Do these promos give + game? Check my math, please

[Shiny]

Not really a math guy, but I’m trying to revisit that subject when it comes to promos.  Ok, here are my offers:
Promo 1: Get a $50 gas card when earning 500 Base reward credits (RC); for these purposes, I will count this as “cash”
Promo 2:  Get $5 instant cash back when earning 45 Base reward credits (I get this offer 2x month)
The $50 promo 1 is over a 2 month period so I will break it up into 3 trips.
 
It takes $10 coin in to get 1 RC.
 
500 RC=$5000 in coin in. Thus, $5000/3 trips=$1666.67 coin in per trip.
 
$50/3trips=earn $16.66 per trip in gas “cash”
 
$1666.67 coin in (per trip) will get me $16.66+$5 cash (promo 2)=$21.66. Thus 21.66/1666.67=.012.
 
Playing Jacks or better (99.54 game) 99.54+.012=99.552 (not positive)
 
Did I miss something?  What do you think? Questions? Thanks in advance.

[shadowman]

Close, but no cigar. The value .012 should be added to .9954 giving you 1.0066 or a 100.66% return. Always move the decimal point two spots when converting from fractions to percentages.


 
Another way to look at it is to just compute your expected loss. .46% of $5000 is $23. You earn $50+3*$5 = $65.

[Shiny]

Thanks, shadowman!
 
A positive game, huh.  I know, I know, that means hitting a royal (which probably won't happen) etc. In the back of my mind I thought about moving the decimal points, but didn't do it. Thanks, again.

[Eduardo]

If your goal is to almost always play "positive" games, then this is a good one for your "collection" of games to play. That is the only reason to say "you need the royal" because yes, royal flushes figure in for long term expectations.
 
You don't have to hit a royal to come out ahead for the day of course. You might win, you might lose. At the very least you'll end up with a gas card so it's better than playing the same game without the promotion.
 
Obviously there is no guarantee one way or another of how you will do. Seems like a good play to me though because you at least know you aren't going home "broke."
 
It seems like a flat benefit. For example if you bring $500 then instead of coming home with -$500 to +$1000 you will go home with $-450 or +$1050 (just an example) by getting the exact same cards. So you are better off playing with this promotion than any time without it on the same pay table.
 
In other words, you don't have to play forever or be an "advantage player" to benefit from this promotion.

[BillyJoe]

Forget the math, Shiny - you can't play enough hands for it to make sense. Just become a 7Star at Harrah's properties, and then just have fun with all the comps..

[shadowman]

Strange theory billyjoe. Every hand a person plays has an expectation and every hand is independent. It doesn't matter what anyone believes, this is a just a simple fact. Therefore, over time a person's results will approach the average of whatever expectation they have played.

You can ignore it, but it's still going to occur no matter how many hands you play. Playing for fun is fine but that has nothing to do with the math. Everyone is different and some of us actually enjoy finding the best possible situations.

[cddenver]

Strange theory billyjoe. Every hand a person plays has an expectation and every hand is independent. It doesn't matter what anyone believes, this is a just a simple fact. Therefore, over time a person's results will approach the average of whatever expectation they have played.


 
I think billyjoe might have been referring to results over the 3 trips mentioned originally, in which case his statement would be correct that one doesn't know what's going to happen over a small amount of play.

[shadowman]

CE, I disagree. If any small number of hands doesn't matter, then one can just claim that a lifetime of play is made of many small number of hands and so it never makes any difference. In fact, we all know someone who makes this claim over and over again.

[pokeherguy]

Strange theory billyjoe. Every hand a person plays has an expectation and every hand is independent. It doesn't matter what anyone believes, this is a just a simple fact. Therefore, over time a person's results will approach the average of whatever expectation they have played.

You can ignore it, but it's still going to occur no matter how many hands you play. Playing for fun is fine but that has nothing to do with the math. Everyone is different and some of us actually enjoy finding the best possible situations.
 
 
I played for 16 years at one casino and learned to trust the math, then I played for four years at another casino and finally decided those rules didn't apply to me there.