Ask The Wizard #397

The button below provides further insights regarding single-zero, double-zero, and triple-zero roulette, focusing on the occurrence of numbers once, twice, or three times each.

The next button will display the integral calculations for the nine scenarios outlined previously.

Here is my recommended integral calculator .

The 'law of thirds' suggests that when spinning a roulette wheel for every number available, around one-third of those numbers will not show up.

1/3 is really a pretty poor estimate. A much better one would be 1/e = 36.79%. The true percentage, in double-zero roulette, is 36.30%.

The table below illustrates the chances of seeing between 1 to 38 unique numbers during a session of 38 spins of double-zero roulette.

According to the table, the most common result is that 24 distinct numbers appear, with a probability of 20.49%. The average is approximately 24.20656478.

Some misguided individuals suggest that players should track the first nine unique results and then place bets on those numbers, believing they are more likely to repeat. This notion is fundamentally flawed! The roulette wheel and ball have no memory, ensuring that each number has an equal chance of coming up, regardless of prior results.

Here are the dice configurations suitable for a game with three players:

• Die #1: 3,4,9,10,13,18
• Die #2: 2,5,7,12,15,16
• Die #3: 1,6,8,11,14,17

To accommodate four players, I had to utilize 12-sided dice, organized as follows:

• Die #1: 5,6,11,12,15,20,31,32,37,38,41,46
• Die #2: 4,7,9,14,17,18,30,33,35,40,43,44
• Die #3: 3,8,10,13,16,19,29,34,36,39,42,45
• Die #4: 1,2,21,22,23,24,25,26,27,28,47,48

For a scenario involving five players, the optimal solution I found involved using 840-sided dice, whose faces I will specify in the following. this post in my forum at Wizard of Vegas.

I explain how I created the dice in my previous statement. March 21, 2024 newsletter .