JOB 9-6 vs 9-5 strategy

What is the difference in EV, if the 9-6 JOB simple strategy is used on a 9-5 JOB game, instead of using the full 9-5 JOB strategy?

Quote: technics

What is the difference in EV, if the 9-6 JOB simple strategy is used on a 9-5 JOB game, instead of using the full 9-5 JOB strategy?
link to original post

Are you ready? You're going to love this solution! Because I'm an idiot, I started doing this a much more difficult way.

What we are going to do is get the 9/6 JoB Perfect Strategy Analysis here:

https://wizardofodds.com/games/video-poker/strategy/a-1-b-74-c-1-d-0-d-1-d-2-d-3-d-4-d-6-d-9-d-25-d-50-d-800/

What we are really interested in are the probabilities---since we would not be changing our decision making. We're going to want this to be as specific as possible, so we have to do combinations(result)/(total combinations), thus:

Royal: 41,126,022/1,661,102,543,100
Straight Flush: 181,573,608/1,661,102,543,100
Four of a Kind: 3,924,430,647/1,661,102,543,100
Full House: 19,122,956,883/1,661,102,543,100
Flush: 18,296,232,180/1,661,102,543,100
Straight: 18,653,130,482/1,661,102,543,100
Three of a Kind: 123,666,922,527/1,661,102,543,100
Two Pair: 214,745,513,679/1,661,102,543,100
One Pair: 356,447,740,914/1,661,102,543,100
Nothing: 906,022,916,158/1,661,102,543,100

Okay, so now we look at the total return for the 9/6 game of 0.995439 and we see how much of that relates to the flush. Since we are assuming that we are going to play perfect 9/6 JoB strategy on a 9/5 game, we can simply change our return from the flush to five (as opposed to six) and see what happens.

(18,296,232,180/1,661,102,543,100) * 6 = 0.0660870658

(18,296,232,180/1,661,102,543,100) * 5 = 0.05507255484

0.05507255484 - 0.0660870658 = -0.01101451096

With that, we simply subtract this difference from the normal return of 9/6 Jacks:

0.995439 - .0110145 = 0.9844245

Okay, so now all that remains is to do the 9/5 game with perfect strategy for 9/5 and look at what the difference is:

.9844245-0.984498 = -0.00007349999

With that, we see that we lose about .00007349999 or 0.00735% by way of not deviating from the 9/6 Perfect Strategy playing a 9/5 game.

Not that you asked and not that I am going to figure out how much, but a big portion of this EV lost can be avoided by simply figuring out which Four Flush w/Three Royal Holds (9/6 Jacks) simply become holding Three Royal on 9/5 Jacks.

For example, a hand such as 10s-Js-As-Qh-4s is a Four Flush hold on 9/6, but would become Three Royal hold on 9/5...and by a pretty big margin.

On 9/6, this is actually a really close decision such that holding Three Royal doesn't even really cost you much, in fact, it's the Qh acting as a straight penalty card (in this case) that changes the decision. However, with 9/5 Jacks, the decision to hold Three Royal isn't even close---you drop the Qh and 4s by a huge margin.

NOTE: I did this with 9/6 Optimal (as opposed to simple), but you now know how to do it with Simple...or with any other game!

Most games that pay 5 for a flush also hold less KTs, avoiding it when holding a 3d suited card. 9/5 Jacks is one of them.

Woah, I didn’t expect a full blown calculation like this, so thanks for that. The Wizard has stated that the cost of using the simple strategy instead of using the full optimal strategy for 9-6, is only.08%, so I won’t go through the calculations . I think I’ll just use the simple strategy for both 9-6 and 9-5 since the cost of use is minimal and I’m less likely to err.