Ask The Wizard #282

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%.
Probability of NOT getting either = 100% -7.09% = 92.91%.
Probability of getting either once in 161 hands = 161*0.9291¹⁶⁰*0.0709¹ = 1 in 11,268.

This question is discussed in my forum at Wizard of Vegas.

I claim that the answer is less. The way I would put it is the center of gravity is shifting downward as the cork moves upward, because water is denser than cork. The scale is measuring force applied against it. As the center of gravity moves down, force is being released, thus less is applied against the scale.

This question is discussed at my forum at Wizard of Vegas.

I'm going to assume the odds are 25 for 1, which is available on the half point card at the Golden Nugget, South Point, and William Hill sports book families.

The table below shows the line you got and the market price line.

First, the probability of an underdog beating the spread is 51.6%. That equates to a fair line of -106.6 on the underdog. So, you're getting 6.6 basis points on the underdogs, and losing them on the favorites.

Second, my table on buying a half point in the NFL shows the fair price to pay for each extra half point. For example, getting the extra half point off of 3 is worth laying -121.4, or 21.4 basis points.

The table breaks down how many basis points you're getting. For the Bears, I doubled the basis points for 1 and 2, since you're turning a loss into a win if you cross those numbers.

The table then converts the total basis points to a probability of winning. The formula is p = (100+b)/(200+b), where p = probability of winning and b = number of basis points.

The bottom row takes the product of each leg winning, for a probability of winning the parlay of 0.046751. At odds of 25 for 1, that bet has an expected return of 0.046751*25-1=0.168783. In other words, a 16.9% advantage. Well done!

The following table shows the choices, the odds they pay, the probability of winning, assuming it is a fair bet, and the adjusted probability to give each bet an equal house edge.

The overall expected return is the inverse of the sum of the fair probabilities. You can see the sum is 1.733465, so the overall expected return is 1/1.733465 = 57.69%. That would make the house edge 100% - 56.69% = 42.31%.

The following table shows the possible outcomes, assuming the player is not banking, and the Trump Plaza house way. The lower right cell shows a player advantage of 16.09%.