Betting System that works.

Suppose you have found/developed a flaw in a game. It could be hole carding, dice influence, knowledge of other cards. Whatever. You still don't win every bet. You do win more than 50%. Let's take an even money bet. Now the premise of the progression is to eliminate as much as possible the variance. I'm thinking the stepladder, AKA D'Alembert, is your friend. Anyone else with a thought?

You are not talking about a betting system , but something to influence the actual odds of the game. Kind of like roulette computers which claim to help eliminate some portion of the wheel, thus increasing the players odds to over 50%.

For the lowest variance, flat-bet.

I would also recommend a money management strategy. It'll reduce your variance by restricting your losses. Won't change the house edge any, but it'll reduce your frustration from losing your rent money.

Quote: DeMango

I'm thinking the stepladder, AKA D'Alembert...

I didn't even know what that was. Man, the Wiz has a article on just about everything: https://wizardofodds.com/gambling/tenbet.html


He also has an article about betting strategies in in general at https://wizardofodds.com/gambling/bettingsystems.html. In that article is a betting strategy on a hypothetical coin toss game, where the coin has a 1% bias, and a coin with a 2% bias. Read about it about half-way down on that page, under the heading "Don't waste your money." I figure that's close to what you're proposing.

You can also read a thread that I started with a question about that biased coin flip: https://wizardofvegas.com/forum/gambling/betting-systems/708-wizs-1-advantage-coin-flip-simulation/

I think that you could show, that even if the odds are in your favor, such a system will result in bankroll losses from time to time. Just because the odds are in your favor doesn't necessarily mean that you will not run out of money (in any system, including flat betting) because you could conceivable lose enough bets in a row. It just makes it less likely, that's all.

Take a deck of cards where somehow the dealer always forgot the 5s so that the deck always has a count of say +4 and you always have a 2% advantage. Even with a 2% advantage (PA: 2%) vs a 2% disadvantage (HA: 2%), you could still lose 20 hands in a row. The odds of doing that mind you are about 4.95 times as less, but it is still possible.

Or if you think of it this way, when the HA is 2%, the odds of losing 10 in a row is .52^10 = 0.00144555
When the Player advantage is 2%, the odds of losing 10 in a row is .48^10 = 0.000064925.
When the Player advantage is 2%, the odds of losing 9 in a row is .48^9 = .00277991, which is greater than the odds of losing 10 in a row when the house has a 2% advantage.

So even though there is a swing in the advantage of 4%, you really only get one more chance in 10 tries to win your money back through any betting system.