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Ask The Wizard #92
What impact does the casino's approach of labeling the traditional come bet odds as \"off\" during the initial roll have on the house's advantage? How is this calculated, and how does keeping the odds on come bets during come out rolls influence the overall house edge?
That's an interesting inquiry. For those unfamiliar with the topic, it's important to note that normally odds on come bets are inactive during the come out rolls unless stated otherwise. Therefore, if a player rolls a seven during a come out roll, all come bets will lose, and the odds on those bets will be returned. Similarly, if the player's point number is rolled during the come out phase, the come bet wins, but the odds will not change. The answer varies depending on how we interpret the house edge. If we see it as the expected losses against all bets made, then deactivating the odds doesn't make a difference, since the bet still counts even if returned as a push. Conversely, if we view the house edge as the anticipated losses compared to settled bets, turning off the odds during a come out roll does raise the house edge. I used a computer simulation to explore this effect. Given that a player wagers odds five times, deactivating the odds during come out rolls elevates the ratio of losses to total resolved bets from 0.326% to 0.377%, indicating an increase of 0.051%. Therefore, to optimize outcomes on resolved bets, keep those come odds active.
Can you elaborate on the process of 'buying in' at a craps table? Is cash the only accepted form of payment by dealers? If I want to make a significant buy-in, does that mean I need to bring a large sum of cash to the casino (which feels risky, especially in Las Vegas)? What about using travelers’ checks? Is it feasible to arrange for credit ahead of time with the Cashier’s Office at the casino? If yes, could you detail how that works?
Reflecting on my initial visit to a casino, I was unsure about how to acquire chips for gaming and ended up purchasing them at the cage before heading to the blackjack table. The correct method of buying in at the table involves simply placing your cash on the table. At the right moment, the dealer will convert that cash into chips. If you’d rather not carry large sums of cash for security reasons, you can transfer funds to the casino in advance. When you arrive, simply request chips from the pit boss, who will have you sign a document acknowledging that you are purchasing chips against your cash balance. On a side note, I believe the U.S. Treasury should consider issuing $500 bills to make transporting large sums of money more convenient; after all, a 500 Euro note is already in circulation, equivalent to about $598 in U.S. currency at the time of writing.
I came across an unconventional bonus at Aqua Online casinos, where a deposit of $100 prompts them to lend you an additional $200. However, any leftover amount upon cashing out will have the borrowed $200 deducted. What strategies would you suggest to maximize the benefits of this bonus?
My suggestion would be to aim for an exceptionally large win, or at least take the risk of losing everything in the process. The greater your winning target—up to a certain point—the higher your potential returns. Personally, I would strive for around $2000. It seems counterintuitive, but to truly benefit from the bonus, you may have to go all in and risk it all. Ultimately, you are hoping for a fortunate outcome that will leave you with a substantial profit.
When playing deuces wild, if I already have three deuces, what are the odds of drawing a fourth deuce? What if I begin with only two deuces?
If you start with three deuces, you can draw the fourth deuce from one of 46 remaining options, along with another card from the deck. The total combinations of choosing two cards out of the 47 left in the deck equals combin(47, 2) = 1081. Therefore, the probability of retrieving four deuces when starting with three held is 46/1081, which equates to approximately 4.26%, or about 1 in 23.5 chances. On the other hand, holding onto two deuces provides 45 possible outcomes for acquiring two more deuces and an additional card, with combin(47, 3) = 16215 ways to select three cards from the 47. Hence, your likelihood of drawing four deuces after beginning with two is 45/16215, or roughly 0.28%, translating to about 1 in 360.33.
In a single-deck game, what is the likelihood that all three players and the dealer will each receive a blackjack during the first round after a shuffle?
Following are the probabilities:
Player 1 0.048265
Player 2 0.036735
Player 3 0.024823
Dealer 0.012560
The product is 1 in 1,808,986.
Mr. Wizard, your website is exceptional. You might just be the most trustworthy expert there is online. I'm curious—while I understand how odds in craps are calculated, I can't shake the feeling that when a player has multiple bets in play, either from placing them directly or by betting the pass line and making consecutive come bets, that the odds seem to dramatically tilt in favor of the house. One roll of seven can wipe out all those bets at once. To win, a player needs to hit every number in the right order, and if a seven comes up, it nullifies all the other numbers.
I appreciate the kind words. However, I maintain that the house edge remains consistent regardless of the number of come bets placed. Sure, it can feel discouraging to establish numerous come points only to lose them all to a seven. Yet, there are instances where the shooter takes considerable time to roll a seven, allowing players to benefit from several come bets in the meantime.
If playing Basic Strategy greatly reduces the losses to casinos, why do some establishments freely distribute Basic Strategy cards and permit players to refer to them while gaming? I've observed this in places like Shreveport, Vicksburg, and Black Hawk, Colorado, and friends have mentioned seeing similar practices in Las Vegas.
Throughout my blackjack experiences at various casinos in the United States, I have never encountered Basic Strategy cards being handed out for free. That said, it's common for casino gift shops to sell them, and they are indeed allowed at the tables. I suspect that while casinos might not favor the cards, they realize that enforcing a ban on them could lead to more significant player dissatisfaction. Additionally, where would they draw the line? If a player were to jot down Basic Strategy on their arm, could the casino prohibit them from reviewing their own notes?
Can you shed light on how online casinos (through Random Computers) determine their payback percentages? For instance, in blackjack, one should anticipate losing about 2.5% to 3% over time when employing basic strategy. Is this percentage calculated based solely on the hands being played at that moment, the number of players online, or over a specific time frame taking into account all hands played at that casino? I'm curious if high-stakes players winning in other games can impact the cards I’m dealt, ultimately influencing the casino's ability to secure its profit margin.
When a casino states it returns 98% in blackjack, this figure typically reflects historical performance data, usually from the past month or so. The time frame for this statistic should ideally be disclosed. The 98% indicates the ratio of money returned versus total money wagered, encompassing bets from doubles and splits. Hence, if all players utilized basic strategy, their return rate would likely fall beneath the house edge, which is calculated solely on the opening bet. High-stakes players can certainly skew these percentages, potentially causing a casino to report returns exceeding 100% if a high roller wins more than what others have lost.