Probability of a Mega Millions rollover or having a single winner decrease as sales approach 600M

As tonight's record Mega Millions drawing approaches, ticket sales are going off the charts. We originally expected that 400 million tickets would be sold, but with the recent increases in the jackpot prize from $476M to $540M $640M, we now believe that up to 600 million tickets may be sold.

Thus, we asked ourselves two questions:

1. What is the probability that there will be no winner in tonight's drawing?
2. What is the probability that there will only be one sole winner?

Using our brute force duplicate ticket estimator, we have produced two tables for your reference.

The first summarizes the probabilities of: 0 to 8 individual winning tickets. As shown, the probability of not having a winner tonight and rolling over again drops from 18% to 3% as ticket sales increase from 300 million to 600 million. Similarly,  we can see that the probability of having a single winner decreases from 39% to 27%, while that of two winners decreases slightly from 28% to 26%. Interestingly, we find the probabilities of 3 to 5 winners rapidly increase as sales approach 600 million. We believe the likelihood that 6 or more winning combinations will be sold is rather slim.

	Table 1: Probability of Mega Millions Winning Tickets
Winning Tickets	300M Sold	400M Sold	500M Sold	600M Sold
None, No winner	18.1%	10.3%	5.8%	3.3%
1 Winner Only	39.3%	35.4%	31.2%	27.4%
2 Winner Only	28.2%	29.5%	28.2%	25.9%
3 Winner	12.4%	18.4%	21.5%	22.2%
4 Winner	1.9%	5.9%	11.0%	14.9%
5 Winner		0.5%	2.3%	5.6%
6 Winner			0.1%	0.6%
7 Winner
8 Winner
Total Probability	100.0%	100.0%	100.0%	100.0%

The second table summarizes the distribution of the tickets sold. It estimates the absolute number of tickets in each category. Here we find that approximately 31.9 million combinations will not be generated when sales are at the 300M level, but only 5.8 million combinations will be unsold when 600M tickets are printed. In all other cases, the absolute number of tickets per category increase as sales increase. Interestingly enough, we can see how the size of the 6 and 7 tuplets begins to grow.

	Table 2: Distribution of Mega Millions Tickets Sold
Numbers	300M Sold	400M Sold	500M Sold	600M Sold
All Combinations	175,711,536	175,711,536	175,711,536	175,711,536
Unsold	31,864,733	18,036,279	10,209,010	5,778,566
1 Only (Singles)	143,846,803	157,675,257	165,502,526	169,932,970
2  (Doubles)	103,460,042	131,466,722	149,526,982	160,511,932
3 (Triples)	45,526,185	82,214,057	114,388,867	137,818,542
4 (Quadruples)	7,022,773	26,431,098	58,127,495	92,689,034
5 (Quintuples)	144,138	2,198,990	12,023,012	35,013,149
6 (Sextuplets)	59	13,876	430,590	3,988,410
7 (Septuplets)	0	0	528	45,963
8 (Octuplets)				0
Sum	300,000,000	400,000,000	500,000,000	600,000,000

We wish everyone the best of luck tonight and hope your dreams come true. But, as we can see from the above, remember to set your expectations according to the probability that you may have to share the jackpot prize with somebody else.

Cheers,

JL...............