making a small profit
Right, this is what people always gloss over to just say that eventually the bet will be too big to sustain. Even if you win repeatedly, the bets you make after 3 or 4 losses are vast in comparison the amount you’ll ‘gain’ per win. For the doubling (Martingale strategy), if your bet starts at $1, and you win $2 off of that, it doesn’t matter how much you are eventually betting, you’ll only make $1 for the whole cycle.
The tripling helps for the profit angle, somewhat. I ran the numbers for total amount of times betting before a win for net win. I wish the formatting let me make tables, but oh well.
Total Times Bet(bet amount): total of bet: net winning: 1 (1) 1 1 2 (3) 4 2 3 (9) 13 5 4 (27) 40 16 5 (81) 121 41 6 (243) 364 122 7 (729) 1093 365 8 (2187) 3280 1094 9 (6561) 9841 3281 10 (19683) 29524 9842
edgemaster72@lemmy.world 5 months ago
So looking at your would-be-a-table-if-formatting-allowed, I noticed the net winning was close to 1/3 of the net wager. Given that the premise is tripling a losing bet, I thought it a little too convenient to have an expected profit of 1/3 so I recreated the table in a spreadsheet then started tinkering with the multiplier after a loss. I’m not smart enough to explain why it’s the case, but it appears that the limit of the net winnings / net wager as your number of bets increases is n-2 / n, where n is the factor you multiply by after losing a bet.