Intermediate Player Insight for JorB Double STP

[alpax]

Disclaimer: Double Super Times Pay Poker is NOT a video poker game variant that has been released recently. This is also not strictly for recreational DDB Players either.



I would like to dedicate my efforts to tringlomane, a well versed and knowledgeable person in gambling regulations and video poker (along with other casino games) participating on mainstream gambling forums. On the thread regarding Moving Multipliers, tringlomane has expressed an opinion that Double Super Times Pay is the best multiplier video poker variant on the market and personal favorite. Time to time there are many responses from tringlomane for many Vegas travelers seeking advice into finding cost efficient ways to advance in status tiers on Caesars Entertainment Total Rewards program. In the Vegas jurisdiction, there are becoming much less and less viable choices. I read that it is the most ideal to grind out a single line Bonus Poker, Double Bonus, or Double Double Bonus game for many hours during the day to achieve status, but for people looking for excitement while playing for status, this 9/5 Jacks or Better Double Super Times Pay could be the next best thing. This will be the game that will be focused on this Insight


The motive behind this insight is that a player of Intermediate level might want to know more about the game prior to playing, so he/she will be more aware of the dynamics of the high variance Double STP which can cause memorable jackpots or such agony that comes with the dry spells of no multipliers.

The Wizard of Odds website has much details for Super Times Pay, but the section on Double Super Times Pay seems to be an extension to describe the differences from the original.

Information that the Novice Player is aware of for Double Super Times Pay:

-     Bonus Feature requires 7 credits per line to play
-     Odds of Super Times Pay Multiplier event is 1 in 15 on average on the deal and the draw, the average multiplier is 4.01X
-     The maximum multiplier capacity increases from 10x to 20x
-     A STP triggering on the deal along with a natural royal flush dealt will automatically award 10x for both deal and the draw for a jackpot of 80,000 credits per line played
-     Adds about 0.50% to the return in the long run at the expense of higher variance (not knowing to exact extent)
-     Like STP, no strategy adjustment is required

The HELP Page



Super Times Pay Actual Multiplier Probabilities (Source courtesy of wizardofodds.com)

2x – 17% Frequency – 0.34 Expected
3x – 33% Frequency – 0.99 Expected
4x – 16% Frequency – 0.64 Expected
5x – 24% Frequency – 1.2 Expected
8x – 6% Frequency – 0.48 Expected
10x – 4% Frequency – 0.4 Expected

The Expected Multiplier Value adds up to 4.05x

For Double Super Times Pay, there will need to be 4x worth of multipliers less than STP to achieve the 4.01x average multiplier value.

There will be 2% less of 10x multipliers in replacement for 2% more of 8x multipliers

2x – 17% Frequency – 0.34 Expected
3x – 33% Frequency – 0.99 Expected
4x – 16% Frequency – 0.64 Expected
5x – 24% Frequency – 1.2 Expected
8x – 8% Frequency – 0.64 Expected
10x – 2% Frequency – 0.2 Expected

Areas in which this Insights will cover to help people understand more about Double STP

#1 – Distribution of Odds of the Possible Multipliers formed by Double STP
#2 – Variance differences between Single Line 9/5 Jacks or Better – Single Line / 6 Credit Super Times Pay / 7 Credit Double Super Times Pay
#3 – Odds of encountering W2G payouts on Single Line / 3 Play / 5 Play / 10 Play JoB DSTP
#4 – Bankroll Simulation to achieve Total Rewards status in a day for JoB DSTP
#5 - Theoretical Simulation of 1 Million rounds played
# Extra Technical Section for those that are interested

#1 – Distribution of Odds of the Possible Multipliers

This applies to every Double STP variants, not just 9/5 Jacks or Better

Part 1 – Finding the chance of the STP Multiplier not triggering

When the STP trigger occurs on the deal or the draw at 1 in 15 odds, the converse is that the STP does not happen 14 out of 15 times on two events.

(14 / 15) * (14 / 15) = 196 / 225 -OR- 0.933333 x 0.933333 = 0.87111

Part 2 – Breakdown of all possible multipliers

The odds of the STP Multiplier triggering will be

1 – 0.87111 = 0.12888 (About 1 in 8)

Using the makeshift Multiplier Frequencies, I look at the possible multipliers that can result during play. The expected values of all events must add up to 0.12888.

2x Multiplier

a) 2x Single STP on the Deal - (0.17 x 0.066667) x (1 x 0.933333) = 0.0113333333333333
b) 2x Single STP on the Draw - (0.17 x 0.066667) x (1 x 0.933333) = 0.0113333333333333
Total Percentage for 2x Multiplier - 0.021156
Odds for 2x Multiplier - 1 in 47.268908

3x Multiplier

a) 3x Single STP on the Deal - (0.33 x 0.066667) x (1 x 0.933333) = 0.022
b) 3x Single STP on the Draw - (0.33 x 0.066667) x (1 x 0.933333) = 0.022
Total Percentage for 3x Multiplier - 0.041067
Odds for 3x Multiplier - 1 in 24.350649

4x Multiplier

a) 4x Single STP on the Deal - (0.16 x 0.066667) x (1 x 0.933333) = 0.0106666666666667
b) 4x Single STP on the Draw - (0.16 x 0.066667) x (1 x 0.933333) = 0.0106666666666667
c) [Double STP] 2x STP on the Deal and 2x STP on the Draw - (0.17 x 0.066667) x (0.17 x 0.066667) = 0.000128444444444444
Total Percentage for 4x Multiplier - 0.02004
Odds for 4x Multiplier - 1 in 49.901306

5x Multiplier

a) 5x Single STP on the Deal - (0.24 x 0.066667) x (1 x 0.933333) = 0.016
b) 5x Single STP on the Draw - (0.24 x 0.066667) x (1 x 0.933333) = 0.016
c) [Double STP] 3x STP on the Deal and 2x STP on the Draw - (0.33 x 0.066667) x (0.17 x 0.066667) = 0.000249333333333333
d) [Double STP] 2x STP on the Deal and 3x STP on the Draw - (0.17 x 0.066667) x (0.33 x 0.066667) = 0.000249333333333333
Total Percentage for 5x Multiplier - 0.030365
Odds for 5x Multiplier - 1 in 32.932291

6x Multiplier

a) [Double STP] 3x STP on the Deal and 3x STP on the Draw - (0.33 x 0.066667) x (0.33 x 0.066667) = 0.000484
b) [Double STP] 4x STP on the Deal and 2x STP on the Draw - (0.16 x 0.066667) x (0.17 x 0.066667) = 0.000120888888888889
c) [Double STP] 2x STP on the Deal and 4x STP on the Draw - (0.17 x 0.066667) x (0.16 x 0.066667) = 0.000120888888888889
Total Percentage for 6x Multiplier - 0.000726
Odds for 6x Multiplier - 1 in 1377.832211

7x Multiplier

a) [Double STP] 4x STP on the Deal and 3x STP on the Draw - (0.16 x 0.066667) x (0.33 x 0.066667) = 0.000234666666666667
b) [Double STP] 3x STP on the Deal and 4x STP on the Draw - (0.33 x 0.066667) x (0.16 x 0.066667) = 0.000234666666666667
c) [Double STP] 2x STP on the Deal and 5x STP on the Draw - (0.17 x 0.066667) x (0.24 x 0.066667) = 0.000181333333333333
d) [Double STP] 5x STP on the Deal and 2x STP on the Draw - (0.24 x 0.066667) x (0.17 x 0.066667) = 0.000181333333333333
Total Percentage for 7x Multiplier - 0.000832
Odds for 7x Multiplier - 1 in 1201.923077

8x Multiplier

a) 8x Single STP on the Deal - (0.08 x 0.066667) x (1 x 0.933333) = 0.00533333333333333
b) 8x Single STP on the Draw - (0.08 x 0.066667) x (1 x 0.933333) = 0.00533333333333333
c) [Double STP] 3x STP on the Deal and 5x STP on the Draw - (0.33 x 0.066667) x (0.24 x 0.066667) = 0.000352
d) [Double STP] 5x STP on the Deal and 3x STP on the Draw - (0.24 x 0.066667) x (0.33 x 0.066667) = 0.000352
e) [Double STP] 4x STP on the Deal and 4x STP on the Draw - (0.16 x 0.066667) x (0.16 x 0.066667) = 0.000113777777777778
Total Percentage for 8x Multiplier - 0.010773
Odds for 8x Multiplier - 1 in 92.821782

9x Multiplier

a) [Double STP] 4x STP on the Deal and 5x STP on the Draw - (0.16 x 0.066667) x (0.24 x 0.066667) = 0.000170666666666667
b) [Double STP] 5x STP on the Deal and 4x STP on the Draw - (0.24 x 0.066667) x (0.16 x 0.066667) = 0.000170666666666667
Total Percentage for 9x Multiplier - 0.000341
Odds for 9x Multiplier - 1 in 2929.6875

10x Multiplier

a) 10x Single STP on the Deal - (0.02 x 0.066667) x (1 x 0.933333) = 0.00133333333333333
b) 10x Single STP on the Draw - (0.02 x 0.066667) x (1 x 0.933333) = 0.00133333333333333
c) [Double STP] 8x STP on the Deal and 2x STP on the Draw - (0.08 x 0.066667) x (0.17 x 0.066667) = 6.04444444444444E-05
d) [Double STP] 2x STP on the Deal and 8x STP on the Draw - (0.17 x 0.066667) x (0.08 x 0.066667) = 6.04444444444444E-05
e) [Double STP] 5x STP on the Deal and 5x STP on the Draw - (0.24 x 0.066667) x (0.24 x 0.066667) = 0.000256
Total Percentage for 10x Multiplier - 0.002866
Odds for 10x Multiplier - 1 in 348.945409

11x Multiplier

a) [Double STP] 3x STP on the Deal and 8x STP on the Draw - (0.33 x 0.066667) x (0.08 x 0.066667) = 0.000117333333333333
b) [Double STP] 8x STP on the Deal and 3x STP on the Draw - (0.08 x 0.066667) x (0.33 x 0.066667) = 0.000117333333333333
Total Percentage for 11x Multiplier - 0.000235
Odds for 11x Multiplier - 1 in 4261.363636

12x Multiplier

a) [Double STP] 4x STP on the Deal and 8x STP on the Draw - (0.16 x 0.066667) x (0.08 x 0.066667) = 5.68888888888889E-05
b) [Double STP] 8x STP on the Deal and 4x STP on the Draw - (0.08 x 0.066667) x (0.16 x 0.066667) = 5.68888888888889E-05
c) [Double STP] 2x STP on the Deal and 10x STP on the Draw - (0.17 x 0.066667) x (0.02 x 0.066667) = 1.51111111111111E-05
d) [Double STP] 10x STP on the Deal and 2x STP on the Draw - (0.02 x 0.066667) x (0.17 x 0.066667) = 1.51111111111111E-05
Total Percentage for 12x Multiplier - 0.000144
Odds for 12x Multiplier - 1 in 6944.444444

13x Multiplier

a) [Double STP] 5x STP on the Deal and 8x STP on the Draw - (0.24 x 0.066667) x (0.08 x 0.066667) = 8.53333333333333E-05
b) [Double STP] 8x STP on the Deal and 5x STP on the Draw - (0.08 x 0.066667) x (0.24 x 0.066667) = 8.53333333333333E-05
c) [Double STP] 3x STP on the Deal and 10x STP on the Draw - (0.33 x 0.066667) x (0.02 x 0.066667) = 2.93333333333333E-05
d) [Double STP] 10x STP on the Deal and 3x STP on the Draw - (0.02 x 0.066667) x (0.33 x 0.066667) = 2.93333333333333E-05
Total Percentage for 13x Multiplier - 0.000229
Odds for 13x Multiplier - 1 in 4360.465116

14x Multiplier

a) [Double STP] 4x STP on the Deal and 10x STP on the Draw - (0.16 x 0.066667) x (0.02 x 0.066667) = 1.42222222222222E-05
b) [Double STP] 10x STP on the Deal and 4x STP on the Draw - (0.02 x 0.066667) x (0.16 x 0.066667) = 1.42222222222222E-05
Total Percentage for 14x Multiplier - 2.8E-05
Odds for 14x Multiplier - 1 in 35156.25

15x Multiplier

a) [Double STP] 5x STP on the Deal and 10x STP on the Draw - (0.24 x 0.066667) x (0.02 x 0.066667) = 2.13333333333333E-05
b) [Double STP] 10x STP on the Deal and 5x STP on the Draw - (0.02 x 0.066667) x (0.24 x 0.066667) = 2.13333333333333E-05
Total Percentage for 15x Multiplier - 4.3E-05
Odds for 15x Multiplier - 1 in 23437.5

16x Multiplier

a) [Double STP] 8x STP on the Deal and 8x STP on the Draw - (0.08 x 0.066667) x (0.08 x 0.066667) = 2.84444444444444E-05
Total Percentage for 16x Multiplier - 2.8E-05
Odds for 16x Multiplier - 1 in 35156.25

18x Multiplier

a) [Double STP] 8x STP on the Deal and 10x STP on the Draw - (0.08 x 0.066667) x (0.02 x 0.066667) = 7.11111111111111E-06
b) [Double STP] 10x STP on the Deal and 8x STP on the Draw - (0.02 x 0.066667) x (0.08 x 0.066667) = 7.11111111111111E-06
Total Percentage for 18x Multiplier - 1.4E-05
Odds for 18x Multiplier - 1 in 70312.5

20x Multiplier

a) [Double STP] 10x STP on the Deal and 10x STP on the Draw - (0.02 x 0.066667) x (0.02 x 0.066667) = 1.77777777777778E-06
Total Percentage for 20x Multiplier - 2E-06
Odds for 20x Multiplier - 1 in 562500

I did add up the Total Percentage using a spreadsheet wizard to come up with the 0.12888 value that is to be expected with the STP occurrence percentage. As you can see, some of the multipliers appear very rarely, even more infrequent than the Royal Flush!

#2 - Variance Breakdown of 1-3-5-10 Play 9/5 Jacks or Better in Standard / STP / Double STP

Many thanks to the following as reference utilized to calculate N-line Video Poker Variance

a)     Jazbo Enterprises – An Analysis of N-Play Video Poker – http://www.jazbo.com/videopoker/nplay.html
b)     Wizard of Odds – Standard Deviation for Multihand Video Poker – https://wizardofodds.com/games/video-poker/appendix/3/
c)     Wizard of Vegas Forum Thread – http://wizardofvegas.com/forum/gambling ... deo-poker/
d)     Video Poker for Winners for the standard video poker games

Summary of facts gained from the references.

-     Mr. Jazbo discovered that the variance of a multigame can be derived from a formula

Where N equals the number of hands to play

Total Variance of N-Play = Variance of Single Line + (N – 1) * CoVariance of Single Line
Net Variance of N-Play = Total Variance of N-Play / N

-     Mr. Shackleford (The Wizard) interprets CoVariance portion of the video poker as “Variance on the Deal”
-     The Wizard of Vegas Forum Thread interprets the Variance on the Deal as the variance of expected return for each of the 2598960 possible hand deals

After much trial and error for a long period of time, I was able to grasp the concept.


Unfortunately, I ran into the Wizard of Odds Video Poker Calculator too late. It would have saved a good amount of effort as I was unaware that it had the ability to compute the variance of Double STP based games. The WoO webmaster JB discovered that DSTP increases the variance of the video poker game by 2.52x folds. The limitation for the calculator is just for single line.

Variances for Single Line 9/5 Jacks or Better

Standard: 19.4956 with 10 Possible Payout Values
Super Times Pay: 31.286 with 41 Possible Payout Values
Double Super Times Pay: 49.158 with 100 Possible Payout Values

CoVariances for Single Line 9/5 Jacks or Better

Standard: 1.94596
Super Times Pay: 3.62086
Double Super Times Pay: 17.0014

The biggest reason for such a high CoVariance factor for DSTP is due to the 20X dealt royal stipulation that increases the maximum potential video poker payout from 4000 credits per line to 80000 credits per line. The Dealt Royal situation (whether STP occurs on the deal, on the draw, or not at all) itself accounts for 14.44 of the 17.0014 CoVariance factor.

With a high CoVariance factor, the net variance playing multiple lines in DSTP will be lowered on a lesser scale than Standard variants of the game.

Variances for Three Play 9/5 Jacks or Better

Standard: 7.796 with 114 Possible Payout Values

Total Variance = 19.4956 + (3-1) * 1.94596 = 23.38752
Net Variance = 23.38752/ 3 = 7.796

Super Times Pay: 12.843 with 554 Possible Payout Values

Total Variance = 31.286 + (3-1) * 3.62086 = 38.52772
Net Variance = 38.52772 / 3 = 12.843

Double Super Times Pay: 27.720 with 554 Possible Payout Values

Total Variance = 49.158 + (3-1) * 17.0014 = 83.1608
Net Variance = 83.1608 / 3 = 27.720


Variances for Five Play 9/5 Jacks or Better

Standard: 5.456 with 406 Possible Payout Values

Total Variance = 19.4956 + (5-1) * 1.94596 = 27.27944
Net Variance = 27.27944 / 5 = 5.456

Super Times Pay: 9.154 with 2049 Possible Payout Values

Total Variance = 31.286 + (5-1) * 3.62086 = 45.76944
Net Variance = 45.76944 / 5 = 9.154

Double Super Times Pay: 23.433 with 4782 Possible Payout Values

Total Variance = 49.158 + (3-1) * 17.0014 = 117.1636
Net Variance = 117.1636 / 5 = 23.433


Variances for Ten Play 9/5 Jacks or Better

Standard: 3.701 with 2011 Possible Payout Values

Total Variance = 19.4956 + (10-1) * 1.94596 = 37.00924
Net Variance = 37.00924 / 10 = 3.701

Super Times Pay: 6.387 with 9527 Possible Payout Values

Total Variance = 31.286 + (5-1) * 3.62086 = 63.87374
Net Variance = 63.87374 / 10 = 6.387

Double Super Times Pay: 20.217 with 21323 Possible Payout Values

Total Variance = 49.158 + (10-1) * 17.0014 = 202.1706
Net Variance = 202.1706 / 10 = 20.217


Since this is an Intermediate level insight, the variance and return will be described on the Technical Section.


#3 - Odds of encountering W2G payouts on Single Line / 3 Play / 5 Play / 10 Play

Double Super Times Pay should not be played by those that are conscientious of W2G tax forms that will raise his/her adjusted gross income to become ineligible for tax credits. For those that hold themselves responsible and see jackpots as a thrilling event, it is not trivial to know exactly when to expect the jackpot of $1200 or more in Double STP. The Variance that Double STP adds to Jacks or Better creates a Double Double Bonus feel to the player.

It stands to reason that higher denominations and higher number of lines can increase the chances of triggering.

25¢ denomination – 4800 credit win
50¢ denomination – 2400 credit win
$1 denomination – 1200 credit win
$2 denomination – 600 credit win

The Average Odds of W2G for Single Line

25¢ Denomination: 1 in 311635.257406858
50¢ Denomination: 1 in 39550.568740441
$1 Denomination: 1 in 26057.8297288011
$2 Denomination: 1 in 6758.84276911163

The Average Odds of W2G for Three Play

25¢ Denomination: 1 in 88760.8303674638
50¢ Denomination: 1 in 12863.8159951622
$1 Denomination: 1 in 5967.04075298341
$2 Denomination: 1 in 1347.99658189003

The Average Odds of W2G for Five Play

25¢ Denomination: 1 in 44736.8117094247
50¢ Denomination: 1 in 7017.15013225372
$1 Denomination: 1 in 2718.63887708715
$2 Denomination: 1 in 455.502067504806

The Average Odds of W2G for Ten Play

25¢ Denomination: 1 in 17487.3108048464
50¢ Denomination: 1 in 2635.10254609697
$1 Denomination: 1 in 524.108084773103
$2 Denomination: 1 in 127.252703616368

#4 - Bankroll Simulation to achieve Total Rewards status in a day for JorB DSTP

This is assuming the player plays every dealt hands perfect strategy. The Player should bring additional funds for bankroll should they feel they’ll make minor errors.

EDIT: All simulations run for 100,000 trials due to the high variance nature of this game.

The Double STP is available in $1 and $2 denominations, and those will be utilized.

For Total Rewards, most video poker games award 1 Tier Credit for $10 coin-in

Platinum in a Day: If a player earns 2500 Tier Credits in a single gaming day period, 5000 Bonus Tier credits will be awarded. This is $25,000 worth of coin-in. Though it requires 5000 Tier Credits to reach Platinum Status, the player will get 7500 Tier Credits.

Diamond in a Day: If a player earns 5000 Tier Credits in a single gaming day period, 10000 Bonus Tier credits will be awarded. This is $50,000 worth of coin-in. It requires 15000 Tier Credits to reach Platinum Status. The player may consider doing this 10 different days in the eligible period to reach 7Star status.

Remember, if the player fails to meet the threshold, he/she will not get the bonus tier credits. They would really need to reach the threshold.

Single Line (100 Possible Payout Outcomes)

$2 Denomination Platinum in a Day requires 1786 rounds ($25000 / $14 a round)

Chance of Winning Session when played at 99.9% No Ruin Bankroll – 32.037%
Average Loss Amount when played at 99.9% No Ruin Bankroll - 135.96 Credits or $272 at $2 Denomination

$3520 (1760 $2 Credits) Bankroll produce 95.498% Chance of No Ruin
$4310 (2155 $2 Credits) Bankroll produce 99.152% Chance of No Ruin
$5050 (2525 $2 Credits) Bankroll produce 99.888% Chance of No Ruin

$1 Denomination Platinum in a Day requires 3572 rounds. ($25000 / $7 a round)
$2 Denomination Diamond in a Day requires 3572 rounds. ($50000 / $14 a round)

Chance of Winning Session when played at 99.9% No Ruin Bankroll – 29.827%
Average Loss Amount when played at 99.9% No Ruin Bankroll - 256.16 $1 Credits or $512.32 at $2 Denomination

$2725 ($5450 for $2 Denomination) Bankroll produce 95.374% Chance of No Ruin
$3200 ($6400 for $2 Denomination) Bankroll produce 98.551% Chance of No Ruin
$3870 ($7740 for $2 Denomination) Bankroll produce 99.867% Chance of No Ruin

$1 Denomination Diamond in a Day requires 7143 rounds. ($50000 / $7 a round)

Chance of Winning Session when played at 99.9% No Ruin Bankroll – 29.285%
Average Loss Amount when played at 99.9% No Ruin Bankroll - 522.55 $1 Credits

$4300 Bankroll produce 95.275% Chance of No Ruin
$5220 Bankroll produce 99.098% Chance of No Ruin
$6040 Bankroll produce 99.852% Chance of No Ruin

Three Play (1293 Combinations)

$2 Denomination Platinum in a Day requires 596 rounds. ($25000 / $42 a round)

Chance of Winning Session when played at 99.8% No Ruin Bankroll – 34.954%
Average Loss Amount when played at 99.8% No Ruin Bankroll - 140.52 Credits or $281.04 at $2 Denomination

$4220 (2110 $2 Credits) Bankroll produce 95.274% Chance of No Ruin
$5250 (2625 $2 Credits) Bankroll produce 99.173% Chance of No Ruin
$5940 (2970 $2 Credits) Bankroll produce 99.807% Chance of No Ruin

$1 Denomination Platinum in a Day requires 1191 rounds. ($25000 / $21 a round)
$2 Denomination Diamond in a Day requires 1191 rounds. ($50000 / $42 a round)

Chance of Winning Session when played at 99.654% No Ruin Bankroll – 33.413%
Average Loss Amount when played at 99.654% No Ruin Bankroll - 265.59 $1 Credits or $531.18 at $2 Denomination

$3270 ($6540 for $2 Denomination) Bankroll produce 95.395% Chance of No Ruin
$3980 ($7960 for $2 Denomination) Bankroll produce 98.992% Chance of No Ruin
$4380 ($8760 for $2 Denomination) Bankroll produce 99.654% Chance of No Ruin

$1 Denomination Diamond in a Day requires 2381 rounds. ($50000 / $21 a round)

Chance of Winning Session when played at 99.6% No Ruin Bankroll – 34.196%
Average Loss Amount when played at 99.6% No Ruin Bankroll - 508.62 $1 Credits

$5140 Bankroll produce 95.603% Chance of No Ruin
$6150 Bankroll produce 98.925% Chance of No Ruin
$6650 Bankroll produce 99.577% Chance of No Ruin


Five Play (4782 Possible Payout Outcomes)

$2 Denomination Platinum in a Day requires 358 rounds. ($25000 / $70 a round)

Chance of Winning Session when played at 99.9% No Ruin Bankroll – 36.186%
Average Loss Amount when played at 99.9% No Ruin Bankroll - 136.77 Credits or $273.54 at $2 Denomination

$4800 (2400 $2 Credits) Bankroll produce 95.538% Chance of No Ruin
$5800 (2900 $2 Credits) Bankroll produce 99.013% Chance of No Ruin
$6960 (3480 $2 Credits) Bankroll produce 99.907% Chance of No Ruin

$1 Denomination Platinum in a Day requires 715 rounds. ($25000 / $35 a round)
$2 Denomination Diamond in a Day requires 715 rounds. ($50000 / $70 a round)

Chance of Winning Session when played at 99.9% No Ruin Bankroll – 35.304%
Average Loss Amount when played at 99.9% No Ruin Bankroll - 273.81 $1 Credits or $547.62 at $2 Denomination

$7250 (3625 $2 Credits) Bankroll produce 94.782% Chance of No Ruin
$9060 (4530 $2 Credits) Bankroll produce 99.132% Chance of No Ruin
$10720 (5360 $2 Credits) Bankroll produce 99.898% Chance of No Ruin

$1 Denomination Diamond in a Day requires 1429 rounds. ($50000 / $35 a round)

Chance of Winning Session when played at 99.9% No Ruin Bankroll – 34.196%
Average Loss Amount when played at 99.9% No Ruin Bankroll - 530.52 $1 Credits

$5650 Bankroll produce 95.144% Chance of No Ruin
$6950 Bankroll produce 99.123% Chance of No Ruin
$8370 Bankroll produce 99.924% Chance of No Ruin

Ten Play (21323 Possible Payout Outcomes)

$2 Denomination is not available for Ten Play

$1 Denomination Platinum in a Day requires 358 rounds. ($25000 / $70 a round)

Chance of Winning Session when played at 99.9% No Ruin Bankroll – 37.791%
Average Loss Amount when played at 99.9% No Ruin Bankroll - 255.77 $1 Credits

$4430 Bankroll produce 95.204% Chance of No Ruin
$5400 Bankroll produce 98.945% Chance of No Ruin
$6560 Bankroll produce 99.918% Chance of No Ruin

$1 Denomination Diamond in a Day requires 715 rounds. ($50000 / $70 a round)

Chance of Winning Session when played at 99.9% No Ruin Bankroll – 37.791%
Average Loss Amount when played at 99.9% No Ruin Bankroll - 255.77 $1 Credits

$6880 Bankroll produce 95.650% Chance of No Ruin
$8370 Bankroll produce 99.057% Chance of No Ruin
$9730 Bankroll produce 99.854% Chance of No Ruin

#5 – Theoretical Simulation of 1 Million Rounds of 5-Play DSTP

Although a few thousand rounds of play is needed to attain membership to higher levels of the Total Rewards casino clubs, obtaining it a few times does not nearly represent the long term result. This simulation is just a theoretical representation if the player has lots of time and money on their hands to play 1 million rounds of 9/5 Jacks or Better DSTP. At a pace of 400 rounds an hour, it will take 2500 hours to complete which is more than what the typical adult works in an entire year. It costs 35 credits per round of play on DSTP, a millions rounds will equate that the player put in 35 million credits in.

9/5 Jacks or Better has a theoretical long term return of 98.9483%

35,000,000 x (1 – 0.989483) = 368097.6

After a million rounds, the player stands to lose 368,098 credits on average. Even at quarter denomination, that rounds out to about $92,024.50. Can most people’s annual income after taxes meet that kind of loss? That is the reason I mentioned that this part is all in theory.

Ran 1000 (one thousand) simulation trials of 1 Million Round play to obtain a breakdown of the returns. It does take hours to execute.

< 97.95% - 0.2%
97.95% to 98.05% - 0.4%
98.05% to 98.15% - 0.4%
98.15% to 98.25% - 1.5%
98.25% to 98.35% - 2.8%
98.35% to 98.45% - 4.4%
98.45% to 98.55% - 6.3%
98.55% to 98.65% - 8.2%
98.65% to 98.75% - 11.7%
98.75% to 98.85% - 10.2%
98.85% to 98.95% - 11.3%
98.95% to 99.05% - 10.0%
99.05% to 99.15% - 8.6%
99.15% to 99.25% - 7.3%
99.25% to 99.35% - 2.8%
99.35% to 99.45% - 2.7%
99.45% to 99.55% - 1.0%
99.55% to 99.65% - 1.4%
99.65% to 99.75% - 1.4%
99.75% to 99.85% - 1.0%
99.85% to 99.95% - 1.0%
> 99.95% - 5.4%

The Variance of DSTP is so high that after 1 million rounds, a majority of the returns when played perfectly are within 1% of the theoretical return.


[QUOTE]


To conclude as a recap

- The player will receive a multiplier about 1 in 8 average. Some of the multipliers (16x and 20x) appear at the rate of once in over 120k rounds. This means a standard single line video poker player will have hit 3 Royal Flushes.
- The variance Double STP adds to the game can make Bonus Poker and Jacks or Better feel like DDB. It can make Bonus Deluxe and DDB feel like Triple Double Bonus.
- Taxable outcomes are more frequent
- The player achieving total rewards status must have a sizable bankroll handy


[/QUOTE]


Technical analysis used in this Insight

Brief description on how the variance and return is calculated. It is best to utilize a macro script on a spreadsheet than it is by doing it by hand; more fast and efficient with less chance for errors.

Start with the original pay table payouts/odds. Be sure the odds are in the form of decimal percentage where 1 represent 100%. Preserve this as it will be utilized multiple times.

0     0.544964250445511
5     0.215135325753636
10     0.129303235146641
15     0.074465232383601
20     0.0112305460830752
25     0.010892385278778
45     0.0115139709781573
125     0.00236292854604446
250     0.000107230384866881
*4000     2.4895000114125E-05

*To handle the Royal Flush situation, create another 4000 payout which indicates the odds of being dealt one, this is because of the special situation where if a STP Multiplier is triggered on the deal, the payout will automatically will be 80000. The other one will be the odds of getting a Royal on the draw.

2.4895000114125E-05 – (1 / 649790) = 2.335604E-05

4000 2.335604E-05
4000 1.53895E-06

Prepare a translation of outputs starting from non-STP. The odds of STP multipliers not appearing is about 87.1%. Take a copy of the original payout odds and on a separate part of the spreadsheet, multiply 0.871 to each value.

For each of the possible multipliers, listed out on section #1, you would have to multiply the odds with the percentage the number comes out, AND the payout value needs to be multiplied by the multiplier.

e.g. 11x Multiplier odds is 0.000171, so for the Full House it would be

From: 45 0.0115139709781573
To: 495 [45 x 11] 0.00000196888 [0.0115139709781573 x 0.000171]

Be careful with handling the dealt Royal value, be sure to subtract out the percentage of Single STP triggers for 2x, 3x, 4x, 5x, 8x, 10x.

In the end, add up all the totals. Merge the common payout values if they appear more than once.

To run a bankroll simulation, keep track of number of hands to play, the starting bankroll, the cost to play, and the number of trials to run.

1.     Subtract cost to play from bankroll
2.     Evaluate a random outcome
3.     Add back the outcome result to the bankroll
4.     If the number of hands does not reach the desired hands to play, keep repeating Step 1

With the odds plotted out for all the possible payouts. The simple way to perform bankroll simulation is to pick a random fractional value function between 0 and 1 inclusive, the decimal places really does matter so do not round off.

Let’s say the number 0.835 was selected on this Single Line Double STP payout plot.

0 0.544964250445511
5 0.187406772656501
10 0.117724240096671
15 0.0734346580708372
20 0.0171584572795505

First compare 0.835 with each payout spots

Is 0.835 greater than 0.544964250445511, Yes
Is 0.835 greater than 0.544964250445511 + 0.187406772656501, Yes
Is 0.835 greater than 0.544964250445511 + 0.187406772656501 + 0.117724240096671, No

Thus, the end result payout will be 10 for the hand. Repeat as many times until you played the necessary amount of hands or you ruined.

[pokerpokerpoker]

Great analysis, Alpax.

I never used to play STP, it seemed that the extra coin was buying a feature that seldom came up. Finally get a multiplier, then brick the hand.

Lately, I have taken a liking to DSTP, BDLX or DDB, for single hand quarters. There is a lot of excitement with the frequent multipliers and nice payout potential - without "betting big".

But, if you don't connect on multiplied quads, your credits can tank in a hurry. 3X straights and 4X flushes will only take you so far.

Playing a short pay schedule really hurts in this game. A 5X flush is only 125 credits instead of 150. That extra 25 credits finances the next few hands.

[alpax]

Thanks PPP!

I think for people who play DDB for dollars, playing DSTP for quarters can nearly match the winning session potential you've described.

It is seldom to find good DSTP, Vegas has a few you played on your last trip.

I think realistically​ most DSTP will be short pay. DSTP on full pay Jack's or Better will exceed 100% payoff so not an option for casinos to offer.

I'll get to Bonus Poker Deluxe when I get a chance since that also seems to be a good option tringlomane suggests.

[pokerpokerpoker]

Yeah, BDLX would be good to analyze. It can be found for 8/6 in some locales. 6 flush games arw easier to play accurately, IMO. One thing that would be interesting is the amount of the payback % is from the long shot hands: quads 5x and higher, multiplied royals and the lottery hit - dealt 20X royal.

[alpax]

PPP,

I got around to complete the 8/6 Bonus Poker Deluxe DSTP report that you were interested in. Hope this will prepare your mindset with the DSTP game in general on top of mastering the optimal strategy with the game (not as difficult as TDB/TTB, but the lone Jack vs Ace+Jack unsuited is the toughest part to grasp).

Single Line W2G Jackpot Odds

No matter if you select 3/5/10 play, you can still play single line with the DSTP feature. Most other specialty games require you to play all the hands at max credits.

The Average Odds of W2G for $1 Denomination: 1 in 3533.71980031837
The Average Odds of W2G for 50cent Denomination: 1 in 15995.3223311284
The Average Odds of W2G for 25cent Denomination: 1 in 237155.228175409

W2G is not possible on standard single line 25cent games, but on DSTP it is possible and will happen once in about every 6 royals you hit.

As someone who plays high variance DDB/TDB/TTB, it will probably make your day if you got a 2000 credit premium quad win. There are no premium quads in Bonus Deluxe, but DSTP makes it possible to win such an amount at similar odds.

The Average Odds of $500+ Win for 25cent Denomination: 1 in 7387.67 Rounds

Single Line Variance for 8/6 Bonus Poker Deluxe Double STP: 71.992
Single Line CoVariance for 8/6 Bonus Poker Deluxe Double STP: 20.113

Bankroll Perspective to play out your standard 2000 hands

Your usual $200 bankroll for TDB applied to this DSTP game will last: 29.47% of the time
If you play 2000 rounds, you will be ahead: 36.7% of the time. You will be averaging a loss of 152 credits.

1000 Credits ($250) – 36.18%
1200 Credits ($300) – 45.24%
1400 Credits ($350) – 53.37%
1600 Credits ($400) – 60.73%
2000 Credits ($500) – 74.49%
2400 Credits ($600) – 86.31%
2800 Credits ($700) – 93.45%
3200 Credits ($800) – 97.32%
4000 Credits ($1000) – 99.90%
4400 Credits ($1100) – 100%

Since I’ve mentioned the Caesars Entertainment Total Rewards program, if you are seeking status at the MGM mLife program when you head out to Vegas, consider playing 3-lines for efficiency purposes.

8/6 Bonus Deluxe DSTP exists in quarter, half-dollar, and dollar denominations at where you played.

The following will represent 1 unit of play which will earn you 25,000 tier points if you play it though. 4762 rounds of 3 line DSTP at quarter denomination. Moving up to half-dollar will be 2 units and dollar will be 4 units.

It is NOT required to play it through on a single day. It can be spanned on multiple trips as long as it is within the October 1 thru the September 30 earning period. If you advance to the next tier, you will have the tier for the next year as well.

mLife Pearl – 1 Unit
mLife Gold – 3 Units
mLife Platinum – 8 Units
mLife NOIR – This is unknown because it is invite only…

8000 Credits – 78.09%
10000 Credits – 89.90%
12000 Credits – 96.41%
14000 Credits – 98.95%
16000 Credits – 99.89%
18000 Credits – 99.93%

The Average Odds of W2G for $1 Denomination: 1 in 995.519915547269
The Average Odds of W2G for 50cent Denomination: 1 in 4679.35168352838
The Average Odds of W2G for 25cent Denomination: 1 in 31340.0772960198
The Average Odds of $500+ Win for 25cent Denomination: 1 in 2483.58658349171

You will be ahead 37% of the time after the unit of play.

Total Variance of 3-Play: 37.4063599986412

Hope this helps PPP and good luck to you moving forward.

[Vman96]

Sorry I missed this earlier. Some good stuff Alpax. My simulator does single line STP and Double STP too. But lately I haven't had any good questions to answer over it.

It's too bad you couldn't find the multiplier breakdown initially.

2x – 17% Frequency
3x – 33% Frequency
4x – 16% Frequency
5x – 24% Frequency
8x – 8% Frequency
10x – 2% Frequency

In my experience I don't feel like I have got 8X's 4 times more often than 10X's though. And very ironically, I have got 20X TWICE, but NEVER 16X. Excluding the dealt royal rule, the odds of getting two 20X's first before a 16X is 1 in 289. Yikes.

[alpax]

Much appreciated that you were able to get a hold of the DSTP 4.01x average multiplier frequencies. I am more than willing to re update the calculations and the odds based on the multipliers. It should not be too much trouble and I should have it completed in the next few days.

Since the DSTP trades 2% of 10x for 2% of 8x in order to compromise 4x worth of multipliers, getting 20x will be much tougher than I ever thought it will be. 16x should be more frequent but is an anomaly you got 20x twice already.

I am also trying to figure out multiline variance on these specialty games and was going to add on to this report.

I learned a lot from how Video Poker for Winners work. From multi line games it plots out the odds of every possible draw combinations. I just did simple vector multiplication of the multipliers with the odds to gain valuable insight to DSTP. I'll have updated information soon.

The Total Rewards bankroll stuff took the most time since it is all guesswork until the percentages match. Probably will do just 95 99 and 99.9 this time before it is really pointless to fall short of the tier bonus threshold. It is freaky how much bankroll is needed to survive.

[pokerpokerpoker]

Great stuff as always, Alpax. Once I get some peace and quiet I will really pour over what you posted. The odds of a $500 win are longer than I would have thought. It seems easy enough: hit a quad with a 5X. But if quads are one in 400 and a mults are one 7 and to get a mult of 5 or higher are X - yeah I guess the odds are long indeed.

But unfortunately, I busted out. After a winning 2016 and a great January, this year has been a nearly complete disaster. After playing on $200 sessions quarters and running average, I bumped to .50 and $1. Mostly TBD and the 5Star playing QQ, DSTP and DC (DDB). Session after session of nothing - often no quads at all. I am stuck $7000 for the year, which was all my "having fun money". The last straw was the other night in which the MS 5 way $1 was getting juicy - royal at $6500 and the others pretty nice too. I lost $800 in 40 minutes, quadless. All this was playing good games with good strategy. I guess these results can happen when you play high variance games.

On the bright side, I did get some good mailers. I will be back, but it will take a while.

[alpax]

You are welcome PPP. I do plan on making the adjustments to Bonus Deluxe as well since Vman was able to provide the true multipliers of Double STP. The updated results will be there once you are ready to get back into action.

I feel your pain. Thousands of dollars in disposable income for video poker or other gambling games is not easy for most to come by, I do not want these reports to make it look easy. I busted out on Bonus Deuces Wild last year and another unlucky Vegas trip earlier this year on $2 denomination Bonus Deluxe / Double Bonus / Airport DW / Jacks or Better. Been doing more insights during the downtime. I completely knew it was going to be a long term grind to get the long term benefit of the game, but these reports are necessary to understand Gambler's Ruin. High variance games just means the player needs to grind longer to get the long term benefit.

Going back to the 1 in high 7000s odds for $500+ wins from single line BDlx DSTP, you are correct it is either from a Royal Flush or a multiplied quad. Technically a multiplied Straight Flush would also count, but the odds of that is not reliable.

12.88% or 0.12888 is the total probability of any multipliers appearing in DSTP. From taking out 2x, 3x, 4x frequencies based on the multipliers I've used it is reduced to

0.12888 (Total) - 0.023644 (2x chance) - 0.039822 (3x chance) - 0.020072 (4x chance) = 0.04535088 (Total 5x or better)

Take the inverse of that by doing 1 divided by 0.04535088 to get 22.05. So 1 in 22.05 rounds you will get 5x or better multiplier to start.

Quads in BDlx happen 1 in 423.9 with optimal play

Thus 423.9 x 22.05 is 9347. 1 in 9347 odds the $500+ win will come via a multiplied quad. This is a rough estimate since I deducted from 3x and 5x rather than 10x. In perspective, the odds of AWAK in quarter single line DDB is about 1 in 16200.

[pokerpokerpoker]

A grind indeed. I reckon I have played 40 hours of VP this year averaging 99.4%, fifty cent average, 800 HPH. My theoretical loss would be around $12/hour. That would be $480 - anumber I can easily live with. I don't really expect to win, and I accept there is a cost to play. But at 15 times expected loss, I just can't continue. In the past, I would have many bad days, but the good days would come and balance them out. With this miserable streak, the good days never came.