Ask The Wizard #392

Which Las Vegas casinos still have buffets?


Good question. Many properties got rid of them during the pandemic closure. Here is a list of those that survived. Please be advised many have limited days and hours of operation.

  • Bellagio
  • Caesars Palace
  • Circus Circus
  • Cosmopolitan
  • Excalibur
  • Main Street Station
  • MGM Grand
  • Palms
  • Rampart
  • South Point
  • Westgate
  • Wynn

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

Consider an 8/5 Bonus Poker progressive with a 0.5% meter rise. Player A must have a player advantage immediately to play. Player B is patient and will play until the jackpot hits, but still requires a long-term advantage. What is the minimum jackpot for each player to play? You may assume a stand-alone machine that is not part of a linked progressive.


The return from the fixed pays in 8/5 Bonus Poker is 0.971776. Let's assume the player uses strategy for a royal that pays 800. The probability of a royal is thus 0.0000248551. Let j be the breakeven jackpot to have an immediate 100% return on the game. Then:

1 = 0.971776 + j × 0.0000248551
j = (1-0.971776)/0.0000248551 = 1135.56.

So, player A would need at jackpot of at least 1136 full 5-credit bets (rounding up) to play. Player A does not need to care about the meter rise.

Player B is in it for the long term. He will eventually get back whatever the 0.5% meter rise. His calculation is similar, except he values that meter rise. His breakeven value of j can be defined as:

1 = 0.971776 + 0.005 + j × 0.0000248551
j = (1-0.971776-0.005)/0.0000248551 = 934.39.

Rounding up, player B would need a jackpot of 935 full 5-credit bets.

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

What is the formula for 13 + 23 + 33 + 43 + ... + n3?


The answer is n2(n2 + 1)/4

Here is a link to my solution (PDF).

The square above has side length 2. One arc is of a circle of radius 1 and the other radius 2. What is the area of the red region? It is allowed to express your answer in trig functions.


4*(arctan(2) + 4*arctan(1/2) – 2) =~ 3.84695661518926


Here is my solution (PDF).

Source of this question: Presh Talwalkar of the YouTube channel Mind Your Decisions.