Lucky for Life

There is a lottery game called Lucky for Life which offers a lifetime annuity as its top prize, $1,000 a day for life, and its second prize, $25,000 a year for life. It is originally from New England but is now offered in over twenty states across the US. It draws from two matrices, much like the other national games like Powerball: five of 48 white balls and one of 18 lucky balls. Tickets are $2 and it draws daily. This is the pay table from the Colorado Lottery:

Match	Payout	Odds
5+LB	$1,000 a day for life*	1 in 30,821,472
5	$25,000 a year for life*	1 in 1,813,028
4+LB	$5,000	1 in 143,356
4	$200	1 in 8,433
3+LB	$150	1 in 3,413
3	$20	1 in 201
2+LB	$25	1 in 250
2	$3	1 in 15
1+LB	$6	1 in 50
0+LB	$4	1 in 32

*As an alternative to these lifetime annuity prizes, you can also claim a cash option: $5,750,000 for match 5+LB and $390,000 for match 5.

There is about a 1 in 8 chance of winning any prize. The annuity lasts for twenty years or the winner's natural life, whichever is longer. I guess if the winner dies before the minimum 20-year annuity period their heir or estate gets to continue collecting.

Here is my analysis of this game. This is ignoring any potential taxation and jackpot sharing, which can affect the top two prizes.

Match	Combinations	Probability	Prize	Return
5+LB	1	0.00000003	*	*
5	17	0.00000055	*	*
4+LB	215	0.00000698	5000	0.034878282
4	3,655	0.00011859	200	0.023717232
3+LB	9,030	0.00029298	150	0.043946636
3	153,510	0.00498062	20	0.099612374
2+LB	123,410	0.00400403	25	0.10010067
2	2,097,970	0.06806846	3	0.204205367
1+LB	617,050	0.02002013	6	0.120120804
0+LB	962,598	0.03123141	4	0.124925636
Any	3,967,456	0.128723768	Various	0.751507001 + Annuity EV

The return is heavily affected by the annuity period; in fact, the top two prizes are the largest part of the equation, with the top prize worth 0.237010095 for a twenty-year annuity period and the second prize worth 0.275781767.

For the house edge, I will provide a few example values I find interesting. Let's take a year to be 365.25 days, which would make the top prize worth $365,250 per year.

• Based on the cash prizes in lieu of the annuity, the game has a 42.341% house edge.
• The minimum 20-year annuity period results in a 36.785% house edge.
• Each additional year added to the annuity period reduces the house edge by 1.282pp.
• The break-even annuity period, where the return of the game is $2, the same as the ticket price, is 48.694 years. I guess this would mean that young, healthy people have an advantage when playing this game.
• The return for the cash prizes is the same as 15.666 years of annuity, so if you win the top prize but won't live longer than that to enjoy it and don't care if your descendants enjoy it, you should take the cash prize .

I just wanted to share my analysis of this game with you all because I didn't see this game on the Wizard of Odds website and only saw a little bit about an older version of the game in past threads. Hope you enjoy, and that I didn't screw anything up!

Quote: grossmyn

The return for the cash prizes is the same as 15.666 years of annuity, so if you win the top prize but won't live longer than that to enjoy it and don't care if your descendants enjoy it, you should take the cash prize .
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I wonder if a strong prenup and getting involved with an attractive younger person becomes a mutually beneficial play.