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Betting Odds, Implied Probability And Beating The Closing Line (Page 1 of 2)
In order to profit long term from gambling, it is essential to understand the underlying mathematical concept behind the odds offered by sportsbooks.
Using a random line at Pinnacle Sports for a mythical Yankees/Royals game we see New York offered at -220 and Kansas City at +206 and from those betting lines, we can calculate the implied probability each team has of winning that particular game.
To calculate the implied probability of winning for a favorite (where the odds are negative), take the absolute value of the odds and divide that by the absolute value of the odds plus 100. For the New York Yankees, the implied probability of winning is:
220 / (220 + 100) = 220 / 320 = 0.6875 = 68.75%
To calculate the implied probability of winning for an underdog (where the odds are positive), divide 100 by the sum of the line plus 100. For the New York Yankees, the implied probability of winning is:
100 / (206 + 100) = 100 / 306 = 0.3268 = 32.68%
Looking at the percentages, the sum of them is over 100 which is never a good sign for percentages; in fact, the sum of them is 101.43%. The additional 1.43% represents the theoretical hold for the sportsbook or more commonly called the vigorish (and generally shortened to vig) which is the % amount charged by the sportsbook for its services. Assuming that the sportsbook draws in equal action on both sides it will then make 1.43% profit on the total amount of bets placed but since they are unlikely to attain equal action in most betting lines, it is only a theoretical hold.
Since the winning percentages contain an element of vigorish, we need to remove that in order to end up with the actual, rather than the implied, winning percentages and this will give us the no vig line; this is done by dividing each implied winning percentage by the sum of both winning percentages.
For the New York Yankees, the actual probability of winning is:
0.6875 / 101.43 = 0.6778 = 67.78%
For the New York Yankees, the actual probability of winning is:
0.3268 / 101.43 = 0.3222 = 32.22%
Now we can convert the two actual win probabilities into a no-vig line.
For an actual win probability equal or greater than 0.50 – or 50% in percentage terms – the formula (where FV is equal to the decimal win probability of the favored team) for the Yankees line is:
-100 / ((1 / FV) – 1) = -100 / ((1 / 0.6778) – 1) = -210.4
For an actual win probability less than 0.50 – or 50% in percentage terms – the formula (where UD is equal to the decimal win probability of the underdog) for the Royals line is:
((1 / UD) – 1) * 100 = ((1 / 0.3222) – 1) * 100 = +210.4
Since the sportsbook vig has been removed from the lines, the lines are identical in absolute terms.
This above example is where there is a clear favorite (with negative odds) and a clear underdog (with positive odds). However in the cases where there are two teams which are similarly favored by the market or, more commonly, the betting lines which use a point spread the calculation is slightly different. In this case the implied probability and actual probability can be calculated by using the New York Yankees example of calculating the implied and actual probability of winning.
100 Ten Gram Nevada Jacks Poker Chip Set with Mahogany Case Critical Overview
If you’ve ever experienced a night of poker with those Plastic Poker Chips with ridged edges, you know all the nightmares that come along with it. People getting confused over denominations, getting shorted chips in the beginning, and just a crazy merry-go-round that continues everytime we get together. So after our annual Thanksgiving tournament in 2007 we had to try something different .
That’s when everyone started searching for poker chip sets online. We all decided to spend an hour (there is 12 of us) surfing the net once out of the week so we could come up with something. Oddly enough when we all talked about our findings three of the twelve suggested the 100 Ten Gram Nevada Jacks Poker Chip Set with Mahogany Case. Personally, I never saw it myself, but everyone else had different choices so we had to look here first.
It’s really all we needed once everyone got a good look at the picture. The case itself looked like something that should be in a cigar store. The mahogany finish and appeal is enough to turn heads, but we wanted to know more about the poker chips. Don’t get me wrong, the case got us there, but the chips are going to keep us playing each time we all get together. Point well taken right?
Anyways, we all made lists of the pros and cons about the 100 Ten Gram Nevada Jacks Poker Chip Set with Mahogany Case. What we came up with was that the only cons were there wouldn’t be enough Custom Poker Chips. Then when reading over all the information Barry figured out there was really 500 Casino Poker Chips there as opposed to the 100 we originally thought. So that was a bonus and something we didn’t need to worry about anymore.
The next thing we discussed was the denomination amounts. Since we aren’t gung-ho poker players for big stakes we were afraid there weren’t Poker Chips For Sale that had denominations, but this set has everything from .25 cents to $500. Definitely more then enough for our little tournaments, plus if we ever do go over a dollar an ante then we’ll already have the 100 Ten Gram Nevada Jacks Poker Chip Set with Mahogany Case at our disposal.
While we thought it was a coincidence that the 100 Ten Gram Nevada Jacks Poker Chip Set with Mahogany Case just happened to be found by three of our friends, it really wasn’t an accident. The truth of the matter is they are considered one of the most popular products throughout the poker industry. Either way, we’re glad they’re now in our possession. Poker night is much more entertaining without all the bickering over money and misplaced chips.
One thing we did like and was surprised about was the three decks of playing cards that are also included, various color schemes, and pullout trays for easy access. Okay, so that was more then one thing, but you get the idea. We just like the 100 Ten Gram Nevada Jacks Poker Chip Set with Mahogany Case. What else can we say. This product is officially approved by Brian Garvin and Jeff West from Poker Stars Direct Poker Supply Outlet.