Ask The Wizard #372
I see the Face Up Pai Gow Poker Mega progressive at the Caesars properties in Las Vegas is over $3.9 million. Is this currently a good bet?
I checked various Caesars properties on October 1 and found this pay table for the $5 progressive Face Up Pai Gow Poker bet.
- Seven-card straight flush = $3,922,620
- Five aces = $185,104
- Royal flush = $2,969
- Straight flush = $500
- Four of a kind = $375
- Full house = $20
I analyze this bet in my page on Face Up Pai Gow Poker. In this case, the Mega Jackpot, for a seven-card straight flush, is unusually high. I believe it to usually be in the low five-figure range. The bottom line is this $5 bet has an expected return of $9.55! That means an expected profit of $4.55.
You still have to make a negative bet on the base game. The minimum on that ranges from $15 to $100. At a house edge of 1.81%, here is the expected loss by bet amount on the base game.
- $15 bet = $0.27 loss
- $25 bet = $0.45 loss
- $50 bet = $0.90 loss
- $100 bet = $1.81 loss
At a base bet of $251.61 and $5 on the progressive, the combined game would have zero house edge.
However, two big reasons not to bet it are the 37% highest marginal federal income tax rate and the huge volatility. The average player who doesn't hit any of the top three progressives can expect to lose $3.38 a hand at a $15 base bet and $3.56 at $25. That adds up on an hourly basis.
Still, it is, mathematically, a very positive bet. At a $15 base bet, the combined player advantage is 21.39%. You don't see that every day.
This question is asked and discussed in my forum at Wizard of Vegas.
I hear the MGM properties in Vegas now charge the vig on buy bets after a win only. How does this change the house edge?
I believe the already charged the vig after a win only on the 4 and 10. So, there is no effect there. Here is the house edge on the 4 and 10 all three ways you might bet them:
- Place bet (pays 9 to 5) — 6.67%
- Buy bet (commission always paid) — 4.76%
- Buy bet (commission paid on wins only) — 1.76%
On the 5 and 9, this is good news, lowing the house edge from 4.00% on a place bet to 2.00%.
- Place bet (pays 7 to 5) — 4.00%
- Buy bet (commission always paid) — 4.76%
- Buy bet (commission paid on wins only) — 2.00%
On the 6 and 8, it doesn't matter, as the house edge on place bets is still lower.
- Place bet (pays 7 to 6) — 1.52%
- Buy bet (commission always paid) — 4.76%
- Buy bet (commission paid on wins only) — 2.27%
This question is asked and discussed in my forum at Wizard of Vegas.
In episode 4 of season 37 of Survivor, there was a challenge in which four puzzles pieces could be arranged into both a square and an equilateral triangle. What would be the exact dimensions of the pieces for this to work?
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First, let's make a proper diagram and label it.
Following is just the diagram of the solved triangle.
![haberdasher solution triangle](/wizfiles/img/3537/triangle2.png)
Next, assuming the sides of the square are length 1, here is just the length of each letter in the diagram above.
a = d = e = h = 1/2
b = g = SQRT((4-SQRT(3))/(4*SQRT(3))) =~ 0.572145321740575
c = f = 1-SQRT((4-SQRT(3))/(4*SQRT(3))) =~ 0.427854678259425
k = m = 1/SQRT(SQRT(3)) =~ 0.759835685651592
n = (3-SQRT(4*SQRT(3)-3))/(2*SQRT(SQRT(3))) =~ 0.386767938902275
p = (SQRT(4*SQRT(3)-3)-1)/(2*SQRT(SQRT(3))) =~ 0.373067746749317
Finally, here is my full solution (PDF).
This question is asked and discussed in my forum at Wizard of Vegas.