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.

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%

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%.

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:ThatDonGuyI 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:rsactuaryQuote:ThatDonGuyI 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:ThatDonGuyQuote:rsactuaryQuote:ThatDonGuyI 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.

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

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:ThatDonGuyShockwave 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:rsactuaryQuote:ThatDonGuyQuote:rsactuaryQuote:ThatDonGuy

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.

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

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

Quote:ThatDonGuyQuote:rsactuaryQuote:ThatDonGuyQuote:rsactuaryQuote:ThatDonGuy

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.

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

I probably missed something.

Quote:ThatDonGuyI 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%

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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.

Quote:rsactuaryI 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.

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

Quote:rsactuaryI 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.

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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?

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.

Quote:doceggheadUsing 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.

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

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

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

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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.

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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.