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Ask the Wizard #148

Great website! Would you please tell me how often the player and the dealer will both bust, on the same hand, when the player is using the basic strategy? I went to the math links that you have listed, but couldn’t figure out how to set up the equation. I would appreciate any help you can provide.

Paul from Portland

The following table shows the probability in a single-player game. Remember, the dealer will not play out his hand if the player busts first. If you add players the dealer’s probability of busting will go up because there will be a greater probability of at least one player not busting.


Bust Probabilities

Decks Soft 17 Player Dealer
6 Stand 15.72% 24.07%
6 Hit 15.68% 24.40%

I just got back with my boyfriend and was wondering if I can tell if he’s cheating on me besides flirting with the other chick.

Ashlee from Bemidji

The joke is that you can tell a man is cheating if he is happy. Seriously, look for any changes in his behavior. If he spends less time with you, looks better, goes to different places, or does different things then he probably cheating.

What is the advantage to a player to add one ace to and remove one 2 from a 6-deck BJ game with AC rules?

Scott from Toronto

My blackjack appendix 7 can be used to approximate the answer to this question. Adding the ace would favor the player by 0.005816/24 = 0.00024. Removing a two would favor the player by 0.003875/24 = 0.000161. So the total effect would be 0.000404, or a decrease in the house edge of 0.04%.

Hi, I thought I would ask you this since I cannot find it anywhere on the web. I hope you answer this; What are the odds of existing? Whether it be on Earth or somewhere else in the universe? It’s not a gambling question but an answer we should all know so we can appreciate what kind of odds we beat just being alive!

Andreas from Edmonton

The probability that intelligent life exists anywhere in the galaxy I believe is very high. The Drake Equation seeks to estimate the number of incidents of intelligent life in the galaxy, which depending on the numbers you put into comes up with a figure of about a million. However there is also no good evidence that these civilizations have ever visited us or made contact. So the famous Fermi Question is "Where is everybody?" I do think the lack of evidence of other intelligent life casts some doubt on the Drake Equation but I would still put the number of intelligent civilizations in our galaxy in the ballpark of 1000. That is just our galaxy, there are billions of galaxies out there. However the distance between galaxies is so vast there is really not much point in discussing travel or communication between them. So to answer your question I would say roughly 99.9%.

My local casino has a rule where if the initial 2 cards, for example a pair of 4s, are split to form 2 hands and then the next card is another 4, if the player opts not to split again he will not be given the option to split should a 4 come out as the next card on the second hand of his initial split. My question is: does this rule give the house an advantage and if so, how?

Ken from Tenian Island

No. If splitting is the right play you should do it every time, and if not never. So this rule is moot if you play properly.

Party Poker has a high hand jackpot awarded to tables showing down a Royal Flush. What are the odds in a 10 handed Texas Holdem game of a table hitting a Royal Flush?

Dan from San Diego

If we assume all hands are played to the end the probability of any given player having a royal flush is 4*combin(47,2)/combin(52,7) = 1 in 30,940. To make things simple lets assume each hand is independent. The probability of at least one player in 10 having a royal flush would be 1-(1-(1/30940))10 = 0.00032, or 1 in 3094.

My boyfriend and I usually hang out together but now we barley do that anymore because he goes over to his best friends house and that’s where his ex lives too. What should I do?

Jennifer from Hillsboro, Oregon

Tell that bum to hit the road.