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Ask The Wizard #217

PKR.com, along with some other platforms, has introduced a gambling game inspired by 'Deal or No Deal'. According to the site, the house edge is set at 4.54%. The game features 26 cases, each containing prizes that can range from 2% up to 1000% of your initial stake. For the $100 game, these probabilities are represented as 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 200, and 1000. The total value sums up to 2482, and the difference of 118 accounts for the 4.54% house advantage (which is derived from 2482 divided by 2600, yielding 95.46%). Unlike what happens in televised versions, the banker’s offer in this game reflects the actual average value of the remaining cases throughout each round, rendering it pointless to wait in hopes of a better deal. Is there a strategic approach that players could utilize effectively?

Andy B. from Embrun, ON

I concur with your calculations. The average value of those cases stands at 95.46, which results in a house edge of 4.54% based on the $100 wager. There’s no effective strategy that can influence the outcome either positively or negatively; it’s essentially a gamble based on chance.

I was just reading Dave Matthews column In one of my experiences, I decided to try my luck at video poker and played 26 lines at a dollar each. Anyone who regularly plays video poker understands the reason behind choosing to bet on 26 lines specifically. This was done on a machine offering a hundred lines, but why select that number?

Steven H. from Hilo, HI

I often place my bets on 26 lines at the $1 level as well. This particular choice is strategic; hitting a win of $1,200 or more requires a manual payout, which can be time-consuming and necessitates tipping the dealer. For instance, if you hit a dealt full house while playing 9/6 jacks, which I happen to know was the game at that moment, you would earn $5 multiplied by 9 multiplied by 26, totaling $1,170. If you went one line higher, your payout would trigger the hand pay at $1,200. If betting on 26 lines, equating to a total wager of $130, seems too minimal, I then switch to 39 lines, where a dealt flush results in a payout of $5 times 6 times 39, reaching $1,170. The next significant threshold occurs at 59 lines, where a dealt straight would payout $5 times 4 times 59, yielding $1,180. However, I tend to avoid 59 lines because winning three of a kind often leads to hand payouts too frequently.

How many successful pass line bets can we typically expect a shooter to achieve?

Robert M from Summit, NJ

Here you go:

Average winning pass line bets = 1.244898
Average total pass line bets = 2.52510
Expected points made = 0.683673
Expected rolls = 6.841837

Which Las Vegas casinos feature a smaller table, often referred to as a tub, specifically for craps games?

Dave P.

According to the Bone Man at NextShooter.com Here’s a breakdown of where and when you can find these tubs:

There’s a Tub located at Wild, Wild West, likely operational only in the evenings on weekdays and throughout the weekend.
A Tub can also be found at Ellis Island, probably accessible in the evenings on weekdays and weekends as well.
At Circus Circus, in the West Casino section, there’s a Tub, though it's rarely open except during peak holiday periods.

As of 2010, I’ve been informed that Ellis Island replaced its tub with a full-sized craps table.

Recently, I visited a casino in Oklahoma where I played craps, and I discovered several alterations to the standard rules. Instead of traditional dice, they use a deck of 54 cards ranging from Aces to 6s. The stickman will request a number between 1 and 3, then discard that many cards before flipping over the next two to represent the dice roll. Once approximately half to three-quarters of the deck is exhausted, a new deck replaces the old one, which is then shuffled.

Additionally, if you wish to place a bet at the table, there’s a required $1 ante paid to the casino. You only pay this once for the come out roll; after establishing the point, you can wager any amount without needing to contribute another ante. The betting limits at the table range from $5 to $300.

Imagine if the dealer goes through 39 cards out of 54 before reshuffling. If you’ve been able to see or track 26 of those cards, you previously mentioned that if there's a good number of 5s and 6s left, you’d consider making the 'yo 11' bet. Is it possible to develop a more refined betting strategy for this casino game? I genuinely believe this game can be beaten. Would a high/low count system, similar to card counting in blackjack, be effective here? I appreciate your insights.

Chuck from New York

I maintain that hop bets, like the yo-11, are the optimal choice. Utilizing chips can aid you in tracking how many of each card remain in the deck.

When you have 26 cards that are not visible, if any single face has 6 cards left in the deck, you'd gain a 43.1% advantage on a hard hop bet (where you bet on two of the same face), assuming it pays 30 to 1. If only 5 are left, then the house would have a 4.6% edge.

The more straightforward hop bets offer even better opportunities for profit. If two numbers dominate and have at least 10 cards left combined, with a minimum of 3 for each, among the 26 unseen cards, it would be wise to place an easy hop bet on those numbers. If both numbers have 5 cards remaining, you would enjoy a 23.1% advantage. If one has 4 and the other 6, your advantage drops to 18.2%. And with a combination of 3 and 7, the advantage is a mere 3.4%. All of this is predicated on the assumption that easy hop bets yield a 15 to 1 payout. None of this considers the $1 fee mentioned earlier. However, if you're making significant bets, the fee hardly affects the overall equation.