Ask The Wizard #54

Let’s express f(x,y) to denote the probability of drawing x cards from one suit and y cards from another. This concept is not restricted to just two variables.

For two variables, the equation can be represented as f(x,y)= combin(13,x)*combin(13,y)*12/combin(52,5).

For three variables, we can write it as f(x,y,z)= combin(13,x)*combin(13,y)*combin(13,z)*12/combin(52,5).

For four variables, the formula f(w,x,y,z) is given by combin(13,w)*combin(13,x)*combin(13,y)*combin(13,z)*4/combin(52,5).

The probability of obtaining cards from all four suits can be calculated using COMBIN(13,1).³*COMBIN(13,2)*4/combin(52,5) = 26.37%.

When considering the probability of three suits appearing, the calculation is COMBIN(13,3)*COMBIN(13,1).²*12 + COMBIN(13,1)*COMBIN(13,2)^2*12/combin(52,5) = 58.84%

The probability of drawing cards from two suits combines multiple considerations: COMBIN(13,3)*COMBIN(13,2)*12 + COMBIN(13,4)*COMBIN(13,1)*12/combin(52,5) yields approximately 14.59%.

The likelihood of drawing from just one suit, which includes both straight and royal flushes, is calculated as 4*combin(13,5)/combin(52,5), amounting to 0.20%.

From my observations, drawing three suits seems to be the most common result.

To clarify, let’s explain what a match play coupon entails for those unfamiliar. This coupon is typically featured in casino promotional booklets. When a player places a qualifying even money bet alongside the match play coupon, it transforms into an equivalent amount of cash if the wager results in a win. For instance, if a player holds a $5 match play coupon and places a $5 bet on red in roulette, a win on that bet results in earning $5 in cash and converting the match play into an additional $5. No matter the outcome, whether winning or losing, the match play coupon is forfeited. In cases of a tie, the player retains the coupon.

In the context of blackjack, utilizing the Match Play tends to yield just an even money payout. This results in a reduced worth of the Match Play by around 2.3%, which is quite significant. Among true even money bets, the Player bet in baccarat is the wisest choice for applying a match play, with a winning probability of 49.32%. In contrast, the don’t pass option in craps has a slightly lower probability of 49.30%. Therefore, the effective value of the Match Play when used on the Player bet is 47.95% of its original value, on the assumption that the player wouldn't have made that bet otherwise.

While calculating the precise numbers may prove complex, your assumption holds merit; the dealer indeed has an advantage if numerous high cards remain in the discard pile while small cards are returned to play. This paradigm mirrors preferential shuffling, where the dealer chooses to shuffle a good count but proceeds with the deal during detrimental counts. Such practices are known to occur here in Las Vegas, making your observations not surprising.

I delve into the cut card effect in depth in my work, but essentially, most house edge statistics are calculated assuming a game without a cut card. This approach is likely rooted in tradition and the desire for straightforward mathematics. Nonetheless, you raise an important point that adjusting the house edge statistics to reflect the presence of the cut card would enhance accuracy. That said, I continue to base my house edge calculations on the initial hand drawn from a freshly shuffled deck. Analyzing blackjack without factoring in the cut card effect can be challenging enough. blackjack appendix 10 I've encountered multiple mentions regarding instances of bonus exploitation by players from Denmark. Do you have any insights into what's occurring? What actions are being taken, and how can we prevent ourselves from falling into the category of bonus abusers?

I have a query about 'progressive betting' strategies, similar to 'Another Experiment', particularly regarding Player 2 highlighted on your Betting Strategies page. It's clear that during standard blackjack gameplay, players encounter streaks of wins and losses. Where does the flawed reasoning lie in the approach of 'minimizing losses by resetting to 1 unit and enhancing winning streaks by increasing the bet by 1 unit for each win?' To share my experience, I actually implement a slight variation of that approach: 15, 30, 45, 50, 75, 100, 125, and so on. Thank you for your time. And please avoid embarrassing me like Ann did on The Weakest Link; I truly enjoy your site and appreciate all the valuable information.

I provide mathematically sound strategies and insights for various casino games, including but not limited to blackjack, craps, and roulette, as well as countless others.