I'm at a roulette table. I only bet on red. When I lose I triple my bet, when I win I restart. Is this a roulette strategy?
Ok so here's the rules
I just bet on red every time
I start with 1 dollar
every time I lose, I triple my previous bet
every time I win I restart
I'm going to simulate 10 games
Game 1 - Bet $1 Lose
Game 2 - Bet $3 Lose
Game 3 - Bet $9 Win $18
Game 4 - Bet $1 Lose
Game 5 - Bet $3 Lose
Game 6 - Bet $9 Win $18
Game 7 - Bet $1 Lose
Game 8 - Bet $3 Lose
Game 9 - Bet $9 Lose
Game 10 - Bet $18 Win $36
In this simulation I'm losing at a rate of 70%. In reality the lose rate is closer to 52%. I put in $54 but I'm walking away with $72, basically leaving the building with $18.
Another example. Let's pretend I walk in with $100,000 to bet with. I lose my first 10 games and win the 11th.
1 lose
3 lose
9 lose
27 lose
81 lose
243 lose
729 lose
2187 lose
6561 lose
19683 lose
59049 win $118098
$88573 spent out of pocket, $118098 won
Walk out with roughly $29525.
I get most casinos won't let you be that high but it's a pretty extreme example anyway, the likelyhood of losing 10/11 games on 48% odds is really unlikely.
Assuming you don't have infinite money, and that there are limits at the table, this is a good example of a non-ergotic system, where the mean and the median diverge. Because the rules of the game you defined dictate that at some point, you run out of money and have to stop playing, the outcomes for the median dip below that of the lucky few, who win more than lose owing to random chance. This is a super cool concept in a lot of systems, not just gambling fwiw