Dream Card expected value: on vs. off

[Minn. Fatz]

Here's some back of the envelope stuff I came up with comparing the expected value of a game with the Dream Card promotion on with the "underlying" game without Dream Cards.
 
Let:
C = the cost for turning Dream Cards on, expressed as a multiple of the cost for leaving it off
F = the percentage of time the Dream Card is activated when it is on
E = the expected value of the game with Dream Cards off
E' = the expected value of the game when the Dream Card is on and activated
 
Then the EV of the total game with Dream Cards on is:
 
[ (1-F)*E + F*E' ] / C
 
which simplifies to:
 
[ E + F*(E'-E) ] / C
 
Setting this >= E and solving for E' gives us:
 
E' >= E + [ E*(C-1) ] / F
 
Using the "game values" on this site, C = 2 and F = .26, we get (approximately):
 
E' >= 4.85*E
 
So for the expected value of the game with Dream Cards on to be better than the EV with Dream Cards off, the EV of the hands when Dream Cards are on and activated should be something short of five times the EV of the "underlying game." I haven't begun to do that math, but my (again back of the envelope) estimate for JB is that the EV of the Dream Cards hands is on the order of 2.3 - 2.6 times that of the non-Dream Cards hands.
 
As I've noted here previously, looks like the trend in VP is to ramp up the variance while cutting down the expected value a la the more traditional one-armed banditti.
 

[Webman]

Note that the frequency of Dream Cards varies by game family... In Deuces they come up much more often than in DDB or TDB. They come up fairly frequently in Jacks or Better as well. This frequency is available within the Help menu on the game itself.

[New2vp]

Hey Minnesota,Good to hear from you again.  I always like reading the thoughtfulness that you put in your posts.You have a small error in logic here.  For Jacks or Better, F = 0.505, so your comparative inequality becomes E' >= 2.9802*E.  The proportion of Dream Cards (DC) is different for different games.  Since there is a huge increase in return for the number of quads (about 10 times as many quads as in non-DC mode), the manufacturers even out the increase in return in the non-wild games that have higher quad payoffs by providing fewer Dream Cards.It's a much more difficult calculation to determine the ratio E'/E, but I'm going to cheat and not do the calculation.  Instead, I'll use what the Wizard of Odds recently posted.  He has the key ratio for 9-6 Jacks as 2.967211/0.995439, which turns out to be 2.9808, so it barely satisfies your condition, which means that 9-6 Dream Card Jacks or Better overall has a slightly higher EV than regular 9-6 Jacks or Better.For some reason in the help screens of the game the frequency of Dream Cards is truncated to the next lower percent.  The 9-6 Jacks game shows 50%, but recent posts by Bob Dancer and the Wizard of Odds agree that this probability is 50.5%.The 26% number that you are using is from the Triple Double Bonus game and here the same two sources suggest that this figure is 26.7%, so your key ratio for determining whether DC TDB is better than regular TDB is a bit different than you calculated; instead, it is E' >= 4.75*E.So, it's possible these games are better.  In fact the DC Illinois Deuces pay schedule reportedly returns 99.91% while the base game returns only 98.91%.(Edit:  Sorry Webman, your post came while I was preparing mine; but nothing I said contradicts your correct and more concise response.)

[shadowman]

Although not very scientific I have been playing more of the deuces game just to get a feel. It also doesn't hurt that your chances of getting a bonus score are significantly increased (about 75% of the time in my small number of samples).
However, I did have a *feeling* that the game was quite a bit better than the base game. I'm not surprised at the 1% increase.

[damule]

Although not very scientific I have been playing more of the deuces game just to get a feel. It also doesn't hurt that your chances of getting a bonus score are significantly increased (about 75% of the time in my small number of samples).
However, I did have a *feeling* that the game was quite a bit better than the base game. I'm not surprised at the 1% increase.
 
I can tell everyone that with real world experience playing Dreamcard deuces with the 15/9 pay table for real money the game has low variance. The dream card averages at 58%, I cannot see coming out a short term loser in this game with proper money management and setting realistic parameters. Shhh don't tell the casinos yet.

[Minn. Fatz]

Thanks for the information and the kind words. A bit lazy of me not to check out the F values for the other games but thanks for filling in some of the blanks. I'm not at all sad to hear there are still good, and fun, games out there for the advantage players of the world.

[Lucky Larry]

Thanks for the information and the kind words. A bit lazy of me not to check out the F values for the other games but thanks for filling in some of the blanks. I'm not at all sad to hear there are still good, and fun, games out there for the advantage players of the world.

Minn. Fatz, et. al.

Thanks for taking the time to do the calculations for us mathematically challenged players. I really love playing Dream Card and can't wait until our local get it next month. I may have to wait until the wee hours to play it but I can sleep.. until then. LOL

LL

[mirose]

This game is red hot at the Red Rock casino in Las vegas.Deuces is the game to play.  I hit 4 Deuces on the deal on 5 play, and a Royal on the deal on 5 play (playing Deuces).I've seen others hit the same on these machines.

[kjohn]

thanks for the heads up on the game at RR. Heading that way in a few days and will give it a try...I'm wondering which game has the best odds... Dream card vs reg. Trip play with all things being equal ie: same game, same pay table..If I play the 50 cent TP or the quarter Dream card it's the same investment. Right? So has anyone figures which is the best to play for the short term...