Ask The Wizard #50

On a 4-deck blackjack game if you split aces against 5 or 6, and you get another ace. You should double or hit? (no more splits at this point) I am getting different answers on different sites. So far, I have seen one site double on 5 and 6, one site double on 6 only, and other sites list split on all cases and I assume they didn’t consider this situation. Another question in 4 deck BJ for 10,2 against 4, one site listed a hit. I would like a confirmation from you.

Larry from Austin, USA

Keep in mind most casinos won’t let you do either. However if you can you should double on the 6 only. This is true whether or not the dealer hits a soft 17. If the dealer stands on a soft 17 the expected returns against a 5 are .162849 by hitting and .148228 by doubling, so hitting is the better play. Against a 6 the expected returns are .189020 by hitting and .196249 by doubling. So doubling is the better play. You can see these numbers for yourself in my blackjack appendix 9e. About your other question, yes in a 4-deck game the player should hit a 10,2 against a 4, but only if the dealer stands on a soft 17. I don’t list 4-deck basic strategy exceptions myself because there are so few and they make such a small difference. Following this exception will help you win more unit every 113396 hands, or lower the house edge by 0.000882%. Not worth the bother of memorizing the exception in my opinion.

Will you be doing a risk of ruin analysis for Craps? The only analysis I have found online to date seemed to be flawed.

Brian E. from Raleigh, USA

I wasn’t planning on it. There are so many betting patterns in craps that one analysis would only fit a small percentage of craps players.

We play three card guts with a pay-the-pot if you hold the highest hand and no one goes in. We play with straights and flushes. What is minimum hand you should go in on? Ace high? Any pair? a high pair? If you remove the straights and flushes, what would the odds be? Can you also explain how you came to your conclusion. Much thanks old wise one!

Tebo from London, UK

Good question. I’ve been toying with doing a section on guts for years. I have a computer program half-way finished. One problem is there are so many ways to play guts that one analysis would only fit a small percentage of games. The dummy hand also makes things much more complicated. On a related note let me suggest a good guts variation. If nobody stays in then you go again, everyone with the exact same cards. Knowing everyone else has a lousy hand will induce players with a marginal hand to stay in. The first time my friends and I adopted this rule everybody went in on the second round.

I noticed that use posted odds for double down stud. Have you found this at any on-line casino’s. I played it in Kansas City, but Biloxi doesn’t have it and my wife loves that game. Thanks for any help you can give me.

Jason from Montgomery, USA

No, I haven’t seen it at any online casinos. The only place I have seen it is Atlantic City. The game seems to be going the way of the dodo bird.

I really appreciate all the information on blackjack on you site. I wonder, in jacks or better video poker how is the 99.54% return calculated? For example how do you know what is the best play with an unsuited jack and king?

Meudon from Moisan, France

There are combin(52,5)=2598960 possible combinations of the first five cards. You don’t have to analyze all of them. Personally I break them down into 191659 different kinds and weight each one with the number of similar hands. For example the odds are the same with four aces and a king singleton regardless of the suit of the king. You don’t have to analyze four hands for each possible suit of the king, just one of them and multiply by four. Once you have a hand there are 25=32 ways to play the hand. I analyze each way and take the play with the greatest expected value. To determine the expected value of a play you have to analyze all the ways the replacement cards can fall and score each hand. In the case of throwing all five cards away there are combin(47,5)= 1533939 possible replacement hands. The total number of hands that must be analyzed to determine the best play of a specific hand is combin(47,5)+5*combin(47,4)+10*combin(47,3)+10*combin(47,2)+5*47+1, which coincidentally also equals 2598960. So if we took no short cuts at all we would have to analyze 25989602= 6,754,593,081,600 hands. Just reducing the initial hands to 191659 we still have 498,114,074,640 hands to analyze. Clearly more short cuts are in order. It would take a desktop computer several hours at least to work through this many hands. Personally I don’t actually score any hand but use carefully chosen formulas to determine the probability of improving a hand. For example with any pair and 3 singletons the probability of improving the hand to a two pair is always the same. Things get more complicated with straights and flushes but still manageable. My program can calculate the expected return for a game of jacks or better in about one minute. Considering it used to take me over a day I’m rather proud of it. I hope this answers your question.

I was running your deuces wild video poker program. I had the following cards. QJ8 of spades T7 of diamonds. I opted for the 4 card inside straight draw and kept the QJT8. The advice thing came back and recommended that I keep the JT87 and discard the Q. This looks like one of those situations where there are two plays with the same EV (similar to the case where you have two pair and need to keep just one pair).

Dan from Albany, New York

You’re right. There are two ways you can go for an inside straight, both of which have the same expected value. Sorry my program scolded you, I should correct that.

I recently started playing Spanish 21 because the rules at the local Thunder Bay casino give it much better odds than Blackjack. The dealer stands on soft 17, but uses 8 decks of cards. Does using 8 decks give better or worse odds for the player than the 0.40% you calculated with 6 decks?

Raymond from Thunder Bay, Canada

I always liked the name Thunder Bay for a city. I used to work at a summer camp not too far from there in Missanabie, Ontario. To answer your question 6 decks is better than 8. However the difference in the house edge is small, only about 0.03%.

The Flamingo is offering a single deck blackjack game with regular downtown rules (hs17). The only difference is that they altered the natural payoff to 6 to 5 instead on the normal 3 to 2. My questions are; How does that affect the starting advantage on this game? What would it be? How would it affect the insurance wager? Specifically what would Insurance have to pay in order for the player to get "even money" and be square to the 6 to 5 payoff?

DW from Las Vegas, USA

Using my good ol' blackjack house edge calculator normal downtown rules result in a house edge of 0.1896%. In single deck the probability of a player blackjack and no dealer blackjack is 2*(16/52)*(4/51)*(1-2*(15/50)*(3/49))= 0.046492. Reducing the BJ win from 1.5 to 1.2 results in increasing the house edge by 0.046492*(1.5-1.2)= 1.3948%. So the house edge of this game would be 1.3948%+0.1896%=1.5844% (ouch!). For insurance to result in even money, it would have to pay 5-1 but the player could only bet 20% of the original bet on it.

I won recently at eWorld Casino. They said they would send a payment Western Union 6 days after I withdrew it. It has now been 7 days and every time I call their support line they tell me they don’t know when they payment will be made. Should I worry? What should I do?

David from New York, US

First let me say that eWorld is okay as far as I know. I’ve played them and had no problems. I’m think they will pay you and this is just ordinary inconvenience most players suffer with. Unfortunately Internet casinos in general are not known for paying winners quickly. I’ve seen the range myself from 3 days (Net Club) to 33 days (Casino on Air) of those times I kept track. I would say 2 weeks is about average. After two weeks I would ask about it every 3-5 days until they pay. Perhaps they will tire of the nagging and expedite the payment. Don’t get threatening or abusive until it seems there is no other hope. I would wait until 45-60 days have gone by before getting to this stage. Once you do get tough they may shut off all communication. However if you feel things are hopeless give a final strongly worded warning. Wait a few days and then do your best to get some justice by warning others of your experience at the bulletin boards. This advice is not specific to eWorld but all Internet casinos. Keep in mind most of these casinos operate out the Caribbean and Central America where people take their sweet time to do anything.

What is the house edge for baccarat with 10% commission on a winning banker?


The probability of the banker winning is 45.86% and the player winning is 44.62%. So the house edge would be 44.62%-.9*45.86%=3.346%.

I thought you blacklisted the Golden Palace Casino but I just received an email from you promoting them. What gives?

Grey from Singapore

You’re not the only one to complain. My partner in charge of advertising thought my feud with them was ancient history and accepted the ad. I was not happy about it and I apologize for it. Hopefully this won’t happen again.