Ask The Wizard #21

As a dealer at Casino Niagara, I'm curious about the likelihood of a dealer forming a hand when the face-up card is a 5. It seems that my fellow dealers and I generally agree that we manage to create successful hands more often than not. Also, what are the chances a dealer hits a blackjack when showing an ace as their up card?

The short answer is that the odds are against you, and it's highly unlikely that you will win. The standard 6/49 lottery has odds of 1 in 13,983,816. To achieve a 50/50 chance of winning at least once, you would need to play approximately 9,692,842 times. If you bought 100 tickets each day, it would take you about 265.6 years to reach that probability. For a 90% chance of winning, the timeframe extends to around 882.2 years.

A solid wager holds value on its own, regardless of what it's against. Nevertheless, the substantial house cut at the racetrack is something that must be considered. Additionally, you can never be entirely sure what the actual odds are. If I believed a horse had a 50% likelihood of winning but was offered at 3 to 1, I might start questioning my own assessment about its chances. Similarly, when selecting a mutual fund, it’s essential to evaluate both the historical return rates and the management fees involved.

Parrando's Paradox suggests that if you alternately play two losing games, you can still achieve a positive return in the long run, given that the games are interdependent. This connection makes it less applicable to typical casino games.

Analysis shows the outcomes for both hitting and standing when facing a dealer's 7 with a hand consisting of 10 and 6. Choosing to hit would result in an expected loss of around 39.6%, while standing has a higher expected loss of 47.89%. There isn’t a straightforward explanation for why hitting is the better option; you need to evaluate all possible outcomes, weigh them by their probabilities, and sum them up. In the end, hitting turns out to be the lesser of two unfavorable choices.

For those unfamiliar with your query, these machines take discarded cards from blackjack hands and integrate them back into the deck randomly after each round. If a player is using basic strategy, these machines actually create a slightly lower house edge by removing the cut card effect. As far as I understand, they provide a genuinely random shuffle. On the downside, the use of these shuffling machines allows dealers to spend less time shuffling and more time distributing cards, which means players experience longer game sessions and, consequently, more opportunities for the house edge to take effect.