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Calculating " XXX to 1" Underdog from Win Odds

Discussion in 'The Sports Book' started by DeMoN2318, May 29, 2018.

  1. DeMoN2318

    DeMoN2318 The DERS

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    Now that the NBA finals are set, I checked the odds on Vegasinsder and was shocked that CLE is such underdogs.

    VI has GSW at 1:10 and CLE at 6:1

    So that got me thinking about how describe the underdog to people. CLE is "six to 1" to win the championship, but since GSW is such a huge favorite that really makes CLE a much larger underdog than six to 1...right?

    I look at it as "If this series was played 11 times, GSW would win 10 of 11", "If this series was played 7 times, CLE would win 1 of 7"

    So if we put them in common denominators, "if this series was played 77 times, GSW would win 70 times and CLE would win 7 times"

    Does that make CLE a:

    "10 to 1" underdog (70/7)?
    "63 to 1" underdog (70-7)?
    "17 to 1" underdog (-1000 vs +600)?
    "60 to 1" underdog (6 * 10)?

    Curious how other people interpret these type of odds and how they describe it to non-gambling people.
     
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  2. UKFanatic

    UKFanatic The Arbiter of Taste Caviar Kid

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    I describe it to non-gamblers by saying the snowball has a better chance than the Cavs
     
  3. vetsen

    vetsen Low-Roller

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    To me, underdog implies betting line and therefore I think you're totally fine quoting the 6:1.
     
  4. The Rumor

    The Rumor VIP Whale

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    17 to 1, 63 to 1, and 60 to 1 are all incorrect. A 17 to 1 underdog would have odds of +1700, for example. You don't add the figures together the way you did.

    Technically, saying 6 to 1 is good enough for explaining things to your neighbor. If you're being extremely precise, you could adjust for the the vig as follows:

    GSW: -1000 implies a 10/11 chance of winning, or 90.91%
    CLE: +600 implies a 1/7 chance of winning, or 14.29%

    The house is charging a little over 5% on these bets (90.9%+14.3% = 105.2%) instead of offering a line with no vig. You could adjust them to a vig free line:

    14.29%/(14.29%+90.91%) = ~13.6%. Which is still very, very close to 6 to 1. The heavy favorite is expected to pay most of the vig because they win the vast majority of the time.

    Keep in mind that Vegas odds for long shots tend to be somewhat square lines, because people disproportionately bet straight up on big underdogs relative to betting straight up on big favorites. GSW fans are more likely to go make a point line bet on game 1 instead of betting to win so little on the series.
     
  5. DeMoN2318

    DeMoN2318 The DERS

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    I understand what you are saying, but something just doesn't seem right to me. I can't put my finger on it, which is why I started this thread to hopefully have something spark through the discussion.

    10 to 1 favorite against a 6 to 1 underdog just doesn't compute for me, again I can't put my finger on it yet.
     
  6. The Rumor

    The Rumor VIP Whale

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    Think of it like this. They could offer even lines by having a 10 to 1 underdog and a 1 to 10 favorite. The dog would win 1 out of 11 (or 10 + 1) times and the favorite would win 10 out of 11 according to the odds. The implicitly assigned probabilities would add up to 100% and the bets would pay as follows:

    Assuming their odds are correct and the underdog really wins 1 out of 11 trials:

    - 1/11th of the time, the underdog wins, and the casino would pay out $11 for each $1 bet (the original $1 bet plus $10 for winning). The expected value of this $1 bet is exactly $1 for the player - they lose and get back $0 10/11ths of the time, and they get back $11 on that one time in eleven when they win.
    - 10/11th of the time, the favorite wins. The house pays out $1.10 for each $1 bet (the original $1 bet plus $0.10 for winning). The expected value of this $1 bet is exactly $1 for the player - they lose 1/11th of the time, and they get back $1.10 on the 10 out of 11 trials where they win

    In this scenario above, the casino expects to make no money.

    The reason they offer odds that appear to have a gap like the 1 to 10 favorite versus a 6 to 1 underdog is they want to make a profit. They aren't setting lines to pay out 100% of what they take in. Instead, they create odds which have a gap between the favorite and the underdog that results in profit. If you assume either line is "correct" for the NBA finals. It doesn't matter if you assume GSW wins 10 out of 11 times as a 10:1 favorite with CLE winning once or if you assume the 6:1 underdog CLE wins 1/7 times and GSW wins 6 out of 7 times, you'll note that the expected payout is less than $1 on one of the two potential wagers.

    For example, if we assume that the true odds are that Cleveland will win 1/7th of the time:

    - The CLE payback on a $1 bet is exactly $1 (you get $7 back in the 1 out of every 7 scenarios where they win) -
    - But a $1 bet on GSW pays back less than $1 - you'd get back $1.10 dollars (10 to 1 favorite odds in LV) 6/7th of the time + $0 the other 1/7th of the time. This is an expected value of only $0.943 for the $1 bet for the player, and the house expects to win 5.7 cents on every $1 bet on GSW. This is the casino's expected profit that they have built into their odds.

    In practice, standard lines are set so the house expects to win about 5 cents on every bet that is made (please, other posters, I'm being simple and ignoring other considerations that might cause the edge to vary)
     
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  7. 93 Octane

    93 Octane Chief bottle washer

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    Seems like you're thinking a 10/1 favorite should have a 9/1 dog---or a dime line -- which in theory is correct but reality suggests a downside no book wants to(or should) take. The 6/1 dog are the minimum odds the book can offer and expect a reasonable profit.
     
  8. DeMoN2318

    DeMoN2318 The DERS

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    This helped! Thanks for explaining it! The even line comparison did it for me, looking at them moving together (2:1 vs 1:2, 3:1 vs 1:3, etc), then the expected value calcs helped me see why they don't actually move together
     
  9. Chuck2009x

    Chuck2009x VIP Whale

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    It doesn't sound clean, but that's exactly how I would put it. But you don't normally hear people say both ends of that quote in the same sentence.

    I don't think I agree with that, the odds are a function of shifting the money on each side. Putting it in terms of who would win more often is getting into probabilities, and that's not really what the odds reflect or what their intent is, although you can kind of reverse engineer a probability from it if you want to. If they reflected a book's opinion of probability, it would have to add up to 100%.
     
    Last edited: May 31, 2018
  10. Dearns

    Dearns Low-Roller

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    I did my Maths degree dissertation on betting and it was all about calculating the 'true' odds of outcomes in the EPL. Being British we are used to fractional or decimal odds.

    You were right to say that 1/10 means that you would expect them to win 10 out off 11 times and 6/1 means 1 out of 7. Over here we'd say a '6 to 1 underdog' but we'd say a '10 to 1 on favourite.' The 'on' bit just means thatthe 10/1 should be reversed.

    If you were to write as a common denominator though you would have 70/77 and 11/77 which is a total of 81/77 (greater than 100%.) That's how the bookies build in their house edge.
     
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