Discussion»Statements»Rosie's Corner» Are there computer programs that automatically calculate odds? What goes into that? What information do you need to calculate the odds?
Oh yes - though computers don't do things "automatically".
Calculating odds by combinations and permutations is arithmetically quite simple, where the events are amenable to strict arithmetic.
National Lotteries are a classic example - the formula for finding the odds of winning the jackpot is quite simple but involves multiplying vast numbers so needs the power of a computer to manage it efficiently.
I can't recall the actual formula, but it uses factorials. That is, multiply the top number by the one below, their product by the number below again, and so on down to times by 2. The symbol is !, the exclamation-mark. So for example 6! = 6 X 5 X 4 X 3 X 2 (X 1) = 720.
The lottery in Britain was 6 from the numbers 1 to 49 for the jackpot, giving odds against winning that, of about 13 million to 1 against. Then the Canadian owners sneakily put it up to 6 from 50 - while also doubling the stake from £1 to £2. Therefore, it increased the odds astronomically, by multiplying the already-whopping great 49!, by 50. If you do that to my example, 720 X (6 + 1) = 720 X 7 = 5040. I stopped buying the tickets.
Now, those are for things you can describe numerically. If you need the chances of events that are not themselves numerical, you have to set artificial criteria so the exercise can become very subjective even if the event is fairly simple. You might still use a computer to help you analyse the data and calculate the odds, because a computer can run huge numbers of calculations at high speed. Nevertheless a computer can only ever do "sums", is not automatic, and has to be told what "sums" to do, and on what numerical values.
That opens a vast field called Mathematical Modelling. One use is making predictions based on taking known behaviour by complex statistics - which is highly mathematical - and systematically modifying variables in little steps to see what would happen. It is one big round of "What If?", but is as rigidly arithmetical as that lottery.
You can predict the weather by mathematical modelling, because the weather is amenable to numerical study (temperatures, pressures, wind vectors, altitudes, etc.). You would feed the computer vast numbers of numerical meteorological data, for analysis by great arrays of very complicated formulae tested, modified, corrected and proven by experience. It is no more automatic than your washing-machine though - it has designed to carry out a large task one step at a time without your intervention until it has finished.
You can design a bridge by mathematical modelling - you know the intended traffic and environmental loads, and the mechanical properties of steel and concrete - again, all numerical values. You also know which formulae will calculate the stresses in each part of the structure. The computer does the calculating, because there is so much calculating to do and you can't afford arithmetical mistakes; but you still need programme it with the correct formulae and feed them the right values.
' So can we predict human affairs by computer, as I suspect lies behind your question?
Well, in some respects yes.
Design a simple mathematical model for it, and you might predict a national election result according to how different areas typically vote, but it would only be an estimate of possible results of possible voting patterns. That is because the ballot itself offers a rigid number of, say, 4 choices everywhere, but then you lose arithmetical validity because you can't tell how voters anywhere will actually choose in an election not yet run.
The epidemiologists trying to see how this COVID pandemic will act next, are doing their best but again, can only react to numerical statistics of what has happened, and try to match them to human behaviour; but while statistics is relatively easy for professional mathematicians, humans are so notoriously unpredictable that predictions come down to "What If?" exercises in different possible situations.
' So... no. A computer cannot automatically calculate chance. It can only calculate defined chances by set criteria, values and methods, of things definable in numerical ways - and then only if instructed to do so. It is "automatic" only in containing a set of step-by-step instructions so its operator can enter the variable and constants, press [ENTER] and wait. In fact it's no more automatic than a traditional striking and chiming clock, which contains "instructions" as appropriately-shaped metalwork rather than electrical pulses, to sound the right chimes at the right times.
'
When I was working I had sometimes to write Risk Assessments, by Health & Safety Management law. The method we used was typical, and looked arithmetical because each hazard was assessed by assigning 2 numerical values, 1 to 4, and multiplying them. The product then guided your advised action to minimise the risk. It was hardly mathematical though, not because of the Infants' School level of arithmetic, but because the numbers are subjective estimates of the risk (the chance) of accident and potential severity of its outcome. The only "computer" that can do that, is the brain of a human being experienced in the work and work-place being assessed! X
This post was edited by Durdle at September 13, 2020 1:43 AM MDT
I don't know how to thank you for investing so much time answering my question Durdle. I don't understand all of it but I sure appreciate that YOU DO and are willing to share what you know. And to take so much of your time sharing what you know. I'm always looking for connections and meaning in everything all the time. Here's an example of what I had in mind when I ask "what are the odds?". I may have told you this already. I don't remember. We changed dentists because we wanted to go to one that was local. Jim asked a neighbor if he had one he liked. He did and gave us the name and we are going to him. Here's the very weird part. I'm of Armenian Ancestry. So is the dentist. We both live in Hemet, a very small town. We chatted a bit the first time I saw him and here is where "what are the odds of that? " kick in. I was married in St. Gregory's Armenian church in Pasadena, California the first time many decades ago. My sister and I attended Armenian School there. Attended Armenian Church picnics and dances there. He was married at St. Gregory's Church in Pasadena, California. His children went to Armenian School there. His family attended church picnics and dances and other events there. He is young enough to be my grandson! We had identical experiences at the same place decades apart and we end up here in Hemet? See what I mean? What are the odds of that? Are they incalculable? Too many variables? I will read and reread what you kindly wrote. The odds of connecting with people worldwide with whom you click immediately always amazes me. As I wrote in a question on another thread I amaze easily and often! Hope you and your family are safe and stay that way. Happy Sunday to thee thine m'dear! :)
This post was edited by RosieG at September 14, 2020 3:33 AM MDT
I think you have mentioned your Armenian ancestry, but not that of your dentist. That certainly is one huge set of co-incidences!
A professional statistician might be able to calculate the odds of those, though I think it would only be an estimate. Yes, he or she might use a computer to help, but only as a glorified calculator, and it might be that there are so many variables that it is just not solvable arithmetically.
In a way I would find that rather comforting, showing that for all the talk about "Artificial Intelligence" and "algorithms" running "our" (whose?) lives, human beings and their lives are not nice neat bundles of cohesive numbers, and are far cleverer than computers. The computer can complete vast numbers of mathematical and logical operations in a very short time and extremely accurately, which the human brain can't do - but it does not have the reasoning and emotional powers we have, nor the individuality.
A computer is a tool, for humans to programme and operate to help them with specific tasks. It is not a sentient being like a person.
I've often thought life is, for most people, a long set of consequences; some bad, some good, some very rewarding.
Lots of "If": if I had not taken up this interest I would not have met that person. If he had not introduced me to another interest I would not have met this girl-friend, gone abroad or taken up a third, but related, interest. That interest subsequently led to part-time study courses, a further circle of friends and a later girl-friend.....
My life has been quite varied as a result, but your and your dentist's own list of "Ifs" are evidently much more complicated and branching than mine, and in many ways more deeply rewarding.
I don't think the odds of that chain of circumstances are calculable, and maybe that's as well because it might diminish the personal element of it all.
Well, it's now nearly 9pm here, but Happy Sunday to you too!
Thank you for your thoughtful and comprehensive reply. I have something else that has been nagging at me for quite awhile. It has to do with our "purpose" in life. I'm going to ask about quantum entanglement and how it relates to us. Don't know if anyone will get on board to talk about it but well it doesn't matter because I need to ask. Hope you had happy dreams m'dear! :)
Durdle 