Darren explores the source of denialism and how people justify their denialist beliefs. Adam explains why playing the lottery is "stupid". Elan poses the "Missing Dollar Riddle" to the panel resulting in some interesting reactions.
Where did you get that equation? You have to divide by 80 (80.5) and then you get the number I gave. Think about it, as the percentage awarded goes down, the threshold for when it's good to bet has to go up, not down. If you get half the pot by winning, then the pot has to be double the number you would bet on to get even value.
As for splitting, I kind of addressed this though maybe not too specifically. You can't predict the public buy in. If you could then yeah, there are optimal numbers, but if somehow the numbers are so low that it's better off, how are you to tell that there aren't some 20 million people out there waiting for the same value and playing when you are? You can certainly say in some theoretical jackpot and buy in amount that you should have played, but never that you should play. You'd have to know the results of the lottery before the fact to bet accordingly and if you can do that, might as well just use that time machine or crystal ball to predict the winning numbers.
Regardless, with the numbers I determined there wasn't even a point where you could bet if you guaranteed a unique number, so it wouldn't be worth it. You'd need to have a jackpot higher than 34 million $ where it was less than 30 in the previous draw or one over I think it was 72 million $.
You made a few mistakes in your discussion about lotteries. First, you calculated the minimum jackpot required to break even wrong. The correct equation is:
(# of combinations)*(price of ticket)*(share of pool to the jackpot)
For 6/49 the numbers work out to:
(13,983,816)*($2)*(0.8) = $22.4 million
You were then correct about the problem of jackpot splitting, but you just assumed that enough tickets are always bought that buying a ticket for a large jackpot is always a losing proposition. This is demonstrably not true.
For example, there was a 6/49 draw back in March 2010 where the jackpot was $34 million. Based on the fact that 265,292 tickets got 3 numbers correct, we know that about 15,000,000 tickets were bought. When you include the approx. $10 million in secondary prizes you, can show that the expected value of a $2 ticket was $2.21, including the risk of split jackpots.
The Reality Check - Podcast 
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As for splitting, I kind of addressed this though maybe not too specifically. You can't predict the public buy in. If you could then yeah, there are optimal numbers, but if somehow the numbers are so low that it's better off, how are you to tell that there aren't some 20 million people out there waiting for the same value and playing when you are? You can certainly say in some theoretical jackpot and buy in amount that you should have played, but never that you should play. You'd have to know the results of the lottery before the fact to bet accordingly and if you can do that, might as well just use that time machine or crystal ball to predict the winning numbers.
Regardless, with the numbers I determined there wasn't even a point where you could bet if you guaranteed a unique number, so it wouldn't be worth it. You'd need to have a jackpot higher than 34 million $ where it was less than 30 in the previous draw or one over I think it was 72 million $.
(# of combinations)*( price of ticket)*(share of pool to the jackpot)
For 6/49 the numbers work out to:
(13,983,816)*($2)*(0.8) = $22.4 million
You were then correct about the problem of jackpot splitting, but you just assumed that enough tickets are always bought that buying a ticket for a large jackpot is always a losing proposition. This is demonstrably not true.
For example, there was a 6/49 draw back in March 2010 where the jackpot was $34 million. Based on the fact that 265,292 tickets got 3 numbers correct, we know that about 15,000,000 tickets were bought. When you include the approx. $10 million in secondary prizes you, can show that the expected value of a $2 ticket was $2.21, including the risk of split jackpots.
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