Dream Card Poker Insight for DDB and TDB Players
Posted: Wed Dec 20, 2017 2:03 am
Dream Card Poker has a track record of being one of the most popular specialty video poker game ever in the casinos and on this website. Most notably it is played by Tedlark, a member who achieved earning 3 million club points on videopoker.com
For those who are oblivious to what Dream Card Poker is, here is a description from this website though I do not think they provide the best descriptions for their games in general.
[QUOTE] This game is enhanced with the newest buy-a-pay feature to hit poker: The Dream Card. A maximum bet increases the chances of winning a Dream Card. If the extra wager is placed and the feature awards it, optimal autohold strategy is employed to pick the perfect card to complete the dealt hand. Players are given the card yielding the highest expected return. In other words, players can count on a 4-of-a-kind in place of a 3-of-a-kind on the deal! [/QUOTE]
This is a 10 coin per line game that provides a slight extra return than its base game, and the standard hold strategy is employed on this game as well which makes it easier for players to adapt.
The Motive Behind The Insight
It happened during the most recent December 14th 2017 episode of Gambling With An Edge co-hosted by Mr. Munchkin and Mr. Dancer where the featured guest was “The Wizard of Odds†(Mr. Shackleford), a vpFREE Video Poker Hall of Fame Inductee to boot as well. One of the segments of the episodes talked about Dream Card. Earlier this year, Mr. Shackleford made an interesting observation that the Dream Card frequency shown on the Help pages on this website and at the casinos were incorrect and that the stated value is lower than the actual percentages. Mr. Shackleford brought it up with the appropriate channels at IGT/Action Gaming during a Super Bowl party, and it was concluded that it was a valid point. The general public had to be aware and there may be legal repercussions for presenting misinformation, but the legal team believed that guaranteeing a smaller than the actual percentage will be ok because it at least meets the promise prior to the player playing.
The podcast in MP3 audio format can be found HERE Although I recommend the entire episode personally, the subject in question can be tuned in between the 22:44 and 28:12 mark of the segment.
The 2017 Global Gaming Exposition also showcased a new video poker theme featuring Dream Card. Since it will make an exciting comeback later this year, this will be another motive to explore Dream Card for me.
The Dream Card DDB Return Controversy
When opening the Help pages on videopoker.com for all pay schedules for the DDB variant of Dream Card Poker, they all state 30%.
Mr. Shackleford has a contact with the lead mathematician at VideoPoker.com to obtain the true percentages of the Dream Card feature for all the video poker game variants. It all states 31% for DDB.
This is on top of the many stories on this forum as well as other online forums where the correct Dream Card is not automatically selected. A page on the Wizard of Odds website describes this.
WizardOfOdds.com – Dream Card Controversy
There will be TWO main objectives for this Insight
(1) Analyzing the effect of the DreamCard feature
(2) Finding the true frequency of the DreamCard feature
Objective #1 – Analyzing the effect of the Dream Card feature
Note: On the WizardOfOdds website, the webmaster JB has provided extensive detail on just 9/6 Jacks or Better for the Dream Card feature. In this age of video poker, it is highly doubtful any place will offer that variant any more so it may not be worth much. This report is directed towards the DDB players, which is most members on this site including Mr. Fields the Vice President.
A general view of Dream Card is that 4 cards out of a 52 card deck will be dealt first, the Bonus feature when triggered will go through the remaining 48 cards to pick out the best card for the 5th card.
Thus there will be a total of
52 choose 4 = 270725 Possibilities
As mentioned earlier, the Dream Card when triggered may not always automatically select the best remaining card to yield the highest EV possible. Thankfully, the player is given an option to change out the Dream Card to one that they wish.
Assuming the most optimal Dream Card appears on every Bonus Opportunities AND the player makes the highest expected return hold, here are the returns for the Dream Card feature.
Though a downgrade of the Flush or Full House typically costs the player nearly 1.1% of the overall return, for the Bonus feature the cost drop is much less.
8/5 DDB
9/5 DDB
9/6 DDB
As you can see, the Dream Card bonus will yield an average payout of at least 20.69 Credits with respect to a 5 Credit wager payout. This Bonus feature does payout at least 413% as it really helps the player form big hands more often.
Objective #2 - Finding the true frequency of the Dream Card feature
Figuring the Actual Dream Card Percentage,
Let X = Percentage of the Dream Card Bonus
5-Coin Standard Game Value * (1 – X) + 5-Coin Dream Card Game Value * X = 10 Coin Game Value
5 Coin Standard Game Value for Standard DDB
9/6 DDB: 98.9808% * 5 = 4.94904
9/5 DDB: 97.8729% * 5 = 4.893645
8/5 DDB: 96.7861% * 5 = 4.839305
Theoretical Game Return Values posted on VideoPoker.com
Because this game is 10 coins per line to play, the game value is multiplied by 10 and the return.
8/5 DDB
4.839305*(1 – X) + 20.68521728*X = 9.7520
9/5 DDB
4.893645*(1 – X) + 20.85129562*X = 9.8410
9/6 DDB
4.94904*(1 – X) + 20.93310601*X = 9.9040
By figuring for X, we get a value of 0.31 (or 31%) for all the game pay schedules which is indeed matches the source where the Wizard obtained the percentages from the lead mathematician.
Despite this possible issue, Dream Card Poker is enjoyed every day by members of this site. I hope this report has given you an additional insight of the game you did not know about before today. Good luck out there!
Special Extension for Triple Double Bonus
5 Coin Standard Game Value for Standard Triple Double Bonus
9/6 TDB: 98.1540% * 5 = 4.9077
8/6 TDB: 97.1088% * 5 = 4.85544
Dream Card effect returns for Triple Double Bonus
8/6 TDB
9/6 TDB
The DreamCard pays 23.163 (8/6) and 23.309 (9/6) Credits with respect to a 5 Coin payout, this represents a return of 463.25% and 466.18% respectively.
Verifying the WoO reported DreamCard trigger rate of 26.7%
8/6 TDB
4.893645*(1 – X) + 20.85129562*X = 9. 7434
4.893645*(1-.267) + 20.85129562*(.267) = 9. 7434
3.587041785 + 5.56729593054 ~= 9.7434
9/6 TDB
4.9077*(1 – X) + 23.30889353*X = 9.8210
4.9077*(1 – .267) + 23.30889353*(.267) = 9.8210
3.5973441 + 6.22347457251 ~= 9.8210
The true percentage is indeed higher at 26.7% than it is at 26%.
Heads up with regards to incorrect payouts on videopoker.com
The 8/6 TDB will pay out 25 credits for a Flush instead of 30 credits it supposed to payout
DreamCard Impact on W2G payouts
9/5 DDB 1 Line
The Average Odds of W2G for $2 Denomination: 1 in 622.746897126968
The Average Odds of W2G for $1 Denomination: 1 in 2826.31529525692
The Average Odds of W2G for 50¢ Denomination: 1 in 11062.3930073704
9/5 DDB 3 Line
The Average Odds of W2G for $2 Denomination: 1 in 157.061071867645
The Average Odds of W2G for $1 Denomination: 1 in 582.075949844605
The Average Odds of W2G for 50¢ Denomination: 1 in 1510.31688125346
The Average Odds of W2G for 25¢ Denomination: 1 in 8703.76572241252
The Average Odds of W2G for 10¢ Denomination: 1 in 41690.3792132732
9/5 DDB 5 Line
The Average Odds of W2G for $2 Denomination: 1 in 117.278217065192
The Average Odds of W2G for $1 Denomination: 1 in 216.089662354193
The Average Odds of W2G for 50¢ Denomination: 1 in 811.74044539504
The Average Odds of W2G for 25¢ Denomination: 1 in 4362.8623366165
The Average Odds of W2G for 10¢ Denomination: 1 in 41347.3260689878
9/5 DDB 10 Line
The Average Odds of W2G for $2 Denomination: 1 in 53.5842920068046
The Average Odds of W2G for $1 Denomination: 1 in 152.216476180422
The Average Odds of W2G for 50¢ Denomination: 1 in 240.183675187266
The Average Odds of W2G for 25¢ Denomination: 1 in 1120.90993040644
The Average Odds of W2G for 10¢ Denomination: 1 in 7873.72953165554
The Average Odds of W2G for 5¢ Denomination: 1 in 41730.175517853
9/6 DDB 1 Line
The Average Odds of W2G for $2 Denomination: 1 in 620.922329844086
The Average Odds of W2G for $1 Denomination: 1 in 2789.1454851558
The Average Odds of W2G for 50¢ Denomination: 1 in 10511.6046615507
9/6 DDB 3 Line
The Average Odds of W2G for $2 Denomination: 1 in 156.712968771598
The Average Odds of W2G for $1 Denomination: 1 in 577.326697896405
The Average Odds of W2G for 50¢ Denomination: 1 in 1478.61273397297
The Average Odds of W2G for 25¢ Denomination: 1 in 8702.78931687986
The Average Odds of W2G for 10¢ Denomination: 1 in 41690.3723247949
9/6 DDB 5 Line
The Average Odds of W2G for $2 Denomination: 1 in 116.955211715313
The Average Odds of W2G for $1 Denomination: 1 in 214.996355751805
The Average Odds of W2G for 50¢ Denomination: 1 in 796.456780837326
The Average Odds of W2G for 25¢ Denomination: 1 in 4362.04562087023
The Average Odds of W2G for 10¢ Denomination: 1 in 41347.2584072718
9/6 DDB 10 Line
The Average Odds of W2G for $2 Denomination: 1 in 53.4047522859863
The Average Odds of W2G for $1 Denomination: 1 in 151.136167054704
The Average Odds of W2G for 50¢ Denomination: 1 in 237.492839801208
The Average Odds of W2G for 25¢ Denomination: 1 in 1120.66105853476
The Average Odds of W2G for 10¢ Denomination: 1 in 7873.70019012204
The Average Odds of W2G for 5¢ Denomination: 1 in 41730.1755178519
9/6 TDB 1 Line
The Average Odds of W2G for $2 Denomination: 1 in 665.858776325727
The Average Odds of W2G for $1 Denomination: 1 in 938.2204339138
The Average Odds of W2G for 50¢ Denomination: 1 in 2749.11416933433
9/6 TDB 3 Line
The Average Odds of W2G for $2 Denomination: 1 in 171.449244472907
The Average Odds of W2G for $1 Denomination: 1 in 348.390641855264
The Average Odds of W2G for 50¢ Denomination: 1 in 693.283646305559
The Average Odds of W2G for 25¢ Denomination: 1 in 2910.1314892639
The Average Odds of W2G for 10¢ Denomination: 1 in 13305.6735108403
9/6 TDB 5 Line
The Average Odds of W2G for $2 Denomination: 1 in 127.113358911095
The Average Odds of W2G for $1 Denomination: 1 in 161.533874688508
The Average Odds of W2G for 50¢ Denomination: 1 in 473.135461703298
The Average Odds of W2G for 25¢ Denomination: 1 in 1725.45732682059
The Average Odds of W2G for 10¢ Denomination: 1 in 11140.4113219188
9/6 TDB 10 Line
The Average Odds of W2G for $2 Denomination: 1 in 67.8324072355717
The Average Odds of W2G for $1 Denomination: 1 in 105.807078328255
The Average Odds of W2G for 50¢ Denomination: 1 in 171.42007166855
The Average Odds of W2G for 25¢ Denomination: 1 in 929.947047944111
The Average Odds of W2G for 10¢ Denomination: 1 in 2566.92955518114
The Average Odds of W2G for 5¢ Denomination: 1 in 11706.7330693945
8/6 TDB 1 Line
The Average Odds of W2G for $2 Denomination: 1 in 665.855158844039
The Average Odds of W2G for $1 Denomination: 1 in 938.207840273708
The Average Odds of W2G for 50¢ Denomination: 1 in 2749.00547333163
8/6 TDB 3 Line
The Average Odds of W2G for $2 Denomination: 1 in 171.448528100297
The Average Odds of W2G for $1 Denomination: 1 in 348.385444770064
The Average Odds of W2G for 50¢ Denomination: 1 in 693.262956264216
The Average Odds of W2G for 25¢ Denomination: 1 in 2910.13064739411
The Average Odds of W2G for 10¢ Denomination: 1 in 13305.6735051619
8/6 TDB 5 Line
The Average Odds of W2G for $2 Denomination: 1 in 127.308577293216
The Average Odds of W2G for $1 Denomination: 1 in 161.53201702137
The Average Odds of W2G for 50¢ Denomination: 1 in 473.119438758802
The Average Odds of W2G for 25¢ Denomination: 1 in 1725.45634156743
The Average Odds of W2G for 10¢ Denomination: 1 in 11140.4112821651
8/6 TDB 10 Line
The Average Odds of W2G for $2 Denomination: 1 in 67.8323658029029
The Average Odds of W2G for $1 Denomination: 1 in 105.805579872134
The Average Odds of W2G for 50¢ Denomination: 1 in 171.415889649159
The Average Odds of W2G for 25¢ Denomination: 1 in 929.94576422206
The Average Odds of W2G for 10¢ Denomination: 1 in 2566.92952994212
The Average Odds of W2G for 5¢ Denomination: 1 in 11706.7330693945
For those who are oblivious to what Dream Card Poker is, here is a description from this website though I do not think they provide the best descriptions for their games in general.
[QUOTE] This game is enhanced with the newest buy-a-pay feature to hit poker: The Dream Card. A maximum bet increases the chances of winning a Dream Card. If the extra wager is placed and the feature awards it, optimal autohold strategy is employed to pick the perfect card to complete the dealt hand. Players are given the card yielding the highest expected return. In other words, players can count on a 4-of-a-kind in place of a 3-of-a-kind on the deal! [/QUOTE]
This is a 10 coin per line game that provides a slight extra return than its base game, and the standard hold strategy is employed on this game as well which makes it easier for players to adapt.
The Motive Behind The Insight
It happened during the most recent December 14th 2017 episode of Gambling With An Edge co-hosted by Mr. Munchkin and Mr. Dancer where the featured guest was “The Wizard of Odds†(Mr. Shackleford), a vpFREE Video Poker Hall of Fame Inductee to boot as well. One of the segments of the episodes talked about Dream Card. Earlier this year, Mr. Shackleford made an interesting observation that the Dream Card frequency shown on the Help pages on this website and at the casinos were incorrect and that the stated value is lower than the actual percentages. Mr. Shackleford brought it up with the appropriate channels at IGT/Action Gaming during a Super Bowl party, and it was concluded that it was a valid point. The general public had to be aware and there may be legal repercussions for presenting misinformation, but the legal team believed that guaranteeing a smaller than the actual percentage will be ok because it at least meets the promise prior to the player playing.
The podcast in MP3 audio format can be found HERE Although I recommend the entire episode personally, the subject in question can be tuned in between the 22:44 and 28:12 mark of the segment.
The 2017 Global Gaming Exposition also showcased a new video poker theme featuring Dream Card. Since it will make an exciting comeback later this year, this will be another motive to explore Dream Card for me.
The Dream Card DDB Return Controversy
When opening the Help pages on videopoker.com for all pay schedules for the DDB variant of Dream Card Poker, they all state 30%.
Mr. Shackleford has a contact with the lead mathematician at VideoPoker.com to obtain the true percentages of the Dream Card feature for all the video poker game variants. It all states 31% for DDB.
This is on top of the many stories on this forum as well as other online forums where the correct Dream Card is not automatically selected. A page on the Wizard of Odds website describes this.
WizardOfOdds.com – Dream Card Controversy
There will be TWO main objectives for this Insight
(1) Analyzing the effect of the DreamCard feature
(2) Finding the true frequency of the DreamCard feature
Objective #1 – Analyzing the effect of the Dream Card feature
Note: On the WizardOfOdds website, the webmaster JB has provided extensive detail on just 9/6 Jacks or Better for the Dream Card feature. In this age of video poker, it is highly doubtful any place will offer that variant any more so it may not be worth much. This report is directed towards the DDB players, which is most members on this site including Mr. Fields the Vice President.
A general view of Dream Card is that 4 cards out of a 52 card deck will be dealt first, the Bonus feature when triggered will go through the remaining 48 cards to pick out the best card for the 5th card.
Thus there will be a total of
52 choose 4 = 270725 Possibilities
As mentioned earlier, the Dream Card when triggered may not always automatically select the best remaining card to yield the highest EV possible. Thankfully, the player is given an option to change out the Dream Card to one that they wish.
Assuming the most optimal Dream Card appears on every Bonus Opportunities AND the player makes the highest expected return hold, here are the returns for the Dream Card feature.
Though a downgrade of the Flush or Full House typically costs the player nearly 1.1% of the overall return, for the Bonus feature the cost drop is much less.
8/5 DDB
9/5 DDB
9/6 DDB
As you can see, the Dream Card bonus will yield an average payout of at least 20.69 Credits with respect to a 5 Credit wager payout. This Bonus feature does payout at least 413% as it really helps the player form big hands more often.
Objective #2 - Finding the true frequency of the Dream Card feature
Figuring the Actual Dream Card Percentage,
Let X = Percentage of the Dream Card Bonus
5-Coin Standard Game Value * (1 – X) + 5-Coin Dream Card Game Value * X = 10 Coin Game Value
5 Coin Standard Game Value for Standard DDB
9/6 DDB: 98.9808% * 5 = 4.94904
9/5 DDB: 97.8729% * 5 = 4.893645
8/5 DDB: 96.7861% * 5 = 4.839305
Theoretical Game Return Values posted on VideoPoker.com
Because this game is 10 coins per line to play, the game value is multiplied by 10 and the return.
8/5 DDB
4.839305*(1 – X) + 20.68521728*X = 9.7520
9/5 DDB
4.893645*(1 – X) + 20.85129562*X = 9.8410
9/6 DDB
4.94904*(1 – X) + 20.93310601*X = 9.9040
By figuring for X, we get a value of 0.31 (or 31%) for all the game pay schedules which is indeed matches the source where the Wizard obtained the percentages from the lead mathematician.
Despite this possible issue, Dream Card Poker is enjoyed every day by members of this site. I hope this report has given you an additional insight of the game you did not know about before today. Good luck out there!
Special Extension for Triple Double Bonus
5 Coin Standard Game Value for Standard Triple Double Bonus
9/6 TDB: 98.1540% * 5 = 4.9077
8/6 TDB: 97.1088% * 5 = 4.85544
Dream Card effect returns for Triple Double Bonus
8/6 TDB
9/6 TDB
The DreamCard pays 23.163 (8/6) and 23.309 (9/6) Credits with respect to a 5 Coin payout, this represents a return of 463.25% and 466.18% respectively.
Verifying the WoO reported DreamCard trigger rate of 26.7%
8/6 TDB
4.893645*(1 – X) + 20.85129562*X = 9. 7434
4.893645*(1-.267) + 20.85129562*(.267) = 9. 7434
3.587041785 + 5.56729593054 ~= 9.7434
9/6 TDB
4.9077*(1 – X) + 23.30889353*X = 9.8210
4.9077*(1 – .267) + 23.30889353*(.267) = 9.8210
3.5973441 + 6.22347457251 ~= 9.8210
The true percentage is indeed higher at 26.7% than it is at 26%.
Heads up with regards to incorrect payouts on videopoker.com
The 8/6 TDB will pay out 25 credits for a Flush instead of 30 credits it supposed to payout
DreamCard Impact on W2G payouts
9/5 DDB 1 Line
The Average Odds of W2G for $2 Denomination: 1 in 622.746897126968
The Average Odds of W2G for $1 Denomination: 1 in 2826.31529525692
The Average Odds of W2G for 50¢ Denomination: 1 in 11062.3930073704
9/5 DDB 3 Line
The Average Odds of W2G for $2 Denomination: 1 in 157.061071867645
The Average Odds of W2G for $1 Denomination: 1 in 582.075949844605
The Average Odds of W2G for 50¢ Denomination: 1 in 1510.31688125346
The Average Odds of W2G for 25¢ Denomination: 1 in 8703.76572241252
The Average Odds of W2G for 10¢ Denomination: 1 in 41690.3792132732
9/5 DDB 5 Line
The Average Odds of W2G for $2 Denomination: 1 in 117.278217065192
The Average Odds of W2G for $1 Denomination: 1 in 216.089662354193
The Average Odds of W2G for 50¢ Denomination: 1 in 811.74044539504
The Average Odds of W2G for 25¢ Denomination: 1 in 4362.8623366165
The Average Odds of W2G for 10¢ Denomination: 1 in 41347.3260689878
9/5 DDB 10 Line
The Average Odds of W2G for $2 Denomination: 1 in 53.5842920068046
The Average Odds of W2G for $1 Denomination: 1 in 152.216476180422
The Average Odds of W2G for 50¢ Denomination: 1 in 240.183675187266
The Average Odds of W2G for 25¢ Denomination: 1 in 1120.90993040644
The Average Odds of W2G for 10¢ Denomination: 1 in 7873.72953165554
The Average Odds of W2G for 5¢ Denomination: 1 in 41730.175517853
9/6 DDB 1 Line
The Average Odds of W2G for $2 Denomination: 1 in 620.922329844086
The Average Odds of W2G for $1 Denomination: 1 in 2789.1454851558
The Average Odds of W2G for 50¢ Denomination: 1 in 10511.6046615507
9/6 DDB 3 Line
The Average Odds of W2G for $2 Denomination: 1 in 156.712968771598
The Average Odds of W2G for $1 Denomination: 1 in 577.326697896405
The Average Odds of W2G for 50¢ Denomination: 1 in 1478.61273397297
The Average Odds of W2G for 25¢ Denomination: 1 in 8702.78931687986
The Average Odds of W2G for 10¢ Denomination: 1 in 41690.3723247949
9/6 DDB 5 Line
The Average Odds of W2G for $2 Denomination: 1 in 116.955211715313
The Average Odds of W2G for $1 Denomination: 1 in 214.996355751805
The Average Odds of W2G for 50¢ Denomination: 1 in 796.456780837326
The Average Odds of W2G for 25¢ Denomination: 1 in 4362.04562087023
The Average Odds of W2G for 10¢ Denomination: 1 in 41347.2584072718
9/6 DDB 10 Line
The Average Odds of W2G for $2 Denomination: 1 in 53.4047522859863
The Average Odds of W2G for $1 Denomination: 1 in 151.136167054704
The Average Odds of W2G for 50¢ Denomination: 1 in 237.492839801208
The Average Odds of W2G for 25¢ Denomination: 1 in 1120.66105853476
The Average Odds of W2G for 10¢ Denomination: 1 in 7873.70019012204
The Average Odds of W2G for 5¢ Denomination: 1 in 41730.1755178519
9/6 TDB 1 Line
The Average Odds of W2G for $2 Denomination: 1 in 665.858776325727
The Average Odds of W2G for $1 Denomination: 1 in 938.2204339138
The Average Odds of W2G for 50¢ Denomination: 1 in 2749.11416933433
9/6 TDB 3 Line
The Average Odds of W2G for $2 Denomination: 1 in 171.449244472907
The Average Odds of W2G for $1 Denomination: 1 in 348.390641855264
The Average Odds of W2G for 50¢ Denomination: 1 in 693.283646305559
The Average Odds of W2G for 25¢ Denomination: 1 in 2910.1314892639
The Average Odds of W2G for 10¢ Denomination: 1 in 13305.6735108403
9/6 TDB 5 Line
The Average Odds of W2G for $2 Denomination: 1 in 127.113358911095
The Average Odds of W2G for $1 Denomination: 1 in 161.533874688508
The Average Odds of W2G for 50¢ Denomination: 1 in 473.135461703298
The Average Odds of W2G for 25¢ Denomination: 1 in 1725.45732682059
The Average Odds of W2G for 10¢ Denomination: 1 in 11140.4113219188
9/6 TDB 10 Line
The Average Odds of W2G for $2 Denomination: 1 in 67.8324072355717
The Average Odds of W2G for $1 Denomination: 1 in 105.807078328255
The Average Odds of W2G for 50¢ Denomination: 1 in 171.42007166855
The Average Odds of W2G for 25¢ Denomination: 1 in 929.947047944111
The Average Odds of W2G for 10¢ Denomination: 1 in 2566.92955518114
The Average Odds of W2G for 5¢ Denomination: 1 in 11706.7330693945
8/6 TDB 1 Line
The Average Odds of W2G for $2 Denomination: 1 in 665.855158844039
The Average Odds of W2G for $1 Denomination: 1 in 938.207840273708
The Average Odds of W2G for 50¢ Denomination: 1 in 2749.00547333163
8/6 TDB 3 Line
The Average Odds of W2G for $2 Denomination: 1 in 171.448528100297
The Average Odds of W2G for $1 Denomination: 1 in 348.385444770064
The Average Odds of W2G for 50¢ Denomination: 1 in 693.262956264216
The Average Odds of W2G for 25¢ Denomination: 1 in 2910.13064739411
The Average Odds of W2G for 10¢ Denomination: 1 in 13305.6735051619
8/6 TDB 5 Line
The Average Odds of W2G for $2 Denomination: 1 in 127.308577293216
The Average Odds of W2G for $1 Denomination: 1 in 161.53201702137
The Average Odds of W2G for 50¢ Denomination: 1 in 473.119438758802
The Average Odds of W2G for 25¢ Denomination: 1 in 1725.45634156743
The Average Odds of W2G for 10¢ Denomination: 1 in 11140.4112821651
8/6 TDB 10 Line
The Average Odds of W2G for $2 Denomination: 1 in 67.8323658029029
The Average Odds of W2G for $1 Denomination: 1 in 105.805579872134
The Average Odds of W2G for 50¢ Denomination: 1 in 171.415889649159
The Average Odds of W2G for 25¢ Denomination: 1 in 929.94576422206
The Average Odds of W2G for 10¢ Denomination: 1 in 2566.92952994212
The Average Odds of W2G for 5¢ Denomination: 1 in 11706.7330693945