The purpose of this entry is to compare the various provincial 649 games. The main criteria of comparison is expected value. Other factors are also discussed.
The following is an excerpt from the FAQ on my website that defines expected value:
Expected value is the theoretical value of any given wager or bet. It is calculated by multiplying the probabilities of all the outcomes times the prize awarded for each outcome. The resulting values are added up to arrive at the expected value. For example, if one was awarded $10 for correctly guessing a number from 1 to 10. Then the expected value of the wager is $1. The probability of correctly guessing is 10% times the prize of $10 gives a result of $1. A simplified way of calculating expected value is the amount of money paid out on any given lottery compared to the amount of money taken in. In these cases, expected value is often expressed as a percentage. That is, the percentage of money awarded in prizes. Most lotteries have an average expected value of 50%. The expected value of a $1 wager is therefore $0.50.
The following are the names of the five provincial 649 games along with their price points and expected value.
Atlantic49 - two plays for $1 - 55.7%
Quebec49 - one play for $0.50 - 47.6%
Ontario49 - one play for $0.50 - 47.6%
Western49 - two plays for $1 - 65.2%
BC49 - one play for $1 - $43.7
All games allow a player to select their numbers except Western49 where only one of the two plays can be player selected. They all work out to $0.50 per selection except BC, where one selection costs $1. But, for BC49, the jackpot is $2 million rather than the $1 million for all the other games.
Now to discuss the most important factor and that is expected value. That is, how much of each ticket is returned to the players in the form of prizes.
Western49 is the clear winner in this category. This is mainly because of the $10 prize for a match 3. The match 3 portion of the expected value for the games that pay $5 is 17.5%. For Atlantic49 that pays $6 for a match 3, the payout is 21%. But for Western49, it is a whopping 35% - larger than all the other prize categories combined.
Atlantic49 is in second place overall, not only because of its $6 payout for a match 3, but the match 4, match 5 and match 5+ payouts are $64, $649 and $64,900 compared to the $50, $500 and $50,000 of the other games (except for BC49).
BC49 has the lowest expected value. The jackpot expected value of all the games is 14.3%. This is also the value for BC49 even though its jackpot is $2 million. The double sized jackpot matches the double cost per selection. Where BC49 falls behind is in the lower tier prizes. The jackpot is twice as large as the other games (as expected), but most of the lower tier prizes are only 50% larger than most games. The match 4, match 5 and match 5+ prizes are $75, $750 and $75,000. BC49 does have a prize category that no other game has and that is a match 2 plus bonus. This prize category has an expected value of 6.1% and does not make up for the other weaker expected values.
One factor I did not take into consideration when calculating the expected value is the probability that a jackpot or match 5 plus bonus prize is split among multiple winners. To calculate accurate expected values, this should be taken into consideration. To do so involves using historical sales figures to estimate future sales for the calculation. In general, sales for all the games are relatively low and a jackpot split occurs extremely seldom.
I checked 938 consecutive draws for Ontario49 and there was only one case where the jackpot prize was split. In the case of the second prize ($50,000) there were a total of 27 draws where the prize was split. Therefore, it can be assumed that the Ontario49 expected value is only slightly less than the value listed above. This is probably also true for Quebec49 with a population similar to Ontario. I suspect that the sales for Western49 and Atlantic49 are relatively low and do not affect the expected value because of the relatively low population in those provinces. Sales for BC49 are probably also too low to affect expected value because of the $1 cost per selection. That is, if money spent in BC was the same for say Western49, then the number of selections purchased would be half of Western49 and therefore an even lower probability of a split prize.
The last item to take into consideration is the fact that Western49 gives one quick pick for every player selected selection. From an expected value perspective, I consider a quick pick to have the same value as a player selected selection. I know that some people would not agree with that assumption. Even if it was assumed that a quick pick is of less value, it is a big stretch to assume that a quick pick's smaller value can overcome the large disparity between the expected value of a Western49 ticket and tickets from other provinces.
Therefore in summary, I believe that a Western49 ticket is by far the best bet. In second place is Atlantic49. Quebec49 and Ontario49 are tied for third with BC49 clearly in last place.