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question for math hounds from a non math head

diggingdeeper

New Blood
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Joined
Nov 27, 2005
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23
out of thes 2 which is a measurement or, can they both be measurements of the same thing and if so, why

Odds
Probability
 
Probability is a measure of how likely something is, odds a meaure of how likely people think it is as expressed by what they would be willing to risk for a given reward. If someone says, for instance, that the odds of something are 3 to 1, that means that that theywould be willing to risk 3 to win 1. In a sense, in order for two people to have a bet, they must disagree as to the odds.
 
Probability is the ratio of desired outcomes to total outcomes.

There are two outcomes in a coin toss (heads or tails). The probability of getting heads is 1/2

There are six outcomes in the roll of a die (1, 2, 3, 4, 5, 6). The probability of rolling a 1 is 1/6 The probability of rolling an even number is 3/6 = 1/2 The probability of not rolling a 1 is 5/6

Probability is always a fraction less than or equal to one. The probability of obtaining a desired outcome and the probability of not obtaining a desired outcome add up to 1. Using the examples above:
1/2 + 1/2 = 1
1/6 + 5/6 = 1

Odds is the ratio of desired outcomes to undesired outcomes.

The odds of getting heads in a coin toss are 1:1

The odds of rolling a 1 on a die are 1:5. The odds of rolling an even number are 3:3 or 1:1 The odds of not rolling a 1 are 5:1

To convert probability to odds: a/b => a: (b - a)

To convert odds to probability: a:c => a/(a + c)




Art --

You are confusing mathmatical odds with betting odds. Betting odds are the payoff ratio for a given bet. There are two kinds of betting odds, based on whether the mathematical odds are easily calculated (or can be directly calculated at all).

If the mathematical odds are known, then, in a "fair game" (where there is no "house" acting as middleman and taking a cut), betting odds are the inverse of the mathmatical odds. The odds of rolling a 1 are 1:5, so the payoff odds are 5:1.

But if the "house" takes a cut, the payoff will be slightly less than the inverse of the mathematical odds. This is the case in most casino games, such as craps or roulette.

If the mathematical odds are not easily calculated (as in a horserace), then the house often bases the payout on the ratio of the total amount bet for the outcome to the total amount bet against the outcome, after taking its cut, of course. If there is no house, then the payoff is agreed to as in your post.
 
Gwyn ap Nudd said:
Probability is the ratio of desired outcomes to total outcomes.
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Well, it's more "outcome in question" than "desired outcome".

You are confusing mathmatical odds with betting odds.
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When people say "odds", they mean "betting odds".

If the mathematical odds are not easily calculated (as in a horserace), then the house often bases the payout on the ratio of the total amount bet for the outcome to the total amount bet against the outcome, after taking its cut, of course. If there is no house, then the payoff is agreed to as in your post.
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A bookie always bases the odds on the number of bets placed on each outcome, because this guarantees them that no matter the outcome, they will come out ahead. If someone is basing odds on something else, such as the mathetical probability, they're not a bookie, they're a speculator.

Something else I forgot to mention in my first post: probability and odds are measures, but they aren't measurements. A measure is simply a way of assigning a quantitiative value. A measurement is a measure based on empirical properties.
 
Probability is the ratio of desired outcomes to total outcomes.

There are two outcomes in a coin toss (heads or tails). The probability of getting heads is 1/2

There are six outcomes in the roll of a die (1, 2, 3, 4, 5, 6). The probability of rolling a 1 is 1/6 The probability of rolling an even number is 3/6 = 1/2 The probability of not rolling a 1 is 5/6

Probability is always a fraction less than or equal to one. The probability of obtaining a desired outcome and the probability of not obtaining a desired outcome add up to 1. Using the examples above:
1/2 + 1/2 = 1
1/6 + 5/6 = 1

Odds is the ratio of desired outcomes to undesired outcomes.

The odds of getting heads in a coin toss are 1:1

The odds of rolling a 1 on a die are 1:5. The odds of rolling an even number are 3:3 or 1:1 The odds of not rolling a 1 are 5:1

To convert probability to odds: a/b => a: (b - a)

To convert odds to probability: a:c => a/(a + c)
Click to expand...

So it would appear that they both could be considered measurements.
I guess I had been using english usage in a mathmatical situation and thats where I was geting confused. Thank you for taking the time to explain that for me.
 
The main difference between the two is that you use probability when you are discussing the absolute likelihood or "chance" of an event ("The chances of hitting the Pick-4 lottery are 1 in 10,000"), and odds for comparative likelihood, most often in relation to betting. ("The odds against rolling an eight in craps are thirty-one to five.")
 
Art Vandelay said:
When people say "odds", they mean "betting odds".

A bookie always bases the odds on the number of bets placed on each outcome, because this guarantees them that no matter the outcome, they will come out ahead. If someone is basing odds on something else, such as the mathetical probability, they're not a bookie, they're a speculator.
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When people say odds they don't mean betting odds. Sometimes they do, like "what are the odds on Cleveland tomorrow?", but more often, in "what are the odds of that?" or "what were the odds?", the concept underlying their statement is "what was the probability of that outcome?" rather than "if someone were offering me to bet one way or another on that outcome, how much would I have to wager to win $1?".

Furthermore, a) bookies do not often decide odds. Oddsmakers decide the odds, occasionally bookies shift them. b) the initial odds are *always* set based on the best probability the oddsmakers can come up with; how can you base odds on number of bets when no one has bet?

This is how it works. I am an oddsmaker, setting odds for a hockey team to win. They are favored, so I might set the odds at 1.20 and 0.90, which means you must bet $1.20 for each $2.20 you want to take home if you're betting on the favorite and $0.90 for every $1.90 if not (note: there are many representations of bookie odds, this is just one). For some reason, everyone is betting on the unfavored team. I then shift the odds to 1.10 and 0.90. This is to attempt to make the number of bets on both sides about even, minimizing the losses to any individual bookie. It is in this shifting that oddsmakers respond to the number of bets.

In fact, bookies *cannot* operate as you propose. Consider the case where everyone bets on the same proposition with equal amounts of money. If the bookie is to win when everyone wins, then the odds must have read "Bet $1.00! If you win, you get $0.90 back! If you lose you get $0.00!". Bookies do lose sometimes. Just like casinos, they win only in the aggregate.
 
GreedyAlgorithm said:
the concept underlying their statement is "what was the probability of that outcome?" rather than "if someone were offering me to bet one way or another on that outcome, how much would I have to wager to win $1?".
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Not "how much would I have to" but "how much do I think would be a fair bet?".

the initial odds are *always* set based on the best probability the oddsmakers can come up with; how can you base odds on number of bets when no one has bet?
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The initial odds are just that: initial.

In fact, bookies *cannot* operate as you propose. Consider the case where everyone bets on the same proposition with equal amounts of money.
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I'm not sure that I understand what you mean. Do you mean that everyone is betting for something, and no one is betting against it?

If the bookie is to win when everyone wins, then the odds must have read "Bet $1.00! If you win, you get $0.90 back! If you lose you get $0.00!".
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But the odds change the bookie's profit not only directly, but indirectly by changing how many people bet on what. If he keeps lowering the odds, eventually people will bet for the other outcome, unless they're absolutely sure that the original outcome is certain, in which case why is the bookie taking bets on it?

Bookies do lose sometimes. Just like casinos, they win only in the aggregate.
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They do lose, rarely, but it's like casinos, because casinos take bets on a whole lot of events, and only a few bets (or just one bet) on each. A bookie takes bets on much fewer events, and lots of bets on each one. They therefore do not need to rely on the law on average; they are usually guaranteed to make money.
 
Art Vandelay said:
They do lose, rarely, but it's like casinos, because casinos take bets on a whole lot of events, and only a few bets (or just one bet) on each. A bookie takes bets on much fewer events, and lots of bets on each one. They therefore do not need to rely on the law on average; they are usually guaranteed to make money.
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I think you're overstating just how easy it is to make your fortune as a bookmaker. I once saw an interview with the guy who owns Centrebet and it was quite illuminating. If a professional punter bets (say) $10,000 on some horse with an outside chance of 20 to one, then the bookmaker needs to book forty thousand $1 bets against the favourite at five to one from mugs like me just to cover that single big bet. That's a lot of bets. The bookmaker will lay off big bets with other bookmakers to minimise their exposure, but the fact remains that bookmakers can and do go home with massive losses.
 
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