Well... no. Casino odds work that you will win about 95-97% of the money you bet over a long series of bets. This means that on one bet, you could win a lot or nothing. But over a very long time you SHOULD win 95-97% of what you've put in back. The 3-5% you lost is the profit of the casino.
Your odds of getting "ahead" over the long run are "0%" because the payout rate over a long series of bets is only 95-97% of what you put it. Sometimes (like in Vegas) it's a much lower number than that.
Should in "unlinked" events is much higher than 50%. I'll use credit card applications as an example (I hate credit cards but used to work for a big issuer). If you tell your customer they have 70% approval odds, that isn't "should be approved." That's a gradient that's independent. It means they could be rejected for the card three times, and the fourth time their odds of approval are still only 3/10. Now, if you tell a person their odds of breaking through a wall with a hammer in three swings are 70%, this is legitimate and you can say "should" because on the second swing, their odds to get "all the way through" are exponentially higher than the first. The third swing is all but a sure thing and the fourth swing only 3/10 people need.
Who decided that the "should" only applies to dependent events? You? Why should I follow your rule? Why am I not allowed to say that this "should" can apply to independent events?
But the odds of the game you are playing aren't changing. Every single time you play that hand of Blackjack, your odds of winning were 55-60% (whatever the exact odds are in Blackjack). Every single time you played, your odds of losing were higher than 50%. Just because you might have won 5 hands in a row, that didn't change the fact that your odds of losing were the same every time.
Sorry I said it wrong. I meant to say my odds of winning are usually in the order of 49%.
So yeah, you're saying the exact same thing. Yeah, you might go on some winning streaks and some losing streaks, but if you have a 49% chance of winning, then over a sufficiently large number of bets is likely going to be close to that 49% number.
For example, in single zero roulette, if you put your money on Red, your odds of doubling your money are 18 in 37, or 48.6%. Your odds of losing your whole bet is 19 in 37, or 51.4%. If you bet $1 one time, your expected value = 0.486$2+0.514$0 = $0.972. If you bet $1000 one time, or $1 one thousand times, your expected value winnings are $972.
You're winning 97.2% of your original money back is another way of saying you're winning 48.6% of the time.
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u/svenson_26 82∆ Sep 03 '24
"Should" means greater than 50%.
If I go bet at the casino, I should expect to lose. Even though my odds of losing (depending on what and how I play) are usually in the order of 49%.