|Posted: September 30, 2005, 10:18 am - IP Logged|
Based on my personal rough calculation, driven mainly by an interesting debate here, of the expected values in each of 3 cases, that is, (1) PB with no PP ($1 per ticket), (2) PB with PP but for the regular price ($2 per ticket), and (3) PB with PP but for PA state promotional price ($1.66 per ticket = $10/6), it seems that at 167M annuity
1. PA players are expected to get paid slightly higher when buying 5 tickets for the regular price of $10 and getting one free ticket, all with PP option. But only when they already decided to put some money, $10 or more, into the game. Lowered per-ticket price, from $2 to $1.66, seemingly contributes to an increase in the expected value for every $1 invested, which is slightly higher than with no PP.
2. In the states other than PA?
Playing PB with no PP brings a slightly higher expected value than with PP.
Surprisingly, however, even at 167M annuity jackpot (83.1M cash) for this Saturday drawing, there is just slight difference in the corresponding expected values between with no PP and with PP, the former getting paid just slightly higher.
3. Without any such promotion, I expect the cutoff point would be somewhere around 105M annuity, in which case incremental value is almost negligible.
4. Another interesting point of PP
Even when the prior odds or expected values are favorable for persons playing with no PP like at 300M annuity, as soon as they fail to hit the RED ball (in fact, the jackpot), then they should stand severely against the odds when compared to those who played with PP, as is often the case in many circumstances. The difference between prior and posterior odds may get some serious players' attention. Anyway, regular PB players might consider playing with PP except when the jackpot is extraordinarily high.
Overall, just interesting!
PS: After-tax amount was used in the calculation process, accounting for only 25% Federal income tax but no state or local taxes.