Ask The Wizard #282
During the final table of the World Series of Poker in 2013, J.C. Tran experienced dealing with 161 hands, notably without ever getting a pocket pair except for once receiving an ace-king. This raises an interesting question about the probability of being dealt such high-value hands when playing through 161 rounds.
Probability of a pocket pair = 13* combin (4,2)/combin(52,2) = 5.88%.
Probability of AK = 42/combin(52,2)= 1.21%.
Probability of either = 5.88% + 1.21% = 7.09%.
The chance of not getting either of these premium hands is 100% minus 7.09%, totaling 92.91%.
The likelihood of securing at least one of these hands in 161 deals can be calculated as 161 multiplied by 0.9291.160*0.07091= 1 in 11,268.
This topic is currently open for discussion on my forum at Wizard of Vegas .
Assume that you do the following.
- Put a beaker on a scale.
- Attach a cork to the bottom interior of a beaker using glue.
- Wait for glue to dry.
- Then fill it with water.
Since the adhesive is water-soluble, over time it will degrade, causing the cork to float upwards. Once the cork detaches from the bottom and starts rising but hasn't reached the water's surface yet, will the balance indicate a greater, lesser, or the same weight compared to when it was still affixed?
I propose that the answer is that it will indicate a lower weight. I believe this happens because as the cork rises, the center of gravity shifts downwards, given that cork is less dense than water. Therefore, the balance measures the force exerted on it, and as the center of gravity descends, less force acts on the scale.
This question is being discussed at my forum located at Wizard of Vegas .
Thanks for your new section on parlay cards . Following your guidance, I've compiled these figures (the market point spread is indicated in parentheses):
- Bills +3.5 (+3)
- Chargers +7.5 (+7)
- Cardinals -2.5 (-3)
- Dolphins -2.5 (-3)
- Bears +2.5 (0)
What is my advantage on this bet?
I'm going to take for granted that the odds stand at 25 to 1, which can be found on the half-point card available at the Golden Nugget, South Point, and William Hill. sports book families .
The chart below illustrates the line you've received alongside the market price line.
To start off, the likelihood of an underdog surpassing the spread is estimated to be 51.6%. This translates into a fair line of -106.6 for the underdog. Thus, you gain 6.6 basis points on the underdogs while losing them on the favorites.
Second, my table on buying a half point in the NFL It details the fair cost associated with each additional half point. For instance, acquiring that extra half point from the number 3 is valued at laying -121.4, which corresponds to 21.4 basis points.
The chart illustrates how many basis points you're capitalizing on. For the Bears, I doubled the basis points for the 1 and 2 outcomes because crossing those thresholds turns a loss into a win.
Subsequently, the table converts the total basis points into a winning probability. The formula used is p = (100+b)/(200+b), where p signifies the probability of winning and b represents the basis points.
The last row computes the product of each segment winning, leading to a parlay winning probability of 0.046751. With odds of 25 to 1, this bet anticipates a return calculated as 0.046751*25-1=0.168783, reflecting a 16.9% edge. Kudos to you!
Rudeboyoi Parlay Card
Team | Parlay Card |
Fair | Underdog Basis Points |
Total Extra Points |
Total | Probability |
---|---|---|---|---|---|---|
Bills | 3.5 | 3 | 6.6 | 20.8 | 27.4 | 0.560246 |
Chargers | 7.5 | 7 | 6.6 | 11.9 | 18.5 | 0.542334 |
Cardinals | -2.5 | -3 | -6.6 | 20.8 | 14.2 | 0.533147 |
Dolphins | -2.5 | -3 | -6.6 | 20.8 | 14.2 | 0.533147 |
Bears | 2.5 | 0 | 0 | 18.0 | 18.0 | 0.541321 |
Product | 0.046751 |
William Hill has already begun taking bets on the outcome of the 2016 presidential race. What would the overall house advantage be for these wagers?
The table below lays out the options available, the odds they offer, the winning probabilities based on fair bet assumptions, and the adjusted probabilities ensuring equal house advantage for each bet.
2106 Presidential Election Odds
Candidate | Pays | Fair Probability |
Adjusted Probability |
---|---|---|---|
Hillary Clinton | 2 | 0.333333 | 0.192293 |
Marco Rubio | 6 | 0.142857 | 0.082411 |
Jeb Bush | 9 | 0.100000 | 0.057688 |
Chris Christie | 10 | 0.090909 | 0.052444 |
Andrew Cuomo | 12 | 0.076923 | 0.044375 |
Paul Ryan | 16 | 0.058824 | 0.033934 |
Condoleeza Rice | 20 | 0.047619 | 0.027470 |
Deval Patrick | 20 | 0.047619 | 0.027470 |
Elizabeth Warren | 20 | 0.047619 | 0.027470 |
Mark Warner | 20 | 0.047619 | 0.027470 |
Martin O'Malley | 20 | 0.047619 | 0.027470 |
Rahm Emmanuel | 20 | 0.047619 | 0.027470 |
Rand Paul | 20 | 0.047619 | 0.027470 |
Bob McDonnell | 25 | 0.038462 | 0.022188 |
Cory Booker | 25 | 0.038462 | 0.022188 |
Rob Portman | 25 | 0.038462 | 0.022188 |
Jon Huntsman | 28 | 0.034483 | 0.019892 |
Joe Biden | 33 | 0.029412 | 0.016967 |
Michael Bloomberg | 33 | 0.029412 | 0.016967 |
Mitt Romney | 33 | 0.029412 | 0.016967 |
Sam Graves | 33 | 0.029412 | 0.016967 |
Susana Martinez | 33 | 0.029412 | 0.016967 |
Amy Klobuchar | 40 | 0.024390 | 0.014070 |
Scott Walker | 40 | 0.024390 | 0.014070 |
Bobby Jindal | 50 | 0.019608 | 0.011311 |
David Petraeus | 50 | 0.019608 | 0.011311 |
Mike Huckabee | 50 | 0.019608 | 0.011311 |
Rick Santorum | 50 | 0.019608 | 0.011311 |
Sarah Palin | 50 | 0.019608 | 0.011311 |
Mike Pence | 66 | 0.014925 | 0.008610 |
Dennis Kucinich | 100 | 0.009901 | 0.005712 |
Eric Cantor | 100 | 0.009901 | 0.005712 |
Evan Bayh | 100 | 0.009901 | 0.005712 |
Herman Cain | 100 | 0.009901 | 0.005712 |
John Kasich | 100 | 0.009901 | 0.005712 |
John Thune | 100 | 0.009901 | 0.005712 |
Julian Castro | 100 | 0.009901 | 0.005712 |
Kathleen Sebelius | 100 | 0.009901 | 0.005712 |
Kay Hagan | 100 | 0.009901 | 0.005712 |
Mia Love | 100 | 0.009901 | 0.005712 |
Michelle Obama | 100 | 0.009901 | 0.005712 |
Newt Gingrich | 100 | 0.009901 | 0.005712 |
Rick Perry | 100 | 0.009901 | 0.005712 |
Tim Kaine | 100 | 0.009901 | 0.005712 |
Total | 1.733465 | 1.000000 |
The anticipated overall return is the reciprocal of the total of the fair probabilities. Notably, this sum amounts to 1.733465, which means the overall expected return is 1/1.733465 = 57.69%. Therefore, the house edge would be 100% - 56.69% = 42.31%.
In the game of pai gow poker, what advantage does a player have if they participate only when their first card is an ace or a joker?
The following table illustrates potential outcomes assuming the player is not banking and adheres to the Trump Plaza house rules. The bottom right cell indicates a player advantage of 16.09%.
First Card is an Ace or Joker
Outcome | Pays | Probability | Return |
---|---|---|---|
Win | 0.95 | 0.383010 | 0.363860 |
Tie | 0 | 0.413936 | 0.000000 |
Lose | -1 | 0.203054 | -0.203054 |
Total | 1.000000 | 0.160806 |