Atlantis Triple Play Keno Contest best Keno EV

[Minn. Fatz]

http://www.atlantiscasino.com/landing-p ... poker/This runs today through Nov. 19 and features a Triple Play VP game with a "side bet" on a Keno draw. You get an initial hand plus 10 out of 20 Keno numbers before the draw, the remaining 10 Kenos are picked after the draw. A Keno win also activates a multiplier for the poker hands results.Using the Keno pay tables for Triple Double Bonus (no idea if they're different for the other games) and the Wizard of Odds TDB EV figure of .99878 per hand, here are the EVs for the various Keno pick options, from highest to lowest:[see below for corrected figures]Picking 3 or 5 offers the two highest probabilities of obtaining a x12 multiplier on the poker hands; you could expect at least one x12 in any 100-hand session.Since the Quick Pick defaults to 6, if you're after max EV simply delete three of the six picks.Another consideration is when to go for a higher probability of any paying hand rather than a higher EV draw given how many Keno hits you get in the first ten picks. Not even back of the envelope, I'd hold high cards rather than a low pair (and, in TDB, multiple high cards rather than a single Ace) if I had at least one hit in the first ten keno balls.Good Mathematics all!BTW the Atlantis is a very nice Reno property that had plenty of full-pay VP machines when Mrs. Minn and I cashed in our contest prize two summers ago. If you go be sure to have a meal or several at the Sky Terrace literally overlooking Atlantic Ave.

[Minn. Fatz]

Back of the envelope this time, there doesn't seem to be a situation where holding a combination that's more likely to result in a paying hand has a higher overall EV than holding a combination with a higher EV that's less likely to pay off. So regardless of how many hits turn up in the first 10 Keno balls, I'd hold four cards to a flush, say, over a single Ace. GM all.

[Minn. Fatz]

One more quick note on the game: from the above, the Keno portion has a maximum EV of .65594, so playing with the Keno option drops the overall EV of the game from .99878 to .85984.[See below for corrected overall EV figures, maximum for Mark 10 is .99922.]

[BillyJoe]

Not sure how an EV applies to a contest, since you are not betting anything, and are only tallying the wins. To me, it would be how often you get a contribution from the Keno portion, and how big it is,  during a 100 play session. So what I would be looking for is, given a 100 play session, the number of balls that I should choose to give the maximize number and size of the Keno hand's contribution.

[Webman]

One more quick note on the game: from the above, the Keno portion has a maximum EV of .65594, so playing with the Keno option drops the overall EV of the game from .99878 to .85984.

Are you taking into account the fact that keno wins also trigger a multiplier on the poker hand?

[Minn. Fatz]

...what I would be looking for is, given a 100 play session,
the number of balls that I should choose to give the maximize number
and size of the Keno hand's contribution.Looking at the top scores so far, my working assumption is that the contribution to the best score from getting a big hand with a 12x multiplier is going to be more than the "big" Keno payoff, which tops out at 50000 vs. a theoretical 144000 from a dealt Royal or 4K Aces + kicker in TDB with a 12x mult. So I'm trying to maximize my probability for the 12x multiplier by playing 3 picks on Keno; 10 picks would be the second choice. A side effect of this is that I'm due enough 250 Keno + 12x poker mults that I'm getting about 1/2 my sessions over 2000 for the daily random draw for two nights at a very nice Reno property. As noted below, the Keno EVs above include the contribution of the multiplier for the poker hand.

[Minn. Fatz]

Are you taking into account the fact that keno wins also trigger a multiplier on the poker hand?Yes; the Keno EVs were calculated by adding the product of the Keno win multiplier and the TDB EV (per Wizard of Odds) to the Keno win amount. The top score for three picks is partly due to the higher probability of getting a 12x multiplier. FYI here are the probabilities of getting 12x for each possible Keno pick number:3 picks: 1.39%10 picks: 1.32%5 picks: 1.27%7 picks: 0.94%9 picks: 0.63%10 picks: 0.323%6 picks (default): 0.322%4 picks: 0.31%8 picks: 0.25%2 picks: no 12x mults

[Webman]

I'm not sure how you're arriving at the final numbers, but something is off in them. The optimal return for the game with the keno bonus is better than 99% (better than the base pay table without playing the keno bonus).What are you using as the coin-in for the keno bonus? Max bet here is 15 credits (poker) + 10 credits (keno)Your estimated poker return on a 12x keno win goes from close to 15, all the way up to 180. You would (I think) need to add 180 (or probably 165) to the 12x keno win amounts if you were plugging them into a keno EV calculator. The same goes for all other multiplied values of course.So, I would run the numbers again with all this in mind. If you get something less than 99% for the keno return (factoring in an increase in poker win values) then something is off.I'm not certain if my calculation approach above is correct, but it's the best I can come up with on a Monday morning.  I do know that the optimal return values should end up above 99%.Gold member play so far exceeds a 97% return, which would certainly include a fair amount of error in play.

[New2vp]

Minn Fatz,The keno probabilities are consistent with what I calculated (except for the 2nd listing for "10 picks" indicated below).3 picks: 1.39%10 picks: 1.32%5 picks: 1.27%7 picks: 0.94%9 picks: 0.63%10 picks: 0.323% <=== This line should be deleted.6 picks (default): 0.322%4 picks: 0.31%8 picks: 0.25%2 picks: no 12x multsBut I think that the EV that you are using is not exactly right.  For 9-7 TDB, it is 0.99577809 (to a couple more places than the Wizard shows it).  I'm guessing you wrote down 8 instead of 5 for the 3rd significant digit.  However, I don't think this is why you are getting an incorrect number for the overall payback, though I didn't figure out exactly what you were doing.  Maybe if I show you what I did, we can get to something a little closer to what Webman is suggesting.For 9-7 TDB, after combining the keno payoffs and multipliers, I get EVs ranging from .998199 (marking 2 spots) to .999922 (marking 10 spots).  The EVs for the other keno choices are not in exact order based on number of keno cells marked even though 2 is the min and 10 is the max here.  Most other games, except for 8-5 Bonus Poker (also maxed at 10) and Deuces Wild, maximize EV by marking 9 keno cells, but the differences in EV are extremely tiny.  The Base EV for Deuces Wild is smaller than the rest of the base games; that contributes to its EV being maximized by marking only 3 keno cells.    Here is the calculation for the EV of 9-7 TDB, marking 10 spots.







Hits
Keno Payoff
Poker Mult
Exp Coins
Prob
Cont. in Coins


0
0
1
14.93667
0.0457907
0.683961


1
0
1
14.93667
0.1795714
2.682199


2
0
1
14.93667
0.2952568
4.410153


3
0
1
14.93667
0.2674024
3.994101


4
0
1
14.93667
0.1473189
2.200454


5
25
5
99.68336
0.0514277
5.126485


6
125
12
304.24006
0.0114794
3.492492


7
800
12
979.24006
0.0016111
1.577696


8
5000
12
5179.24006
0.0001354
0.701369


9
20000
12
20179.24006
0.0000061
0.123510


10
50000
12
50179.24006
0.0000001
0.005631


Exp. Coins



24.99805


EV



99.9922%


For each number of Hits, the formula for Expected Coins is  (15 * Base EV * Poker Multiplier) + Keno Payoff.  The final EV is calculated by summing up the Contributions for each number of Hits and dividing by the 25 coins bet.  (The last few probabilities require more significant digits than shown to get the corresponding Contributions to EV.)I don't necessarily opine that marking the number of hits that maxes the probability of a 12 multiplier is the way to go, but it is certainly a major factor.  The likely keno payoff may also have something to do with increasing your probability of winning, as well as the probability of some other intermediate multipliers.Good luck is probably much more responsible for winning this contest than good mathematics, but I agree that making the most of the choices in your control sure feels like the right thing to do!

[New2vp]

Other considerations than the 12x multiplier can be seen from this comparison:Mark 3:  1.39% chance at 12xMark 10: 1.32% chance at 12xBut with this tiny advantage for Mark 3, your next biggest multiplier is only 2x, whereas with Mark 10, you can get a 5x multiplier a little more than 5% of the time.  Mark 3 compensates by giving you a multiplier 15.3% of the time compared to only 6.5% for Mark 10.Mark 4 is the leader in giving you a multiplier (25.9% of the time), with Mark 7 coming in 2nd at 23.7% of the time.Sorry if this makes the choices more confusing, but this problem is not that simple.Good luck!