Ask The Wizard #154

Millennium Sports offers a 6-point 2-team teaser at even odds. I’d like to see the teaser page updated with these odds. Plus I’d like to see another table that states what percentage of individual bets you’d have to win to break even. I calculate the 2 team 6 point teaser witheven odds to be 75% to break even. A difficult task.

John from Herndon, VA

I just updated my Sport Betting Appendix 4 to include the Millennium teasers, as well as using more recent data. Here are is the house edge on teasers including the Millennium odds and whether the pick is on a team or the total.

Two Team 6-Point Teasers

Pays Team Total
-120 12.85% 18.12%
-110 9.25% 14.74%
Ev 4.92% 10.68%

Two Team 6.5-Point Teasers

Pays Team Total
-110 5.85% 10.41%
-120 9.58% 13.97%
-130 12.74% 16.98%

To answer your question, to beat the 6-point teaser you would need an overall probability of winning of greater than 50%, so per pick the probability of covering the tease would need to be the square root of 0.5, which equals 70.71%. To beat the 6.5-point teaser the probability per bet would be 52.38%, or 0.52380.5=72.37% per pick.

What are the odds/probability of each possible five-card hand that could be dealt for from a standard 52-card deck where the suit of a single, unduplicated card in a hand is considered generic? For example, consider the hand A♠ A♣ A A 2. In this hand the suit of the 2 is disregarded and would represent any of the four 2’s in the deck. Another example is A-J-8-6-5. In this hand the suit of all 5 cards is disregarded so that only one such combination can occur. Another example: 3♠ 3 7♣ 7♠ Q. In this hand the suit of the two 3’s and two 4’s is not disregarded because there is more than one in the hand but the suit of the Q is generic. In other words the suit of any card that is not duplicated in a hand is disregarded and that hand is considered to be one of the possible hands even though there would be many possibilities of the hand re-occuring if the suit of each card was not disregarded. Thus a straight or flush made up of five specific cards; say Q J♣ 10 9 8♠ or A♠ J♠ 8♠ 7♠ 3♠ could only occur once since any other combination of those same cards even though in a different suit would be a duplication. Therefore, using this criteria, what is the O/P of any single hand being dealt? In other words how many such five-card hands exist in a std 52 card deck? Thanks for your input.

Mike from Lavallette, NJ

I’m very familiar with this concept. There are 134,459 unique five-card hands. The reason I know this is my first video poker program analyzed all 2,598,960 possible hands and took days to run through a pay table. However by running just one of each of the 134,459 classes of hands, weighting by the number of all hands in its class, you can cut down the run time by 95%. Sometimes when a game is suit specific like my recent analysis of Black Jack Bonus Poker, I have to dust off my old program and do it the slow way.

Wizard, I have been reviewing your site in preparation for a trip to Vegas, because it is the best gambling site period. I was intrigued by the analysis from your December 4, 2001 column about when to stand with 16 vs. dealer 10. Being a math person myself I want to maximize the odds, but also understand the slim gain. Like many basic strategy players, I’ve always hit 16 vs. dealer 10 when I hold a 2, 3, 4, or 5. I’m curious, since this was brought to your attention, have you altered your play to gain that "one unit every 5 years", or have you stuck with just hitting the 16 every time? Thanks for all you do!


Thanks for the kind words. If I’m playing basic strategy (as opposed to counting) I tend to stand if there is already a four or five in my hand. If it is a face-up game, with other players, I scan the table and just use my best judgment.

In blackjack where the dealer exposes both cards (appendix 16), a pair of 8’s is not split against the dealer’s total of 10 or 11; instead, it says hit against the 10 and stand against the 11. Why is this different from regular BS where we split 8’s against the dealer’s ten or ace?

David from Fort Wayne, IN

In regular blackjack the player should indeed split eight’s against a dealer 10 or ace up. However if the dealer accidentally flipped over both his cards, showing a total of 10 or 11, the player should hit against a 10 and stand against an 11. The reason is that when the dealer has a ten or an ace up, by the time it’s your turn you know the dealer does not have blackjack, because he peeked at the hole card to make sure. So you can play your hand more aggressively. But when both dealer’s cards are exposed to show a total of ten or eleven, then the dealer can certainly draw an ace to the ten, or a ten to the eleven, for a total of 21, so in that case you should proceed more conservatively.

My boyfriend has broken up with me a few times, but always comes back. The first time I think he started to like another girl. He went to the movies with her and the next night called me wanting to get back together. Then he broke up with me for a month and then called wanting to get back together. He doesn’t let me have any friends male or female b/c he says he can’t trust me. But when I don’t like it when girls call him he yells and gets mad at me. What should I do and do you think he is cheating on me with one of the girls that call him?

Mandy from Versailles

I can’t stand this jealous waffler from your description. Throw this one back immediately. There are plenty of better fish in the sea.

I’m very glad to see that you are back changing the world 1 mathematically challenged emailer at a time. I have a combination of a dear abby and an odds question. Here goes: A coworker of mine has gone his entire gambling life getting angry at the 3rd base player in blackjack whenever that player doesn’t follow basic strategy. He insists that that "bad" player is hurting his odds. I am 100% certain that it doesn’t change your odds at all. I have tried to explain to him that the reason he thinks it hurts him is because the times that it has in fact hurt him stand out in his mind, and he probably doesn’t even pay attention to the times that it helped him. I told him that mathematically, his odds are the exact same whether he plays at a table of people who never hit, a table of people who never stay, or a table of people playing perfect basic strategy. He doesn’t buy it. But, how can I possibly convince him that he’s wrong? Should I even continue to try? If he admits that he’s wrong, he has to admit that he has wrongly berated countless people at blackjack tables when those people were not hurting anyone else but themselves (and in some cases, if they were counting cards and adjusting their strategy accordingly, they weren’t even hurting themselves). Don’t you think casinos would be better places if people really understood that what I do with my blackjack hand doesn’t change your odds in the long run?

Aaron from Detroit, MI

Your coworker sounds hopeless. As I have said before, the more ridiculous a notion is the more tenaciously it tends to be held. I’d give up on him and let him believe in his delusion. Personally I don’t give unsolicited gambling advice because it is seldom well taken.

me and my bf have been together for a year and 8months he moved away about 8 months ago and we have had a long distant relatioship, and well he has already cheated once when he lived here and once while he was over there in colorado. when i found out we broke up but he ended up having sexual relations with another female i forgave him for that too and now he says he doesnt want to mess up again.. my question is will he do it again are we suppose to be together??

Jess from Albuquerque

Of course he is going to say he won’t do it again. Any man who cheats is also going to lie. I’m reminded of the expression, "Fool me once, shame on you, fool me twice, shame on me." I think forgiveness the first time is optional. Do it again and you’re a fool. The next time he cheats, which is just a matter of time, grow some backbone and get rid of him.

In two different sections on your site, you mention that in general it is better to bet on underdogs rather than favorites against the money line. However, as you point out in your Sports Betting Appendix 3, the money line house edge is LOWER when betting on the favorite. Isn’t that a contradiction? Isn’t it true for a bet of any type to seek out the lowest house edge?

Edward from Placentia

Good point. After giving it some thought I have decided to remove my sports betting appendix 3. It was based on the assumption that the fair line is exactly between the two money lines. For example in the last Super Bowl the money lines were generally Seattle +160 and Pittsburgh -180. My appendix was based on the unrealistic assumption that the fair money lines would be +/- 170. In reality money lines are market driven. Square action on the money line tends to favor the favorite, creating value on the underdog. Assuming Pittsburgh as a 4-point favorite was fair historical data suggests a 4-point favorite has about a 61% chance of winning. That would make the fair money lines +156 on Seattle, and -156 on Pittsburgh. To remind you most casinos had the money lines at +160/-180. Of course Pittsburgh won the game this time, but historically speaking I’m sure you would make out better betting underdogs on the money line over favorites.

My boyfriend and I found out I pregnant about 2 months ago. We have been together for 3 1/2 years and after we found out, he has been going over to his best friend’s house every night until 3:30 in the morning, not talking to me unless it’s necessary, not sleeping in the same bad as me unless that happens to be where he falls at and just pretty much ignoring me. I have asked him if he was cheating and he siad no but his dad and brother cheat on their wives/girlfriends all the time, so my question is do you think he is cheating on me?

Crystal from Clio

Yes. That is not the only problem. This bum clearly is not taking responsibility for his actions. Is there anybody of character who he is close to him that can give a much-needed man to man talk? Clearly his father and brother don’t qualify. I’d give him more time to turn around, but you are going to have to formulate a fall back plan if he doesn’t change. I would encourage you to consider adoption as a possible course of action.

I’d like to know the house edge on blackjack after having 10% rebate on loss. When it’s 8-deck and 6-deck, are the house edges different?

JJ from Seoul

It depends on your playing behavior. Your advantage can get very close to 10% if you play aggressively, always betting half your bankroll, until you multiply it many times over or go bust trying. My advice is keep your sitting short and go for a big win or lose it all, whichever comes first.