BDLX hand, warning long post.

[Mr.Dawes]

This post is going to be long and I understand if no one wants to read through it all. Also, I am not trying to start a debate over EV theory. I accept the reasoning behind EV theory and believe that many minds with much higher levels of mathematics education than myself have done sound work to develop a very strong approach to the game of video poker. I follow EV theory and try to play as accurately as possible. However there are a very few hands where I question if the theory's validity is as strong ( for a non pro)  as it is for the vast majority (99%+) of hands.It is a little slow at work today so I decided to practice 8/6 Bonus Deluxe on my VPW software. At 98.5, BDLX is not a great game but it is .6 better than Biloxi's ubiquitous 9/5 DDB. This is a relatively new game for me. I started by looking at the strategy chart at wizardofodds.com then began to practice on VPW.Today I was dealt the following hand, Ac, 4c, 7c, 3h, Jd. I held the unsuited Ace Jack and the warning window popped up so I investigated the hand using the VPW hand analyzer and the strategy chart at wizard of odds as well as it's hand analyzer. Both analyzers said the correct  play was the Jack only. The wizard of odds strategy chart however says to play the Ace Jack. The rule for this hand according to wizard of odds is to play the Ace jack unsuited unless the three discards are lower than seven and not suited with the jack, in which case you would play the Jack only. Essentially, most hands you will be dealt with an Ace Jack unsuited will contain a flush and/or straight penalty card for the Jack only making the Ace jack the correct play.When I looked at the EV difference between these two holds for the hand above I found that the Jack is better by 0.00003 ( yes four zeros!). When you hold only one card, the jack in this case, there are 178,365 possible combinations that can be drawn and that 0.00003 difference is more than accounted for by just one of these combinations, the royal flush. Removing that one in 178,365 royal flush draw from the Jack hold makes the Ace Jack better by about .22. Futhermore, the Ace jack hold produces 5 additional wins per hundred draws than the Jack hold. I expect to play BDLX for about 1/4 of my play which consists of about 40,000 hands per year. I would expect out of those 10,000 hands I might encounter this one maybe 25 times( I am guessing here ).So what I am asking myself is do I really benefit from an EV increase of 0.00003 that will only be realized by hitting a royal when in my life I will only encounter this hand maybe a few hundred times? Am I not far more likely to benefit from the Ace jack's higher winning hand percentage?Yes I am aware of how silly it is to devote this much time to 0.00003.Any thoughts are appreciated and if no one made it all the way through that is cool too.

[Vman96]

EV is EV. The higher the EV is, the less money you expect to lose.   Would I really worry about whether I would remember that penalty exception though? No.

At some point, you can make your strategy complicated enough that you are more likely to make larger errors because your strategy becomes more unwieldy when you add more and more penalty exceptions and it will be more and more difficult to remember the complete strategy. Getting basic strategy correct is much, much more important.

[Mr.Dawes]

Vman, I respect your thoughts and understand your position. Certainly any strategy for any game is only as good as a players ability to implement it. What I am trying to work out for myself is whether EV should be the only factor that influences my decision making. The EV of a hold is simply the total value of all the draws for that hold divided by the total number of possible draws.Therefore I think it is important to understand what draws comprise that total and how often they will occur.In the above hand the 1 in 178,365 royal draw is the only reason the single jack beats the Ace Jack. Given that I will probably only encounter less than one tenth of 1% of those 178,365 draws shouldn't a factor like the probability of a winning combination serve as a mitigating factor. Also, this same reasoning could be applied to support your assertion that rare penalty card situations can over complicate a strategy and result in more confusion for the player and therefore be a less effective strategy.Also, I hope no one reading my posts thinks I am trying to give advice on how to play. I really use these posts as a way to help myself work through my thoughts about playing video poker.

[alpax]

The easiest method to remember the Ace-Jack offsuit situation.

Hold Jack over Ace-Jack if

(1) The other 3 cards are not a flush penalty to the Jack

(2) The 3 cards does not consist of
a. 8
b. 9
c. 7 AND 10

This situation comes up quite often so might as well master it.

[Mr.Dawes]

Thanks Alpax, that is my understanding as well. You write that this hand occurs often. Would you mind laying out a strategy to determine how often any given hand is dealt. I have tried to work this out for myself but I guess my math background isn't strong enough to figure it out.I suppose for this hand the process would go something like this. Start with one Ace. There are now 51 cards in the deck but you can not draw one of the other Aces so now there are 48 cards to chose from. Also, you can not draw the Jack of the same suit so there are only 47 cards to choose from for the next card and so on and so on. This process seems way too cumbersome. Is there a more formulaic mathematical approach? Thanks Again.

[alpax]

It is indeed cumbersome because other than calculating the number of ways to get Ace+Jack offsuit, you also have to account for 4 to a straight, pairs, two pairs, three of a kinds, 4 to a flush, and such on the deal which have a higher precedence on the strategy charts.

On google search bar, you can type 52 choose 5 to get 2598960. This is the total number of ways you get deal a 5 card hand from a 52 card deck.

However, VPW does the calculations for us in the strategy feature. I highlighted 10 and 11 to account for the number of Ace+Jack offsuit situations, we get 5880 + 2520 = 8400 situations.



EDIT: 8400 hands is the number of situations you hold the Jack over Ace+Jack, let me redo the calculations.



On the BDlx strategy, element #29, it shows there are 162996 ways to get 2 high card with ace high on the strategy charts. This means ace-king, ace-queen, and ace-jack possibilities; thus we can divide that by 3 to get 54332 hands of Ace+Jack offsuit.

2598960 [number of 5 card draws] / 54332 [number of A+J situations] = 47.8

For an average player that plays 600 hands an hour, they can expect to see this scenario every 5 minutes on average, it seems to be frequent and worth knowing.

[BobDancer]

Post unable to migrate

[Mr.Dawes]

Thanks Alpax. I did not know these features existed in VPW. I appreciate your time and input.

[alpax]

First of all, Alpax, good job at writing this up. You have a nice combination of innate knowledge, willingness to work at figuring out a problem, and ability to present your findings clearly in writing. Excellent!
Now, my question on your analysis is one that I don’t have the answer to. I’ve worked with VPW more than most folks, so I was very familiar with the type of charts you included --- although I typically would ignore analyzing a game that only returned 98.5%. Working hard at getting my losses to 1.5% instead of 1.6% has never been a goal because I am fully capable of not playing at all --- which reduces my losses to zero.
However, in the problem at hand, a look at the strategy shows 162,996 occurrence of AH versus 169,884 times holding AH is the correct play. That means there are 6,888 times we are dealt AH when we don’t hold it.
The strategy report you displayed showed 8,460 different situations where we were dealt AH and don’t hold it.
My question is why aren’t these two numbers the same? I’m usually able to reconcile such things (and I regularly write about such idiosyncrasies in strategies) but I appear to be having a senior moment this time.



I thank you Mr. Dancer for the compliment. I am aware you have access to the full pay schedule at the Southpoint, but I realized that the 8/6 and 9/6 strategies are identical just like Jacks or Better. If the flush payout was dropped, that would make so much difference. In this case I chose 8/6 is because that is the payschedule Mr. Dawes has access to, and one of the best games in general in Mississippi.

The best way I can answer your question to describe the 6888 hand difference between the strategy play and the perfect play (you are most interested in) for the 2 high card Ace-High situation is to look at it in two different parts.

1. The unsuited Ace+Jack situation
2. The unsuited Ace+Queen versus the Queen+Ten suited situation

Since I already described the 8400 situations where the lone Jack is held over the suited Ace and Jack on cell 10 and 11. We can just look at the second situation.

On the same screenshot, cell rows 7, 8, 9 covers the situations where the Ace-Queen offsuit is more preferred over the Queen-Ten suited, situations where the Queen-Ten suited has a flush penalty within the remaining two cards.

Cell 7 is 1080
Cell 8 is 216
Cell 9 is 216

Total of 1512 hands where Ace+Queen HC2 is favored over QT RF2.

However on the strategy charts, the QT RF2 has higher precedence over HC2 Ace high. Hence we will add 1512 more situations instead of subtracting situations.

8400 - 1512 = 6888

169884 (strategy situations) - 8400 (exception situations from AJ HC2) + 1512 (excpetion situations gained from AQ HC2 vs QT RF2) = 162996 perfect play situations.

On the side note, more credit goes to you for designing VPW!

Thanks Alpax. I did not know these features existed in VPW. I appreciate your time and input.


You are very welcome. I wish I can quickly take into account the number of hands, but it will be a very long drawn out process. I just wanted to show you a quick way while providing a somewhat accurate answer to your cause.

I purposely hid the full strategy and only shown the significant part since it might go against copyright infringement here.

Regardless, the Ace+Jack may not make too much difference EV wise on a single hand, but the frequent hands will add up quick!

[BobDancer]

On the side note, more credit goes to you for designing VPW!

 

 You are giving me too much credit. Yes I was part of the team, but much of it was done by others. There were big disagreements as to what would and would not be included.