Friday, April 17, 2015

O is for . . .

This month I'm posting Mad-Cool-Math Nuggets.


Image courtesy: mkw87

O is for Odds.

Odds are used in statistics and in gambling. I'll take a wild guess and assume you'd find gambling more fun, so I'll stick to that for this discussion.

Let's start with probability. If you roll a single die, there are 6 possible outcomes. So the probability of rolling a 2, for example, is one-sixth or 16.67 %.

In betting odds, we look at this example a little differently. The odds of rolling a 2 are said to be 5/1, read "5 to 1". Why 5 and 1? Because there are 5 ways the outcome we want will not happen (rolling a 1, 3, 4, 5 or 6) and 1 way the outcome we want (rolling a 2) will happen. This is known as fractional odds, and you can use these two numbers to calculate the same probability of rolling a 2. Here's how:

The probability of an event with A/B odds is B / (A + B). In this case, the probability, or odds, of rolling a 2 is 1 / (5 + 1) = 1 / 6 = 16.67 %.

Fabulous. So how does this work with money? Bet $M on an event with A/B odds. If you win, you get M x (A/B) dollars plus your original $M back. (If you lose, say bye-bye to your $M.)

Bet me $1 that I will roll a 2 on my handy-dandy die, an event with 5/1 odds. If I roll a 2, you win, and you get 1 x (5/1) = 1 x 5 = 5 dollars, plus your original $1 back. Squee! (Don't spend it all in one place.)

If you bet $8 on the same event and win, you get 8 x (5/1) = 8 x 5 = 40 bucks plus your original $5 back.

Ready to hit Vegas? Well, maybe not. The example above is a fair game, statistically speaking. If we were to play enough times, you would win about as much money as you would lose, and so would I. Neither one of us would make a profit. In Vegas, casinos need to make money to stay in business.

Remember Hunger Games and the saying "May the odds be ever in your favor"? Yeah, right. That didn't work out so well for the players. All but one bit the dust. The same holds in Vegas. The odds are definitely in the casinos' favor, by design.

Ever been to Vegas? Play the lotto?

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28 comments:

  1. I went to Vegas last year and it was a lot of fun! I stuck to the slot machines, though. I'm definitely not that much of a gambler.

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  2. You had me then you lost me and then you had me again. lol I don't think I'll be very good at Vegas. I'd have to go with blind, beginners luck. :P

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  3. Once again I studied hard, and I think I got the gist of it! If I broke even in Vegas I'd be very happy.

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  4. Once again I studied hard, and I think I got the gist of it! If I broke even in Vegas I'd be very happy.

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  5. So true and I hate when people use it like in Hunger Games, when they know the "odds" are against everyone!!! Lisa, co-host AtoZ 2015, @ http://www.lisabuiecollard.com

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  6. I happen to be a statistician by day and work for a health system, so odds are the most common way stats are presented (for health conditions or outcome likelihood) so I happen to love them...

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  7. I happen to be a statistician by day and work for a health system, so odds are the most common way stats are presented (for health conditions or outcome likelihood) so I happen to love them...

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  8. very interesting---I guess I have separated odds and statistics ---especially when occasionally playing the lottery ;)

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  9. Been to Vegas, once...card is punched not something I enjoyed all that much. I loved the people watching there though, and the hotels and weather were great. I am not a lucky person, hardly ever even get into something like a football pool.
    Sandy at Bridge and Beyond

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  10. Wish you were my math teacher when we were studying probability! Your explanation made it easy to understand.

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  11. Wish you were my math teacher when we were studying probability! Your explanation made it easy to understand.

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  12. Haven't been to Vegas in years but we want to go back. Its so close. I play poker because I actually have some control over the game rather than playing by chance.

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  13. This is why I don't gamble, and I'm about to hit Vegas next week. :)

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  14. I don't gamble either. I would be the one Vegas makes money from.

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  15. I'm a huge blackjack player.. I love it :)

    (Notice I didn't say I make a living playing blackjack :)

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  16. I've been to Vegas a couple times (I've lived in the US Southwest, so it's not a great effort). The only way gambling works out in your favor is if you like giving money to casinos. The shows were kind of fun, but other than that, it's a big city with people throwing money all over the place.

    As for playing the Lotto, my dad has a saying, "your odds are only slightly improved by buying a ticket." Then again, you're more likely to be killed in a vending machine accident than win the lottery (no, really, look up vending machine deaths, and you'll be shocked--they're almost as deadly as volcanoes!)

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    1. Dude, are you reading my mind? That's part of Saturday's p-blog!

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  17. I always suspected that about Vegas. The nearest I get to gambling is a game of bingo in an English holiday camp, which is not quite as glamourous.

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  18. I sometimes enjoy playing French roulette. the croupiers always impress me with their skills.

    I haven't been to Vegas, but I visited some of these gambler towns (Blackhawk, Central City) in the Rockies when we lived outside Denver.

    Cold As Heaven

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