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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.

Ibeatyouraces

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.

  1. Put a beaker on a scale.
  2. Attach a cork to the bottom interior of a beaker using glue.
  3. Wait for glue to dry.
  4. 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?

anonymous

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?

rudeboyoi

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?

anonymous

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?

Eliot Jacobson

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