So this situation appeared and we had a big discussion with my enthusiast OFC friends. Most of them agree on placing 56 in the middle and then drawing for a 4 outer flush in the back and additional 7,5% chance for an A in the top which secures us a FL.

Some guidelines for calculating the ev of our 2 potential moves (56 in the middle or K in the back and 6 in the middle)

-FL EV with AA in this spesific game is set to be 15 points (someone can correct me if it isnt true)

-No jokers in this game
-66 on top is +2 points and progressing
-Progressive means that we get dealt 16 cards with FL and then dropping one by one if we have re-fantasy

I have made my calculations already but i just want cofirmation form math enthusiasts
Securing the K in the back our EV for this move is -5 directly.

For succesfull calculations and reasoning i will be rewarding a 20$ P2P on stars or Skrill or compensate that amount for planting a tree that will absorb CO2 using Compensate.com.


TL;DR Wich move gives us better EV?
56 in the middle and drawing to a flush and runner FL,
or
K in the back and 6 in the middle and securing only a 5 points loss.




Thanks in advance

Make it $50 🎩

i would put 56 in middle every time.

Lets rewind this hand though. How did u end up drawing at clubs when u have an ace top and the other guys is drawing/made his club flush already. thats mistake number one, overvaluing ur back draw.

looks like u shoulda played the kings earlier in the back and u would be drawing at an aces land (which is worth extra since u are playing progressive)

I guess I'm not understanding the premise -- how does putting K in back and 6 in the middle lock us to a 5 point loss? Can't V still make 97 in the middle and QQQ up top and you're buried for like 50 points here? I mean TBH, V could even rattle off a straight in the middle and the two remaining aces up top! Also, V could play conservatively and eventually make JT88X in the middle and AQX up top and scoop us that way as well.

I started to put together some calcs, but would need some answers regarding the problem before continuing:

1. Are you saying the EV for fantasyland itself is 15 points or are you saying the bonus for getting AA up top is 15 points?
2. If I'm your opponent and I draw QQX (where X is not a 9 or 7, and then let me know how this play varies if it is a 9 or 7) on my turn against either play (or let me know if this varies based on what your play is), do I put Q up top, Q in middle and pray for one of the three remaining 9s (hits ~32%), QQ up top and pray for 97 (hits ~10%), or play safe and play Q in middle, X up top? Obviously the safe play basically never fouls on the last draw, but the other two not only make FL but bonuses when they hit.
3. Can I safely disregard your opponent's previous discards or should we make some guesses as to what they are? As another poster suggested, we may need a full rewind for that, not sure if it's available.
4. If your answer to 2 doesn't provide me a good heuristic as to how your opponent is going to play hands like one pair in the middle or a 9+pair in the middle situation, could you please add some rules for how they'll play those as well?

Anyways overall about the situation I'd say to keep in mind your opponent has a lot of really strong combos -- my best guess is they're going to end up with a hand that is extra-live to make fantasy land around 63% of the time (e.g. make AA or better in the middle on this coming draw), and when they do without hitting a Q as the discard, they'll have around 22% to hit a Q on their last draw and make FL, if they hit AAQ for instance and play the AA in the middle, they'll hit the case Q on their last draw around 11%.

I'll make another post with my calcs for just maximizing your hand in a vacuum, making the (rather significant) assumption that A-high is a lock up top.

For just your hand in a vacuum, if you put 65 in the middle:

There are 3654 (29C3) combinations remaining in the deck at the point we're making our decision. Of them, you're looking for a club to not foul, and ideally a club and an ace to make FL. The odds of you not hitting one of the five remaining clubs are

AKA 1630 combos of 3654; the odds of you hitting a club are 1 - P. So 55.4% to not hit and 44.6% to hit, roughly.

The odds of you hitting a club and an ace are:

FWIW, one play you didn't mention splits the difference -- play K up top for AK4 (which beats V AQX but not V FL), 6 in the middle, and now you have 9 outs to not foul (As/Ks/Jd/Js in addition to the five clubs) --

I don't think you should do this, since playing K in back, 6 in middle is safer.
But it's not completely safe, since you sometimes catch 569A as your final triple and you foul on the end:

So under these circumstances I'd say making it 98.5% to not foul vs. 44.6% to flush (broken down as 6.1%/38.5% FL/no FL) and I'm ignoring the 68.8% in-between play.

Overall, assuming you're correct (and note my previous post regarding these assumptions) that when you don't foul you lose 5 points, when you flush but don't FL you win approximately a point, and when you FL, you're worth about 30 points (I'm saying 5 for the scoop (since sometimes we don't win the middle), 10 for AA on this hand, and 15 for the overall EV of your FL), and finally that a foul loses 10 points, you get...

Play Safe (K in back, 6 in middle):

Play for Flush/FL (65 in middle):

So overall I'm going for the gusto and 65 in the middle. Interesting problem. Let me know if you want to provide further/different assumptions but I think you might be able to just adjust some of the final numbers if you do.