|Posted: March 6, 2006, 9:08 am - IP Logged|
How much more can a Powerball player expect by spending an extra dollar on buying PowerPlay option, as compared to buying an extra PB ticket instead of adding PowerPlay option?
According to ND lottery website, during the promotion period, there will be 16 PP multiplier balls, from which one will be drawn, as follows:
2X : 4 3X : 4 4X : 4 5X : 3 10X : 1
That way, the odds of 10X multiplier coming out in any one drawing until it pops up is 1 in 16. Based on this fact, I could do some math.
Firstly, the weighted average of all multiplier numbers would be now 3.81 instead of 3.5. That is, for all non-jackpot prizes, multiplier number is expected to increase by roughly 9% (=.31/3.5), as compared to no such promotion.
Secondly, the overall expected value, which represents long-tem average winning if such play is being repeated indefinitely, of $1 spent on buying an extra PB ticket OR adding PP option to the existing one will vary, depending on the outstanding amount of jackpot. At the current level of $50M, one can expect the following amount out of an extra dollar spent on two different alternatives A and C: (all before tax)A. .37 : when buying an extra PB ticket instead of adding PP option
B. .43 : when buying PP but assuming normal multiplier numbers (as if there were no current promotion)
C. .46 : when buying PP option, instead of an extra ticket, during this 10X promotion
-The difference between A and C : +24% (would decrease as the amount of jackpot goes up)
-The difference between A and B : +16% (would decrease as the amount of jackpot goes up)
-The difference between B and C : +7% (would remain unchanged regardless of the amount of jackpot)
So, I think that, given such difference in expected values between those two alternatives, the actual choice is up to individual players. If I were able to buy PP option during this promotion, I would do so until PB jackpot exceeds at least $100M and/or until 10X multiplier pops up. For the time being, I think, PP would be a nice toy to at least some in-state PB players who enjoy such add-on to Powerball.