I go bust.
 
All I know is that when I break and the table is open good players almost always run out. I guess they see it as 100% :-)
 
If you have a 90 percent chance of making the ball then the 90 percent chance of getting position on it is no longer relevant. That event is history.

You are right. :bow-down:Double or nothing on a .50 probability would not be a losers bet, It's an even bet.

I was thinking in terms of a losing pool player doubling up after 5 losses in a row because he thinks he is ," due to win a game." His thinking being that the probabilities favor him when in fact the probabilities in the next game are the same as they were in the first game.(given no other changes)
 
I don't think the pro has some second sense of probabilities naturally..... I think they practice more than your normal guy on specific shots until they know their odds.... Shane stated he simply runs racks until he runs into a shot he is not comfortable with or that he misses and then he wroks on it until he doesn't miss it anymore.....

Most amateurs just take it as a miss shoot it from where it ends up and then throw the balls out when they finish the rack... They never stop to establish what their percentages are for any given shot...

I've sat up simple shots before and had decent players shoot them where they had to make the easy shot and stop within a pie plate of center table... Natural angle shots to boot where they really didn't have to do much of anything beside hit the object ball accurately and at the right speed...

You would be amazed at the number of players who were 100% sure they could do it and couldn't even do it after 5 tries......

The shot I used was either shot 3 or 5 in Hennings pro book with the cueball center table and the object ball 1 diamond out from the side rail and end rail of the corner pocket......

I think unless you are putting in serious practice time and not just playing you have no chance of ever understanding your true odd and probabilities......

The best real world pro example is Darren Appleton.... I watched him the last 2 US Open he won and I can tell you the guy that won the 2nd won was not the same player... His understanding of his percentages has increased possibly exponentially.... He shot at almost nothing that was much less than halfball... If it was much thinner than that he ducked.....

He ducked because thin hits allow speed to the determining factor in success and failure.... I am not saying he ducked every thin cut but if it required good shape to get on the right side of the next ball he took no chances and simply played safe.....

I have no idea if anyone else but me noticed the change.... I noticed his patterns had changed and his choice for playing safe had increased... I then set out to pay enough attention to figure out the under-laying change and the balls he chose to shot at vs the balls he was playing safe on made it very plain to see what had changed just in the course of a year.......
 
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