Data
I'll add to this as well since even your analogies don't make sense. The odds of winning and getting all 7 numbers is 1 in 28,633,528. With more tickets sold the odds of there being a winning ticket or multiple winning tickets increases. That's why selling tickets internationally on top of Canada would increase the odds of winning tickets.
Not that that actually has anything to do with what we're discussing because, again, we've witnessed the NHL go from being a Canadian domestic league (composition wise) to a league with elite non-Canadians who won awards and AS nominations. That's proof of what I'm stating. What's your proof that adding non-Canadians doesn't matter? I'm waiting for some for proof, or at least reasoning for the contrary.
I read your response to sleep easy and it did not address my posts or question or question above. Better to skip over that than try to tackle it head on?
Actually the odds of getting all 7 numbers from the numbers 1 to 49 is (7x6x5x4x3x2x1)/(49x48x47x46x45x44x43) which is 1 chance in 85,900,584. Playing the Lotto Max means spending $5.00 for three combinations of seven numbers, one combination that the buyer may choose, the other two, machine generated. So three chances are bought, tripling the odds of winning so divide 85,900,584 by 3, yielding 28,633,528. Selling more tickets regardless of where or how, would increase the chances of having a winner. Specifically doubling the number of Canadian participants would have the same effect as selling an equal number of tickets outside of Canada. Also doubling the number of chances sold per ticket to 6 would have the similar effect. All three scenarios would see roughly the same number of distinct seven number combinations in circulation once multiples of the same combination are factored out.
Previously I have responded to the adding non Canadians to the NHL pool of participating players by looking at the actual results as opposed to the theoretical possibilities that you introduce all the time. After all, hockey is about actual on ice results. Teams and players have to play the games that generate the results.
The actual results, as posted upthread, since the start of the NHL with the 1917-18 season thru the end of the 2014-15 season, show that in a compact NHL, less than 12 teams during the first 50 seasons, 30 different players led the league in scoring.
30 scoring leaders in 50 regular NHL seasons. Regular season schedules were balanced or nearly balanced.
Post 1967 expansion the NHL grew to 12 teams finally reaching its present level with 30 teams. If the growth in teams and the provenance of players mattered, making it more difficult to win the scoring schampionship for each skater then the results should confirm your theoretical model.
The results do not confirm your model or claims. Specifically in the 47 NHL seasons, post 1967 NHL expansion 19 different players have won the 47 regular season scoring championships that have been determined. The three missing season will not change the impact of the results. Factual data that is objective does not support your stance. 19 winners vs 30. Fewer winners post 1967 NHL expansion.
Applying your mathematical model fails to take into account that results may be gamed similarly to a lottery being gamed.
It was possible to game lotteries by buying all the combinations once the the top prize exceded the cost of buying all the possible combinations.The sum of secondary smaller prizes would be extra money. Only obstacle was the time required to manually fill in the tickets,have enough cash on hand, have enough trustworthy people stand in line to process them.Also there was the risk that another party might do the same thing. The chances of winning were not dispersed amongst many but concentrated to the one or perhaps a second party trying the same gambit. The regular one/few ticket player saw their chances or return reduced tremendously, at least by half.
Technology changed this so safeguards were introduced to protect the integrity of the loteries.
Bringing this back to the NHL. Post 1967 NHL expansion, powerhouse offensive teams with enough offensive money were in a position to facilitate their players winning scoring championships against weaker teams especially with an unbalanced schedule. This is one of the reasons you have so few different scoring champions since the 1967 NHL expansion.
The simple fact that non Canadiens won awards or honours or contributed to teams winning team championships does not change the fact that in a 12 to 30 team league its is actually easier to do so because of the unbalanced scheduling and the significantly reduced opportunities for direct confrontation head to head amongst elite players.