The odds, if one was to play just one ticket in each game, would be the product of the individual odds. The number is about 25.67 quadrillion to one.
This is next to impossible, but one needs to keep in mind that "next to impossible" is not impossible.
The odds of a single person being born with one's genome - even ignoring the odds of one's parents having intimate relations in the first place - is about one in 70 trillion. Thus the odds of two people being in the same room having their exact genomes is about in 5 with 27 zeros after it. If one was to predict before either person was born that two people would end up meeting, one would have to regard the event as impossible - well not impossible exactly, but next to impossible.
Thus every time you stand in a room with another person, you are, in fact, experiencing the "next to impossible."
It happens, if one understands the set of scientific laws known as statistical mechanics, that the exact structure of the air in the room in which you now read this post is far less probable than the odds against two particular individuals being born. A container that would contain 22 liters, about 5 gallons, has 6 with 23 zeros after it molecules of air in it. Each of these molecules has a speed and direction. The odds that the particular distributions of direction and speed is so small as to defy conception. And still, those molecules, their directions and their speed, all exist.
It is extremely unlikely however that the same person will ever win both games, no matter how many tickets they buy. To match the odds against this, one would have to buy one ticket per second (for each game) for about 800 million years. That should inform one of the scale of the improbability, but still nothing about such scale totally rules the event out. In fact every event that actually happens is enormously improbable.