The odds or percentage everyone assumes is after a Casino has put expenses. Unless the casino can get someone to play they are in the hole from the start.
Until you find that first player the casino is running up bills. Casinos offer vouchers at no cost to players just to get them to play a game.
Whoever wrote the "math" problem must think acquiring a player is free. As for the player's chances of winning it is better to play fewer times than it is to play a lot.
Those percentages like 1/3 or 2/3 or 1/2 are model based. Compare that to empirical data and discrepancies are usually found.
Simply put playing games more people have beginners luck as long as they stay beginners. Long term gamblers don't develop veterans luck.
There’s no need to look at empirical data for straight forward things.
That’s why confidence intervals exist.
You can literally predict worst case scenarios to about 95% confidence.
Then you make decisions based on that. If you can afford to fade the worst case scenario, then the decision to put on the game or business is made for you as you can’t lose overall.
If you can only fade the worst case for a certain amount of time, then you have to really crunch numbers and then decide if the risk/reward is worth it.
Let’s take the scenario this thread is about for example.
And let’s say we were going to play nine games. And those games are a metaphor for a business or casino game.
We know that we *should* win 6 of those nine games.
But, when we apply 95% confidence interval, we could win as few as 3 games and in very, very rare scenarios, win zero games.
So, the question is, do we have enough bankroll to comfortably lose 6 games? If the answer is yes, there is no more thinking required. You move ahead with the business or game.
If we can only afford to lose 4 or 5 games, then we need to really crunch numbers.
And if you can only afford to lose 3 games, well, that’s probably not a good idea as the exact odds of 66% have to hold up in a short sample size.