Trying to figure out odds on a non traditional bingo game.

[pelorojo7]

I work at a company that tests gaming software. Normally we used mathematical formulas to verify the RTP (return to player percentage) is in fact what was submitted to us. But recently we had a game sent to us that is not like a normal slot machine or a normal bingo game even. Instead of like in traditional bingo where you have a 5X5 card with a free spot in the middle, this game is a 5X6 card. And also unlike traditional bingo the number of balls in the pot is not 75. It is only 30. Instead of trying to get a session pattern before anyone else gets a bingo, in this game 15 balls are drawn, and those spots are then daubed on the bingo card. The pattern is what determines if you win anything, and the amount. In this setting there is roughly 150 million possible patterns (it's actually a little more than that). And to get the top prize you have to get 1 of 15 patterns. Which means your odds of getting one of these patterns rounded off is about 1 in 10 million. But here is the kicker, getting one of these patterns only guarantees you get to a 2nd drawing. Once here there is 442,000 patterns that you win the top prize. There are still 15 balls drawn on this round. The odds of that are 1 in 351. Now here is where my question comes in. To calculate the odds of winning the top prize, shouldn't you multiply 10 million by 351? Which would be 1 in 3.51 billion? Thanks in advance.