Ask The Wizard #21

I'm a dealer at Casino Niagara and want to know what the odds of a dealer making a hand are when the up card is a 5. It seems to me and the other dealers that we all agree that we make a hand more times than not, and usually a good one at that. Also, what are the odds of a dealer having a blackjack with an ace as an up card?

John from Niagara Falls, Canada

You're right, it is more likely the dealer will make a pat hand. From my blackjack appendix 2, the following are the probabilities of the dealer's final total given a 5 as an up card. This assumes the dealer stands on a soft 17, which I believe is what you do.

  • 17: 12.23%
  • 18: 12.23%
  • 19: 11.77%
  • 20: 11.31%
  • 21: 10.82%
  • bust: 41.64%

Assuming 8 decks, there are 16*8=128 10 point cards in the deck. Eliminating the ace there are 52*8-1=415 possible cards under the ace. Thus the odds of a blackjack are 128/415 = 30.84%.

I have been playing lotteries and sweepstakes now for two months straight. Will I ever hit a jackpot? And when?

Mavis from Mattapan, U.S.

The short answer is no, you will never win. The odds of winning the usual 6/49 lottery are 1 in 13,983,816. You would have to play the game ln(.5)/ln(1-1/combin(49,6)) = 9,692,842 times to have a 50/50 chance of winning at least once. Assuming you bought 100 lottery tickets a day, it would take 265.6 years to have a 50% chance of winning. To have a 90% chance of winning, it would take 882.2 years.

I've had this argument with several friends and I hope you can help. They say horse racing is a bad bet because of the "takeout". It's true the track has a takeout that varies from about 16% to 30%, depending on the type of wager, but my contention is that there is no factually correct way to determine a horses "true odds". If you figure a horse has a 50% chance of winning, but the odds are 3-1, isn't that a good bet, no matter what the takeout is? I know some handicappers that set their own odds and only bet when they feel the odds are in their favor, and some do well.

Kevin from Van Nuys, California

A good bet is a good bet, regardless of whom it is against. However, you can't ignore the high house cut at the track. You also can never be sure of what the true odds are at the track. If I thought a horse had a 50% chance of winning but paid 3 to 1, then I would doubt by own judgement that the horse really had a 50% chance of winning. Along the same lines, when choosing a mutual fund you should consider not only the historic rate of return but also how much is charged in commissions.

I have read a couple of articles about "Parrando's Paradox." Is there a way that you could explain what is going on as it is extremely counter-intuitive that two losing games played in a certain sequence could add up to a winner. I thought I understood the mathematics of gambling / probability! I can see that there is a subtle link between games A & B as game B is dependent on capital that is affected by game A; I am unable to carry the logic any further. Does Parrando's Paradox have any implications for negative expectation casino gamblers? I doubt it but would love to hear it from someone with a greater understanding.

Gavin from Burt St Edmunds, England

Parrando's Paradox states that two sub-optimal games of chance can show a long-term gain if played alternately. However the games can not be independent of each other, which eliminates any comparison to casino games.

Mike, On my last trip to Vegas, a dealer I've come to know said he was "toying with the idea" of standing on a 16 against a dealer's 7 because only 5 of the 8 cards give the dealer an automatic win. How does this strategy play out?

Chris from Gaithersburg, Maryland

This would be a bad play. For example, my blackjack appendix 9B shows the return both ways by playing 10 and 6 cards against a dealer 7. Hitting has an expected loss of 39.6% of the bet. However, standing has an expected loss of 47.89%. There is no easy explanation I can give why hitting is better. You have to consider everything that can happen, weight it by its probability, and take the sum. Overall hitting is better of two bad plays.

What is your opinion of the continuous shuffle machines now being used at the blackjack tables in Las Vegas? Do these machines give the house more of and edge even when a person is using basic strategy?

John from London, Canada

For those who don't understand what you're asking, there are new machines that take the blackjack discards and place them randomly back in the deck after each hand. If you are using basic strategy, then the shufflers actually lower the house edge slightly, due to the omission of the cut card effect. It is my understanding that they do provide an honest random shuffle. However, the shuffling machine allows the dealer to waste less time shuffling and spend more time dealing. This means you will spend more time playing, and thus more hands for the house edge to grind you down.

For more information on the mathematical effect of continuous shufflers, please see my blackjack appendix 10.