Right. Your question intrigued me so I looked up the game. And the short answer is that the odds on this aren't quite as terrible as I'd expected, but they're still terrible. If you want some fun, better odds, and the chance of winning a jackpot, you should pick a slot, ANY slot and play that instead. If you like this kind of fixed payout, not very complicated game (seems like total drudgery to me, but to each their own), then print out a blackjack table and switch to blackjack. If you want more info, though, including some maths, read on...
For those that don't know the game, it's just bingo/keno with some slightly unusual parameters. A ticket has just 9 numbers. You choose how many tickets you want, and how many balls (out of a low-seeming 30) you want to draw (the choices are 20, 22 or 24). The game draws the balls and you get paid for every ticket you match ALL 9 balls on. I couldn't find a paytable, but from the experiment I ran (with play money! I'm not insane!), a 10c winning ticket pays $8, $2.70 and $1 for the 20, 22 and 24 ball games respectively. The huge difference in those payout values compared to the (seemingly) small difference in the number of chosen balls should already indicate how human intuition completely breaks where combinatorics are concerned (even more so than with slot variance).
You calculate the odds of winning using the combinatorial function. This is basically the number of different ways of choosing one set of things out of a larger set of things. For example, the total number of possible tickets (i.e., the number of ways to choose 9 numbers out of 30) is a little over fourteen million (14,307,150). The maths for calculating the precise odds of winning has a few more steps, but it's just variants of this function and simple division. I'm happy to explain it if you like - you can easily do it with a calculator, and even with a pen and paper if you have a little patience - but I'll just assume you want the results. I cheated and did it in 30 secs in Excel, which you can see below this post.
But basically, the odds of a SINGLE ticket winning are just over 1%, 3% and 9% for the 20, 22 and 24 ball games, respectively. Multiplying that by the payout gives an RTP of 93.9%, 93.9% and 91.4% for the 20, 22 and 24 ball games, respectively. The 20 ball game is
slightly better (because of rounding), while the 24 ball game is absolutely awful - some of the worst online odds you'll see. If you're not familiar with RTP, basically it means that for every dollar you spend on the 20 ball game, you can expect to get 91 cents back. If it was a bank account, every year they'd take 9% of your money. Online slots tend to have a minimum RTP of 95%, while games like blackjack can be over 99%. But there's no chance of hitting a win bigger than 2.5x your stake with blackjack, so often the slot trade-off is better, sacrificing long-term returns for potential short-term gains. This game is the worst of both worlds.
I'm afraid this still doesn't answer your original question of how unlikely a 150 run loss is, because we don't know the details. Which version of the game were you playing? How many tickets were you buying? If you're buying 100 tickets, then that's like 100 slot spins at once. Instead of asking how many consecutive losing slot spins we've had, you should ask how many consecutive losing slot
sessions we've had. But even that isn't much use, because of variance. There's no way to win a huge jackpot on 30 ball bingo, it's just a pure example of the reverse compound interest formula that makes gambling a losing proposition in the long run. If you play a large number of low value tickets at once it will just eat your money.
I know it's not really my place to say, but please stop playing this... It's not like slots where you're riding a variance rollercoaster, hoping to leap off at the top before the inevitable crash, this is just burning money. If this is the kind of game you like, at least switch to blackjack. The casino wasn't cheating you. It's just a shitty, shitty game.
*EDIT* I guess this isn't quite fair. I didn't realise you can buy individual tickets (it looked like you were stuck with 40-100). I guess if you're playing one ticket at a time, hoping for an 80x payout, then this becomes a super-high variance game you can theoretically get a long way ahead on (and 150 losses in a row would be pretty unlucky, but not that unlucky). But that's not a risk I'd be willing to take, not at these odds. And the 100 ticket version is definitely just a money pit.
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