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Ask The Wizard #308
I managed to win four jackpots in just six bingo games. The condition for winning the jackpot was to achieve a coverall within a limit of 50 balls. Unfortunately, the casino disputed my win, claiming there was a technical issue, and even threatened to confiscate my $100 deposit. This feels quite unjust. What do you think?
The odds of achieving a coverall within 50 balls in any single game stand at 1 in 212,085. The chance of scoring four wins out of six games is an astronomical 1 in 134,882,670,482,530,000,000. This clearly suggests something went wrong. While I understand the casino might have valid reasons to withhold the jackpots due to possible game malfunctions, it's downright wrong for them to take your deposit. Moreover, if the game can manipulate outcomes to such an extent, it raises serious doubts about its fairness, making me question whether the draws are genuinely random.
This topic has been brought up and is being debated in my discussion forum at Wizard of Vegas .
During a game of craps at one of your advertised casinos, I noticed an unusual occurrence of sevens, which were 38% more than expected. I have a strong suspicion they might be manipulating the game. Here's my complete roll history: 7,5,7,2,4,6,8,7,9,4,9,6,6,6,5,12,7,11,8,4,7,7,9,5,12,5,11,5,8,1,7,7,6,6,6,5,5,9,8,10,9,7,7,11,8,9,3,7,6,10,6,7,8,7,8,6,6,5,5,9,6,7. I believe you should reconsider your support for this suspicious casino!
Given the 61 rolls, the expected number of sevens should be approximately 10.17, calculated as 61 multiplied by (1/6). Yet, you rolled 14 sevens. The likelihood of rolling exactly 14 sevens stands at 7.96%, and the probability of rolling 14 or more is 12.77%. This does not indicate anything particularly out of the ordinary. I also conducted a chi-squared analysis of each roll. While it's not ideal to perform such a test on a small data set, I still wanted to share the findings:
Chi-Squared Test on 61 Dice Rolls.
| Dice total | Actual Observations |
Expected Observations |
Chi-Squared Statistic |
|
|---|---|---|---|---|
| 2 | 1 | 1.69 | 0.284608 | |
| 3 | 1 | 3.39 | 1.683971 | |
| 4 | 3 | 5.08 | 0.853825 | |
| 5 | 9 | 6.78 | 0.728597 | |
| 6 | 12 | 8.47 | 1.468944 | |
| 7 | 14 | 10.17 | 1.445355 | |
| 8 | 7 | 8.47 | 0.255829 | |
| 9 | 7 | 6.78 | 0.007286 | |
| 10 | 2 | 5.08 | 1.870219 | |
| 11 | 3 | 3.39 | 0.044627 | |
| 12 | 2 | 1.69 | 0.055100 | |
| Total | 61 | 61.00 | 8.698361 |
The rightmost lower cell indicates a chi-squared statistic of 8.70. The odds of obtaining a statistic that equals or exceeds this with ten degrees of freedom is 56.09%. These results fell near the apex of the bell curve, suggesting that the casino successfully passes the test for randomness based on chi-squared analysis.
In the reality TV competition Survivor, there were two factions, one comprised of nine contestants and another of six. These players were then randomly reassigned into three new teams, each consisting of five members. Each of the new teams included three players from the larger group and two from the smaller group. What are the chances of this arrangement happening?
Let's designate the larger group of nine players as Team 1 and the smaller group of six players as Team 2. The number of ways to select three participants from Team 1 and two from Team 2 is computed as combin(9,3) multiplied by combin(6,2), totaling 1,260 combinations. To find the total combinations for selecting five members from the entire pool of 15, we use combin(15,5), which equals 3,003. Therefore, the odds of the first team being disproportionately composed with a ratio of 3 from Team 1 to 2 from Team 2 stands at 1,260 divided by 3,003, resulting in a probability of 41.96%.
If this scenario holds true, Team 1 would have six players remaining while Team 2 would have four. The number of ways to select three members from the remaining Team 1 and two from the remaining Team 2 can be calculated as combin(6,3) times combin(4,2), amounting to 120. The overall combinations for selecting five from the remaining ten players is found using combin(10,5), which equals 252. Consequently, the odds of the second team being similarly split with a 3/2 ratio in favor of Team 1, contingent on the first team already being arranged this way, is 120 divided by 252, yielding a probability of 47.62%.
If the initial two new teams are allocated with a 3/2 ratio favoring the previous Team 1, it's logical to assume that the last team will consist of leftover players split in a similar 3/2 format.
Therefore, the calculation for your question results in 41.96% multiplied by 47.62% multiplied by 100%, which equals 19.98%.
Formulas:
combin(x,y)=x!/((y!*(x-y)!)
x! = 1*2*3*..*x
This topic has been brought up and is being debated in my discussion forum at Wizard of Vegas .
In my view, casinos that shuffle cards prematurely during favorable counts are engaging in dishonest practices. I plan to lodge a formal complaint against the Stratosphere with the Gaming Control Board for what I experienced. There's no specific question here, just a need to express my frustration.
Shuffling cards early as a preventative measure against card counters has been a customary practice in gambling for the past five decades. If casinos employ computers to signal dealers to shuffle based on the count, that's certainly deceitful. Furthermore, if dealers themselves count and shuffle early against casual players, that constitutes cheating too. However, if shuffling occurs in response to a player increasing their bets, that’s simply part of the game. If you were to win a complaint against the casinos, it could ruin the game for counters, similar to the aftermath of the Ken Uston lawsuit in Atlantic City. Next, we'd likely see every game equipped with continuous shufflers. It would be better for both sides to maintain the current playing scenario.
This topic has been brought up and is being debated in my discussion forum at Wizard of Vegas .
What is the customary practice regarding tipping the shooter in a game of craps?
There's absolutely no obligation to tip the shooter under any circumstances! I would even recommend against doing so, as it could lead to a culture where individuals only engage with the table to receive tips, creating an environment where opportunists prey on others. The entire tipping culture within casinos is becoming excessively excessive.
This topic has been brought up and is being debated in my discussion forum at Wizard of Vegas .