Ask The Wizard #178

The variation in reported house edges for Baccarat often stems from differing definitions of the concept itself. Personally, I interpret the house edge as the expected casino profit divided by the original bet. Other writers in the gambling community may calculate it as the expected casino winnings relative to the resolved bets. The key distinction lies in whether or not ties are factored into the outcomes. In an eight-deck game, the probabilities in Baccarat are as follows:

• Banker wins: 45.8597%
• Player wins: 44.6274%
• Tie wins: 9.5156%

I approach the calculation of the expected return on individual bets by including tie outcomes in my assessment.

• Banker: 0.458597*0.95 + 0.446274*-1 + 0.095156*0 = -0.010579
• Player: 0.458597*-1 + 0.446274*1 + 0.095156*0 = -0.012351
• Tie: 0.458597*-1 + 0.446274*-1 + 0.095156*8 = -0.143596

This leads me to determine a house edge of 1.24% for the player, 1.06% for the banker, and a whopping 14.36% for the tie.

Some gambling authors prefer to disregard ties as if they were nonexistent, postponing the resolution of those bets. In this scenario, the probability of a banker or player winning combines to 90.4844%. Consequently, the odds of the next resolved bet resulting in a player win stand at 49.3175%, while a banker win is at 50.6825%.

In computing the expected return for the player's bet, the other perspective calculates it as 49.3175% * 1 + 50.6825% * -1 = -1.3650%. For the banker bet, disregarding ties yields an expected return of 49.3175% * -1 + 50.6825% * 0.95 = -1.1692%. Thus, when ignoring ties, the house edge is 1.36% for the player and 1.17% for the banker.

I advocate for including ties in calculations because it offers players a true reflection of their anticipated losses over time. For instance, if a player wagers $100 on the banker in Baccarat over a four-hour period, with an average rate of play of 80 hands hourly, the expected loss would be calculated as follows: $100 * 4 * 80 * 0.0106 = $339.20. There's no need to factor ties into this equation. If a casino were to utilize the 1.17% house edge for bankers, it would lead to an inflated expectation of player loss and potentially mislead the player.

Another reason I incorporate ties in my calculations is that leading experts in blackjack and video poker factor in ties when analyzing those games. For instance, disregarding ties in a 9/6 Jacks or Better game would inaccurately suggest that the return is just 99.4193% when hitting a pair of jacks or higher. However, the consensus among experts is that the correct return, with optimal play, is actually 99.5439%.

Lastly, I’m sharing a table containing statistics from various gambling literature regarding baccarat.

Casino Math by Robert C. Hannum and Anthony N. Cabot provides insights on the house edge from both perspectives.

I attempted to register for an account to explore this, but they restrict access for U.S. players. I believe the minimum wager is £2 while the maximum is £50. Even in a no house edge scenario like this zero-zero roulette, no betting system can ultimately yield returns outside of that 0% benchmark. Regardless of strategies employed, the more bets you place, the closer the actual house win will approach 0%.

I have dealt with numerous foreign checks from online casinos that never arrived on official casino letterhead. Often, they appeared more akin to generic money orders, rendering it hard to identify the issuer immediately. Should the situation arise, I believe Bodog would likely employ a nominal check or money order that banks would struggle to trace back. Additionally, I don’t foresee Neteller disappearing any time soon.

In the casinos in Vegas, they typically ensure the cards are tucked below your bet when you are banking, disallowing any early contact until others are done setting hands. If you attempt to sneak a glance beforehand, the dealer tends to react promptly to discourage it. However, in your establishment, I wouldn’t hesitate to sneak a peek if I noticed the banker setting their hand prematurely. Just be cautious, as it’s comparable to a dealer in blackjack unwittingly revealing their hole card. This provides valuable insight, and it’s entirely legal to use.

That is indeed correct. In states like Oklahoma, traditional \"class 3\" slot machines are regarded as illegal. To circumvent this, certain establishments implement machines that randomly select bingo cards and balls. Winning patterns correlate with certain payouts and are presented to players akin to slot machine results. If executed correctly—though they often aren’t—the games would play similarly to those in Vegas. I recall spotting popular Williams slots like Reel 'em In during my visit to a Tulsa casino, which incorporated a small bingo card in the corner of the screen. Otherwise, they appeared identical to standard machines. I’m not aware of what return rates they’re programmed to in Oklahoma, so I can’t provide insight on that matter.

To simplify, let’s assume each person has an equal 1/12 chance of being born in any month. The probability that all five individuals are born in distinct months is calculated as (11/12) * (10/12) * (9/12) * (8/12) = 0.381944. Therefore, the likelihood of at least two individuals sharing a birth month would be 1 - 0.381944 = 0.618056.

Please note that I have interchanged the order for the full house and flush.

As I mentioned previously, the probabilities in an eight-deck game of Baccarat are:

• Banker wins: 45.8597%
• Player wins: 44.6274%
• Tie wins: 9.5156%

Here, the expected value for a banker wager is computed as follows: 45.8597% * (1 - (1/35)) + 44.6274% * -1 = -0.00075. Consequently, the house maintains a 0.075% edge. The breakeven commission on the banker wager stands at 2.693%. If one were to bet $37.14, the odds would shift in your favor.

Sex in an elevator? How is it that such events never occurred during my single days? It took a good six months of dating before I reached second base with anyone. As I’ve often pointed out, while forgiving infidelity the first time can be a choice, a second occurrence is a clear no-go. If you feel he is sincere and remorseful, you might be able to get through this, assuming he doesn't have any significant flaws.

I recommend not mentioning it at all. Doing so is unlikely to lead to any positive outcome and could potentially spark a significant disagreement. Ultimately, with time, you’ll find a way to move beyond this situation. Furthermore, this highlights the importance of ceasing any dishonest behavior if you find yourself in that position, but there’s no necessity to admit to it openly.