Real Lottery and Blackjack

I promised to take requests on blog posts, so this post will be on Ann's comment on the lottery raising its prices. First of all my opinion on the lottery is that it is a tax on the mathematically challenged. My chances of winning the jackpot are about the same whether I purchase a ticket or not. 

When the jackpot is large enough ($323 million) the "break-even point" is the point where the expected return matches the amount invested. That is, if you bet $2, you could expect to win $2 back. The way the expected return is calculated is:

Return= P(winning $3) * 3 + P(winning $4) * 4 +.....+P(winning jack) *jackpot total

The "break-even point" needs to be put in quotations, however, because it is far from breaking even. When the jackpot gets large, the probability of multiple winners increases. Also, you can plan on giving about 40% of those winnings back in taxes. Finally, the posted jackpot is paid over 30 years, so comparing the value of the $2 invested in the ticket to the value of the payout in 30 years is not a fair comparison. Basically, even after paying for operating expenses (advertisements, lottery retailers, bureaucrats, etc) the government still keeps fixed portion of winnings as profits. Plus they get a major kickback on the taxes that come back from the big winners. If the winner plans to choose the cash option the expected return is also negative. Basically, even in the best conditions this is a losing game. Other people have spent much more time than I am willing on the expected returns of the lottery. This one seems ok. I have bought one lottery ticket in my life (the day I turned 18) and don't plan to buy another one ever. As far as the implications of raising the price, my guess is the expected return per dollar will stay roughly the same. This means you can expect to lose twice as much if you buy the same number of tickets.

As you can tell I have very little interest in lottery tickets. I can say, however, that I have had an ok time playing blackjack at the casinos. Individually, the chances of winning money at the casino are much higher than with lottery tickets. You should still definitely plan to lose money when you go to the casino, but at least at the casino you can think of your losses as entertainment.

Now, I can count the number of times I have gone to the casino on one hand (alright maybe two hands), but one thing I do know is you should plan to bring a decent amount of money if you want to play for even an hour. When I went with my freshman corridor my friend and I each brought $20. He played four hands, and I played eight hands before being wiped out. So we were left with drinking the free sodas for about 3 hours until the rest of the group was ready to head back to campus.

Unless you count cards (illegally) playing blackjack perfectly by the book gives you about a 49.5% chance of winning. Most players aren't good enough to play perfectly by the book, so their chances of winning are around 40%. So, if you want to play blackjack for an hour, how much money should you bring to the casino to give yourself a 95% chance that you won't be cleaned out after an hour? To answer this, I simulated going to the casino 100,000 times and take the lowest dollar amount won over a one hour period. I assume 5 people a table= 70 hands per hour, and also you make only the minimum $5 bet per hand. The Money Needed column is how much money you should bring to be 95% sure you can play for the amount of time specified in the Hours Played column.

	Good Player (49.5% of winning)		Average Player (40% of winning)
Hours Played	Money Needed	Prob of Winning	Money Needed	Prob of Winning
1	80	0.417	140	0.034
2	120	0.42	240	0.007
3	150	0.415	330	0.001
4	175	0.409	420	0
10	290	0.381	920	0
100	1120	0.198	7705	0

If you don't know if you are a 49.5% or 40% player, you are likely a 40% player. So if you are an average player you can get 3 hours of entertainment and be quite confident it won't cost you more than $330! You should expect to lose about $210. For about that same price I could be catered in the Champions Club at a Twins game, but I wouldn't have a 0.1% chance of making money. I think I would still choose the Champions Club.