Forget about New York's Sweet Millions. (6/40) It does have the best odds to win a million dollars, and it isn't pari-mutuel, but they dont sell enough tickets to produce a winner. It's been around since Sept of 2009, and the drawings are twice a week. They have had only maybe four or five JP winners. The lastest winner was a week or so ago, but NY has a promotion going on with it, and that's what probably caused the JP hit. The promo is during the month of August, buy $5 on the day of the drawing (either Monday or Thursday) and get a $3 QP free. The lower tier prizes stink...$500 bucks for 5 numbers, $40 for 4, $3 for 3.
Take5 in NY has low odds for a lottery game, (5/39 and 575,757 to 1) but some people say it's a lousy value. JP's are usually split by multiple winners. Most winners are sold in the NYC or Buffalo areas. JP's are usually less than $100,000. More QP JP winners than Player Picked numbers. Unhit JP doesnot rollover, second place players benefit when no first prize is won.
There 's also Lotto, and it has huge odds. Two games for a buck. I dont play it unless the JP is very large, which takes a long time to do, because it only increases by $500,000 per drawing when no JP is hit.