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Ask The Wizard #1
From your Let it Ride In this section, it's advised not to bet on a low pair when considering to 'let it ride.' What are the stakes if one were to disregard this advice?
Placing a bet on a low pair (9s or lower) is certainly not advisable. With three cards, the house advantage stands at 6.37%, and this figure skyrockets to 45.83% with four cards. Thus, you should resist the urge to 'let it ride' on low pairs.
If a slot machine contains five reels and the odds of landing a cherry are consistent across all reels, what would the chances be for achieving a certain number of cherries in a single spin?
Let us define p as the probability of hitting a cherry on each reel, and n as the count of cherries on the payline. The likelihood of scoring n cherries is determined by the formula combin(5,n) * pn * (1-p).5-n. Combin The term (5,n) refers to the various ways in which n cherries can be arranged across five distinct reels. For instance, combin(5,0)=1, combin(5,1)=5, combin(5,2)=10, combin(5,3)=10, combin(5,4)=5, and combin(5,5)=1. This calculation can be utilized directly in Excel and is elaborated in the probabilities section in {poker}. To illustrate, if the chance of obtaining a cherry per reel is 5%, the probability of getting 3 cherries would be calculated as 10 * .053 * .952 = 0.001128125.
When making a bet on two columns in roulette, the odds of winning amount to 24 out of 38, translating to a 63% chance. In your view, does this seem like a successful strategy?
Every bet or combination of bets in roulette comes with a significant house edge. The higher your winning chances, the more you need to wager relative to the potential payout. If you gamble this way 10 times, your chances of making a profit are 46.42%. However, if you do it 100 times, that probability decreases to 24.6%.
While playing baccarat online, I observed that out of 75 rounds, the banker secured 52 wins compared to 23 wins for the player, resulting in a difference of 29. What do you think the likelihood of this event is?
Let's assume ties are not being considered, meaning you are discussing 75 resolved bets. Experiencing 75 hands without a tie is quite rare. The expected number of banker wins in 75 resolved bets is about 38.00913745. To find the standard deviation, you need the square root of the product of 75, the probability of a banker win, and the probability of a player win. The probability of a banker win, excluding ties, is approximately 0.506788499, while the probability for a player win is roughly 0.493211501. This calculation gives us a standard deviation of about 4.329727904. A half-point adjustment for a binomial distribution is needed, followed by looking up the Z statistic in a standard normal table (this step is left for you to figure out). Ultimately, the probability of the banker achieving 52 wins or more is .0009. Your scenario also considered the possibility of the banker winning 23 times or fewer (another difference of 29 or more), resulting in a probability of .0004. Thus, the total probability of a difference of 29 or greater is .0013, or approximately 1 in 769.