Question of the Day 2017-05-29

Tonight, on videopoker.com, I was playing 10-Play Triple Double Bonus Poker. I was dealt the ace, 2, 3, and 5 of diamonds, and the ace of spades. Given the chances of an inside straight flush against what four aces (particularly with the kicker) pays on Triple Double, I held the two aces, which I believe was the right hold. After the draw, the first card in three out of the 10 hands had, in fact, the 4 of diamonds. So I would have connected on three straight flushes had I kept the four- card straight flush. I’m trying to calculate the odds of this result and the nearest I can compute is 1/47 times 1/47 times 1/47 (since the three hands were independent events) or approximately 1 in 103,000.

[Editor’s Note: The answer to this question is provided by the inimitable Bob Dancer, whose blog can be found on our sister site, Gambling with an Edge, where you can also hear a weekly podcast in which Bob and Richard Munchkin, author of our book Gambling Wizards, interview likely subjects.]

You’ve managed to ask a lot of questions in one QOD. Let’s get started.

First, the inside straight flush is the better play by a mile. Yes, four aces with a kicker pays a bunch, but you only get that 1-in-1,622 times from that position. Holding AA from that position in Triple Double Bonus ($10.16) isn’t worth much more than holding in it Double Double Bonus ($9.50). (How much you get for the flush is irrelevant insofar as the value of the aces is concerned, but it does affect the value of the straight-flush draw, as you had 8/47 draws from there that would have given you a flush.) If you concentrate on just the aces, it seems like it should be a much bigger difference, but you end up with 3-of-a-kind about one time in nine — and that pays only $10 in TDB, while it pays $15 in DDB.

Any good video poker software will give you this information. I recommendVideo Poker for Winners, but there are others.

If you’re confused about this hand, which isn’t that difficult, you’re probably making mistakes on a lot of other hands as well. VPW also provides a strategy for the game. Use it, rather than trying to figure it out by your own methods.

Second, the 1-in-103,000 figure you cite would be appropriate if you were playing Triple Play, where you had to connect on the 1/47 shot on each line. In Ten Play, it doesn’t particularly matter which three lines you get it on. The appropriate mathematical function to compute this is called the Binomial Theorem.

This is not an appropriate place for an extended lesson on the Binomial Theorem, but if you use the BINOMDIST function on an Excel spreadsheet, you’ll find out that the odds for hitting three or more 1/47 shots in 10 tries is about 1-in-1,000, not 1-in-103,000.

Insofar as whether you would have hit all three perfect draws had you correctly held the straight flush draw like you did when you held the aces, there’s a very slim chance that would have happened. The draws take place when you hit the button — down to the nanosecond. Unless you hit the button at precisely the same time, you would have gotten a totally different draw on all 10 hands.

Finally, worrying about what you would have gotten this time if you played it the other way is a fool’s game. You have to make your choice and take what you get from that choice. Whatever happened this particular time is a small bit of data and is not a very good predictor of what will happen next time, or the next next time, or the … Go with the math rather than spending time dwelling on what happened this particular time.

Then again, if it makes you happy to feel bad that the other draw would have worked out better this time, go right ahead. Your feelings won’t change the results one bit. But if that’s how you want to spend your time and energy, be my guest.

No part of this answer may be reproduced or utilized in any form or by any means, electronic or mechanical, without the written permission of the publisher.

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Comments

[email protected] May-29-2017

Wow

Why does the answerer of the question have to sound like a complete douche?

Jeff May-29-2017

Too Long at the Game?

I've been reading the QoD for more than a decade, and in my experience this is a first: The author of the answer actually berates and insults the questioner!

Along with the facts relevant to an appropriate answer are several gratuitously snarky  asides culminating with the inexcusably rude, "if that’s how you want to spend your time and energy, be my guest." This calls for an apology from LVA.

It sounds to me like Mr. Dancer may have become burnt-out after too many years of devoting his life to the questionable (no pun intended) profession of applying complex mathematical equations to computerized gambling games that most sensible people play casually for fun once in a while while reserving their mental energies for more productive activities (i.e. ones where the inevitable result isn't lost money) but "if that's how [Mr. Dancer] want[s] to spend [his] time and energy, be my guest."

George May-29-2017

Teaching

Mr. Dancer is a teacher who motivates his students to excel in the game of VP.  Granted, his answer may not be politically correct but it is realistic. No pain no gain.

Jeff May-29-2017

To: George Mikutowicz

You are confusing the pain of challenging one's intellectual or physical limits when learning new things with the pain of being belittled by an instructor. Shaming by an instructor is not part of the learning process and is counter-productive in that it is more likely to discourage and demoralize a student than motivate him.

Steven Larson May-29-2017

Uncalled for

I agree with the other comments.  The answer is nasty - especially saying things about the poster deciding to "feel bad" when there wasn't even anything in the post about how he felt.  He explained what he did and asked a question about odds.  And in  terms of whether Bob was justified in his tone because he was "teaching" - I don't even think he was accurate in his response. His comment about pushing the button at the exact nanosecond is true for VP machines in the casino, but (and I'm just guessing here) I really doubt that the games on videopoker.com work that way.

SkeeterMN49 May-29-2017

Disrespectful

I also agree with the comments and was appalled as I continued to read the answer and the tone just got worse.....

Jim Veith May-29-2017

Way too Sensitive

My goodness. I enjoyed Bob's answer, learned from it, and actually felt his comments were just fine.   

Thank you Bob for sharing your knowledge and insights with us. To those who you somehow offended by the answer, don't be so thin skinned, looking for trouble not intended, GET A LIFE!

Steven Larson May-30-2017

Poor Jim Veith

I feel bad for you Jim.  If you are so unhappy with your life that you feel that you have to insult people then go right ahead!  Your insults won't actually change anything, but if that's how you want to spend your time and energy, be my guest!

Annie May-31-2017

The video poker advisor was out of line.

There's a time and a place for everything. 

"Kicking ass" makes sense for Marine Corps boot camp where, "Sir, you are not holding your rifle in the correct way. Let me show you how, if I may," would be ridiculous. 

But it does not make sense in addressing a stranger on the Internet who may be a 70 year old grandmother  where civility and tact are called for. Personal insults (ad hominem attacks) are most often not allowed on moderated forums, partly because it inevitably leads to flame wars rather than constructive discussion and partly because most people do not enjoy being insulted or insulting others, notwithstanding the above poster who thinks otherwise.

Question of the Day - 29 May 2017

Comments