### Re: Mills Futurity - A cheating Mills Bandit?

the example I gave was not mine, its from a text book.so, all of that must be wrong...fair enough

you say text book quote was correct except the bit i added at the end...I did NOT add anything ,I cut and pasted the complete thing,as was,no changes.

from a different on line text book (note the final line) note, I have NOT added anything

"Probability is defined as the fraction of desired outcomes in the context of every possible outcome with a value between 0 and 1, where 0 would be an impossible event and 1 would represent an inevitable event. Probabilities are usually given as percentages. [ie. 50% probability that a coin will land on HEADS.] Odds can have any value from zero to infinity and they represent a ratio of desired outcomes versus the field. Odds are a ratio, and can be given in two different ways: ‘odds in favor’ and ‘odds against’. ‘Odds in favor’ are odds describing the if an event will occur, while ‘odds against’ will describe if an event will not occur. If you are familiar with gambling, ‘odds against’ are what Vegas gives as odds. More on that later. For the coin flip odds in favor of a HEADS outcome is 1:1, not 50%."

you say text book quote was correct except the bit i added at the end...I did NOT add anything ,I cut and pasted the complete thing,as was,no changes.

from a different on line text book (note the final line) note, I have NOT added anything

"Probability is defined as the fraction of desired outcomes in the context of every possible outcome with a value between 0 and 1, where 0 would be an impossible event and 1 would represent an inevitable event. Probabilities are usually given as percentages. [ie. 50% probability that a coin will land on HEADS.] Odds can have any value from zero to infinity and they represent a ratio of desired outcomes versus the field. Odds are a ratio, and can be given in two different ways: ‘odds in favor’ and ‘odds against’. ‘Odds in favor’ are odds describing the if an event will occur, while ‘odds against’ will describe if an event will not occur. If you are familiar with gambling, ‘odds against’ are what Vegas gives as odds. More on that later. For the coin flip odds in favor of a HEADS outcome is 1:1, not 50%."

### Re: Mills Futurity - A cheating Mills Bandit?

Americans express things differently. 1:1 is just another way of saying 50%.

### Re: Mills Futurity - A cheating Mills Bandit?

I can see where the confusion came from. An expression like 3:7 is another way of saying the ratio 3/7, which emphasizes that it is a ratio comparing two things and not a fraction. If at one point they say even and odd are 1:1, meaning that even and odd have the same chance of coming up, then assuming nothing else can happen than even or odd, both of them have a 50% chance.

The later part of your quote then gave the ratio 3:7. So he assumed it was 3 chances of one thing, as against 7 chances of everything else, the same way as 1:1 was. That would give 30%. But instead it was 3 chances of one thing as against all the chances, of which there were 7. So this time the ratio wasn't to the other possibilities, but to all the possibilities. Giving 3/7 or 42.8%.

The textbook you quoted wasn't "wrong", since you can use ratios to express either the ratio between two different possibilities or the chance of one possibility. But using it two different ways was at least confusing; since, usually, textbooks are nicer than that, I can see why he mistakenly blamed it on you.

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### Re: Mills Futurity - A cheating Mills Bandit?

Yes, I apologize for assuming you made that bit up Paul. I just didn't believe it was in a textbook. The thing is, it wasn't - it came from this online blog, and the author (a pure mathematician) is discussing something that's not very relevant to us when he says:

Swapping our black bag with balls for a ten stop reel with 3 Cherries and 7 Lemons:

Odds for a is 3:7

Odds against a is 7:3

Probability of a is 30%

Probability of a is 70%

The additional information is that we should see 43% or 0.43 as many cherries as lemons, and 233% or 2.33 as many lemons as cherries! Gamblers would probably find this unhelpful, which is why they're not the kind of odds bookies provide.

Paul, what do you think

Out of context this sounds like nonsense. Probabilities don't exceed 100% (except in pure maths). But he'sOdds are often expressed as odds for, which in this case would be three divided by seven, which is about 43% or 0.43, or odds against, which would be seven divided by three, which is 233% or 2.33

*not*converting odds into probability. He's saying*if*you divide three by seven you get some additional information about the odds.Swapping our black bag with balls for a ten stop reel with 3 Cherries and 7 Lemons:

Odds for a is 3:7

Odds against a is 7:3

Probability of a is 30%

Probability of a is 70%

The additional information is that we should see 43% or 0.43 as many cherries as lemons, and 233% or 2.33 as many lemons as cherries! Gamblers would probably find this unhelpful, which is why they're not the kind of odds bookies provide.

That quote is from 'Further Reading' on the odds calculator I linked to. Again, not a textbook (accredited by a department of education), just a website (like this one). They're not contradicting their earlier reference to the "50% probability that a coin will land on HEADS". I think they're

*trying*to say that you express the odds as a ratio of 1:1, not as 50%, which is a probability.Paul, what do you think

*is*the percentage probability of a coin landing on heads?### Re: Mills Futurity - A cheating Mills Bandit?

Just to throw a spanner in the works

Tossing a coin on to the ground (hence why it's usually caught in the hand) is not 1:1.

There is a possibility that it could land on the edge of the coin and sit on its side.

So what's the microscopic probability of that happening.... 1 in a million, I guess... but that would change the odds.

I'm going to go hide in the cupboard now.

All the best Dicky

Tossing a coin on to the ground (hence why it's usually caught in the hand) is not 1:1.

There is a possibility that it could land on the edge of the coin and sit on its side.

So what's the microscopic probability of that happening.... 1 in a million, I guess... but that would change the odds.

I'm going to go hide in the cupboard now.

All the best Dicky

### Re: Mills Futurity - A cheating Mills Bandit?

I haven’t a clue what any of them are talking about probably why I was useless at gambling......it’s all just a jumble of numbers to me, well that is what’s use to tell my maths teacher

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### Re: Mills Futurity - A cheating Mills Bandit?

Well, you've got me there!

Which is it then ... landing on its edge or its side?

Or is it a bit like describing a mate who lived in your road as "he and I went to different schools together"?

BP

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### Re: Mills Futurity - A cheating Mills Bandit?

Mathematically derived theoretical odds are

*never*a perfect description of real world odds. It was a surprise the Bullion came so close. The head and tail relief stamped into coins guarantees asymmetry. But if the odds

*were*exactly 1:1, the probability of heads or tails would be exactly 50%.

### Re: Mills Futurity - A cheating Mills Bandit?

Except for being a generalization, that is pretty much true. Dice aren't perfect cubes, spinning wheels of fortune aren't absolutely perfect, and so on, and so any such device would be slightly biased. Even when great efforts are made to minimize bias, as with dice used in casinos for craps, or casino roulette wheels.pennymachines wrote: ↑Sun Feb 02, 2020 2:28 pmMathematically derived theoretical odds arenevera perfect description of real world odds.

But because the bias is both small and difficult to determine, that's usually forgotten, as usually the mathematical odds are the best we can have.

Why did I mention that it's a generalization? Well, although being physical, no doubt it's still not perfect, there is a technique to deal with real-world bias. It's used in the random-number generators in microprocessors that help with picking secret code keys.

If you have an electronic noise generator that is inherently badly biased - you can't really pick a voltage and say it will be equally likely to be above or below it - instead of taking one sample to produce a random bit, take two samples for equal lengths of time and compare them.

Even for traditional games of chance, turn up two cards from a deck, and bet on whether the first or the second one is higher. Faro is an example of a game where this principle is used.

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### Re: Mills Futurity - A cheating Mills Bandit?

Interesting comment about dice there.

So, what would be the odds of the dice in the window of a Buckley Bones coming up the same?

BP

So, what would be the odds of the dice in the window of a Buckley Bones coming up the same?

BP

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