Double Bonus Shockwave

I found a new version of Shockwave Poker at Choctaw Casinos. A Double Bonus version with extra coins for quads at the expense of two pair only returning your bet. During Shockwave mode, however, all quads continue to be 4000 coins.

I couldn't follow the Wiz's explanation of calculating return for regular Shockwave, was hoping someone could calculate for me please? I've posted the paytable for the $1 version and the quarter version.

Curious also...always thought they needed a bonus version of some sort for Shockwave

I have a feeling I'm calculating this wrong, but here is what I get:

8/5 version:
The normal return is is 94.1897%
1/420 of the time, you get a Four of a Kind
The Shockwave return is 283.067%
The expected number of Shockwave hands, based on 1/391 of them being a Four of a Kind, is 9.8857
Here's the part I'm not so sure about:
Overall expected return = 94.1987% + 1/420 x 9.8857 x 283.067% = 100.8614%

7/5 version:
The normal return is 93.106%
1/420 of the time, you get a Four of a Kind
The Shockwave return is 282.38%
1/380 is a Four of a Kind
The expected number of Shockwave hands, based on 1/380 of them being a Four of a Kind, is 9.8824
Overall expected return = 93.106% + 1/420 x 9.8824 x 282.38% = 99.7502%

That's a head scratcher for me, too.
Shockwave mode in previously analyzed games seems to add around 4.3% to the base paytable; it startles me to see that using a DB base instead of BP base might suddenly increase the value of the feature to +6.5%.

I tried to follow the Wiz's logic on his Shockwave page to figure this out, but he doesn't explain how he calculated the addition of 18.3 to 18.8 to the regular mode 4oaK.

But in looking at his calculation, I noted a small error in his step 2 added at the bottom of his analysis. He puts the probability of 10 spins at 1-P(quads)^10, but it should actually be 1 - sum of P(quads in 1-9 hands). The difference being that he's not accounting for the potential of a quads on Hand 10. The impact is very small, obviously.

Quote: ThatDonGuy

I have a feeling I'm calculating this wrong, but here is what I get:

8/5 version:
The normal return is is 94.1897%
1/420 of the time, you get a Four of a Kind
The Shockwave return is 283.067%
The expected number of Shockwave hands, based on 1/391 of them being a Four of a Kind, is 9.8857
Here's the part I'm not so sure about:
Overall expected return = 94.1987% + 1/420 x 9.8857 x 283.067% = 100.8614%

Focusing on the 8/5 version for now..... I get expected number of Shockwave hands to be 9.882561, calculated through brute force.

Pr Game ending after N hands
1 0.00262810 Pr Quads 0.002628101
2 0.00262119
3 0.00261430
4 0.00260743
5 0.00260058
6 0.00259375
7 0.00258693
8 0.00258013
9 0.00257335
10 0.97659423
Total 1.0000000

Expected hands in Shockwave mode 9.882560507

Quote: rsactuary

Quote: ThatDonGuy

I have a feeling I'm calculating this wrong, but here is what I get:

8/5 version:
The normal return is is 94.1897%
1/420 of the time, you get a Four of a Kind
The Shockwave return is 283.067%
The expected number of Shockwave hands, based on 1/391 of them being a Four of a Kind, is 9.8857
Here's the part I'm not so sure about:
Overall expected return = 94.1987% + 1/420 x 9.8857 x 283.067% = 100.8614%

Focusing on the 8/5 version for now..... I get expected number of Shockwave hands to be 9.882561, calculated through brute force.

That is assuming the probability of getting quads in 8/5 is about 1 / 380.5. Are you sure that's not the probability of "quads or better"? Remember, Shockwave isn't ended by a Royal or a SF.

Quote: ThatDonGuy

Quote: rsactuary

Quote: ThatDonGuy

I have a feeling I'm calculating this wrong, but here is what I get:

8/5 version:
The normal return is is 94.1897%
1/420 of the time, you get a Four of a Kind
The Shockwave return is 283.067%
The expected number of Shockwave hands, based on 1/391 of them being a Four of a Kind, is 9.8857
Here's the part I'm not so sure about:
Overall expected return = 94.1987% + 1/420 x 9.8857 x 283.067% = 100.8614%

Focusing on the 8/5 version for now..... I get expected number of Shockwave hands to be 9.882561, calculated through brute force.

That is assuming the probability of getting quads in 8/5 is about 1 / 380.5. Are you sure that's not the probability of "quads or better"? Remember, Shockwave isn't ended by a Royal or a SF.
link to original post

I ran the shockwave mode through WinPoker. This is the probability of a Shockwave Quad.

Output from WinPoker for Shockwave Round:

Shockwave DB - Shockwave

Hand Name	Payout	Frequency	% Prob.	Occurs Every	% of Ret.
Royal Flush	4000	55.887579	0.002%	46503.36	1.72%
Straight Flush	250	177.02807	0.007%	14681.06	0.34%
4 of a Kind	4000	6830.3282	0.263%	380.5029	210.25%
Full House	40	17854.737	0.687%	145.5614	5.50%
Flush	25	22165.918	0.853%	117.2503	4.26%
Straight	20	25291.327	0.973%	102.7609	3.89%
3 of a Kind	15	218361.03	8.402%	11.90212	25.21%
Two Pair	5	252803.12	9.727%	10.28057	9.73%
Jacks or Better	5	576254.16	22.172%	4.510093	22.17%
NOTHING	0	1479166.5	56.914%	1.757044	0.00%
Total Return		2598960			283.0670%
Variance					1689.78816

Quote: ThatDonGuy

Shockwave isn't ended by a Royal or a SF.

This is an excellent time for me to once again share my dealt royal in Shockwave mode. I can verify that Shockwave mode did not end.

Quote: rsactuary

Quote: ThatDonGuy

Quote: rsactuary

Quote: ThatDonGuy

I have a feeling I'm calculating this wrong, but here is what I get:

8/5 version:
The normal return is is 94.1897%
1/420 of the time, you get a Four of a Kind
The Shockwave return is 283.067%
The expected number of Shockwave hands, based on 1/391 of them being a Four of a Kind, is 9.8857
Here's the part I'm not so sure about:
Overall expected return = 94.1987% + 1/420 x 9.8857 x 283.067% = 100.8614%

Focusing on the 8/5 version for now..... I get expected number of Shockwave hands to be 9.882561, calculated through brute force.

That is assuming the probability of getting quads in 8/5 is about 1 / 380.5. Are you sure that's not the probability of "quads or better"? Remember, Shockwave isn't ended by a Royal or a SF.
link to original post

I ran the shockwave mode through WinPoker. This is the probability of a Shockwave Quad.
link to original post

In that case, the calculated return is 100.8592% - again, assuming I am using the right method.

Quote: ThatDonGuy

Quote: rsactuary

Quote: ThatDonGuy

Quote: rsactuary

Quote: ThatDonGuy

I have a feeling I'm calculating this wrong, but here is what I get:

8/5 version:
The normal return is is 94.1897%
1/420 of the time, you get a Four of a Kind
The Shockwave return is 283.067%
The expected number of Shockwave hands, based on 1/391 of them being a Four of a Kind, is 9.8857
Here's the part I'm not so sure about:
Overall expected return = 94.1987% + 1/420 x 9.8857 x 283.067% = 100.8614%

Focusing on the 8/5 version for now..... I get expected number of Shockwave hands to be 9.882561, calculated through brute force.

That is assuming the probability of getting quads in 8/5 is about 1 / 380.5. Are you sure that's not the probability of "quads or better"? Remember, Shockwave isn't ended by a Royal or a SF.
link to original post

I ran the shockwave mode through WinPoker. This is the probability of a Shockwave Quad.
link to original post

In that case, the calculated return is 100.8592% - again, assuming I am using the right method.
link to original post

I just don't see Choctaw putting a 100%+ game out on the floor.

All I saw in the compact was 75% minimum return, which must be maintained at minimum coin play.

I probably missed something.

I'm guessing this is in the 98% range but just can't seem to get there. I'm hoping the Wiz wanders into this thread at some point.

Quote: ThatDonGuy

I have a feeling I'm calculating this wrong, but here is what I get:

8/5 version:
The normal return is is 94.1897%
1/420 of the time, you get a Four of a Kind
The Shockwave return is 283.067%
The expected number of Shockwave hands, based on 1/391 of them being a Four of a Kind, is 9.8857
Here's the part I'm not so sure about:
Overall expected return = 94.1987% + 1/420 x 9.8857 x 283.067% = 100.8614%

7/5 version:
The normal return is 93.106%
1/420 of the time, you get a Four of a Kind
The Shockwave return is 282.38%
1/380 is a Four of a Kind
The expected number of Shockwave hands, based on 1/380 of them being a Four of a Kind, is 9.8824
Overall expected return = 93.106% + 1/420 x 9.8824 x 282.38% = 99.7502%
link to original post

Doesn't this double count the EV from normal mode when adding in the Shockwave hands? Let the average number of shockwave hands be N. If you think about taking the average EV of any random hand, I think it should come to:

8/5
(420)/(420+N)*94.1987% + N/(420+N)*283.067%
When subbing in N = 9.8857, we get 98.5419%

7/5
Similarly, subbing N = 9.8824 into
(420)/(420+N)*93.106% + N/(420+N)*282.38% = 97.4571%

These numbers seem more like what a casino would like to have on the floor.

I like the concept, but I think the normal return is incorrect, the number of hands between four of a kind is incorrect and the expected number of shockwave hands is incorrect, as discussed earlier in the thread.

Quote: rsactuary

I like the concept, but I think the normal return is incorrect, the number of hands between four of a kind is incorrect and the expected number of shockwave hands is incorrect, as discussed earlier in the thread.
link to original post

I just corrected that post. You should be able to plug in different numbers yourself.

Quote: rsactuary

I tried to follow the Wiz's logic on his Shockwave page to figure this out, but he doesn't explain how he calculated the addition of 18.3 to 18.8 to the regular mode 4oaK.
link to original post

From the WOO page:

"The strategy for Shockwave goes is more aggressive after the four of a kinds in regular mode and extremely agressive in Shockwave mode. My analysis assumed that the average number of games in Shockwave mode is 9.8836. The value of Shockwave mode ranges from 18.3 to 18.8, depending on the pay table. So proper strategy in regular mode should be based on adding 18.3 to 18.8 to the value of a four of a kind."

Hmmm. This WOO write-up would definitely benefit from some editing!

I am new to the Shockwave subject, but I am assuming that 18.8 is for the 12-8-5 payout table and 18.4 is for the 9-6-4 payout table and that they are the returns on the (up to) 10 games in the shockwave mode. Naturally, the shockwave mode is triggered at a frequency of a 4oak, given an aggressive strategy for making a 4oaK.

Can anyone summarize what the major strategy differences are from a non-shockwave game (with the same paytable) for the normal mode and shockwave mode of Shockwave?

Using the WOO video poker analyzer, we get a return of 2.830670 for the shockwave hands for 8/5. We don't care about that number, but we can use the table of numbers in the analyzer output to computer numbers we care about.
Each 5-coin hand in shockwave mode that isn't a quad has an EV of -1.349 coins.
Quads will be hit once every 380 hands in shockwave mode meaning each hand has a 99.74% chance of not being a quad.

Using that info, a quick python script generates the following EV for the up to 10 hand shockwave mode:



Shockwave mode is worth 90.459 coins on top of the normal quad payout. Using the WOO analyzer, add 90 coins to each quad and get a return of 0.985.

Quote: docegghead

Using the WOO video poker analyzer, we get a return of 2.830670 for the shockwave hands for 8/5. We don't care about that number, but we can use the table of numbers in the analyzer output to computer numbers we care about.
Each 5-coin hand in shockwave mode that isn't a quad has an EV of -1.349 coins.
Quads will be hit once every 380 hands in shockwave mode meaning each hand has a 99.74% chance of not being a quad.

Using that info, a quick python script generates the following EV for the up to 10 hand shockwave mode:

|-------------+----------+----------+---------|
| hit on hand |     prob |       ev |  return |
|-------------+----------+----------+---------|
|           0 | 0.974028 |  -13.495 | -13.144 |
|           1 | 0.002628 | 3995.000 |  10.499 |
|           2 | 0.002621 | 3993.651 |  10.468 |
|           3 | 0.002614 | 3992.301 |  10.437 |
|           4 | 0.002607 | 3990.952 |  10.406 |
|           5 | 0.002601 | 3989.602 |  10.375 |
|           6 | 0.002594 | 3988.253 |  10.345 |
|           7 | 0.002587 | 3986.903 |  10.314 |
|           8 | 0.002580 | 3985.554 |  10.283 |
|           9 | 0.002573 | 3984.204 |  10.253 |
|          10 | 0.002567 | 3982.855 |  10.222 |
|-------------+----------+----------+---------|
|         tot | 1.000000 |        - |  90.459 |
|-------------+----------+----------+---------|

Shockwave mode is worth 90.459 coins on top of the normal quad payout. Using the WOO analyzer, add 90 coins to each quad and get a return of 0.985.
link to original post

This is gold.. I think. Not sure I understand it yet, and will spend some time with it. Thank you!

Quote: rsactuary

This is gold.. I think. Not sure I understand it yet, and will spend some time with it. Thank you!
link to original post

I think I understand it.
Once Shockwave mode is started, the probability of getting a quad on the first hand is 0.002628 (about 1/380.5), and it has a value of 3995 (4000 minus the 5 bet), so it is worth 3995 x 0.002628 = 10.499.
The probability of not getting a quad on the first hand, but getting one on the second, is (1 - 0.002628) x 0.002628 = 0.002621, and it has a value of (3995 - 1.3495) = 3993.651, so it is worth 3993.651 x 0.002621 = 10.468. (1.3495 is subtracted because this is the EV of a Shockwave hand that is not a quad.)
The probability of not getting a quad on the first two hands, but getting one on the third, is (1 - 0.002628)² x 0.002628 = 0.002614, and it has a value of (3995 - 1.3495 x 2) = 3992.301, so it us worth 3992.301 x 0.002621 = 10.468.
Repeat this for getting a quad on the fourth, fifth, ..., tenth hand.
Finally, add in the value for not getting any quads; the probability is (1 - 0.002628)¹⁰ = 0.974028 and the value is (-10 x 1.3495) = -13.495, so it is worth 0.984028 x (-13.495) = -13.144.
Add up the 11 "worth" values to get 90.459, which is the EV of a Shockwave "round."
To calculate the "normal play" strategy, use the normal values, but add 90.459 to each quad.

Quote: ThatDonGuy

Quote: rsactuary

This is gold.. I think. Not sure I understand it yet, and will spend some time with it. Thank you!
link to original post

I think I understand it.
Once Shockwave mode is started, the probability of getting a quad on the first hand is 0.002628 (about 1/380.5), and it has a value of 3995 (4000 minus the 5 bet), so it is worth 3995 x 0.002628 = 10.499.
The probability of not getting a quad on the first hand, but getting one on the second, is (1 - 0.002628) x 0.002628 = 0.002621, and it has a value of (3995 - 1.3495) = 3993.651, so it is worth 3993.651 x 0.002621 = 10.468. (1.3495 is subtracted because this is the EV of a Shockwave hand that is not a quad.)
The probability of not getting a quad on the first two hands, but getting one on the third, is (1 - 0.002628)² x 0.002628 = 0.002614, and it has a value of (3995 - 1.3495 x 2) = 3992.301, so it us worth 3992.301 x 0.002621 = 10.468.
Repeat this for getting a quad on the fourth, fifth, ..., tenth hand.
Finally, add in the value for not getting any quads; the probability is (1 - 0.002628)¹⁰ = 0.974028 and the value is (-10 x 1.3495) = -13.495, so it is worth 0.984028 x (-13.495) = -13.144.
Add up the 11 "worth" values to get 90.459, which is the EV of a Shockwave "round."
To calculate the "normal play" strategy, use the normal values, but add 90.459 to each quad.
link to original post

Yeah, thought about this quite a bit last night, and will factor into the calculations when I have some time later this week. It makes total sense, but sure couldn't come up with this on my own.