[noal]

Interesting read; I was playing with similar thoughts over my lunch break a couple of days ago.

The base of my sample program [implemented in ruby] was based (in theory) of Proportional Betting "The Martingale" - http://www.bjmath.com/bjmath/progress/prog1.htm

The game I picked was "Casino War" [ http://wizardofodds.com/games/casino-war/ ], as it was very quick to implement in a few lines of code. I selected the base rules as played in Garden City Casino [Bay Area] (50c drop per every $100), and came up with the following:

Game/House Rules: - 6 deck of cards. - Played until 1/2 is gone. - 50c drop for every $100 [Example: $200 bet costs $1, $300 $1.5.]

Betting Rules:

- Base Bet is always 1% of current wallet, at starting point - $10. - If the proportional bet can not be covered by wallet, the round is surrendered and the player waits until re-shuffle. [Example: Lost up to $500, next bet is $1000, wallet has $700, game ends/waits and the player accepts a loss of $300.] - Bets are doubled on loss as defined in the Proportional betting link.

Here's my data, though I believe something is wrong due to its results:

- I ran the initial program, as is, expecting the player to play one round every day for 10 years. - Losses and earnings were added together. - The average win % went to 58.4%. - The average cash win [the times the player didn't go bankrupt] was $1590. - Max loss [consecutive] cash $2980. [Bankroll covered over multiple sessions]

* A key point here is the average cash win. It was highly consistent and never below 1500.

I then added a factor that stated in the software:

- If winnings are at $1500, the player stops, takes the winnings and waits for a re-shuffle.

* Win percentage went up to 64.8% !

If anyone is interested, I'd be happy to share/pastebin the code or similar. Overall, due to the percentages I'm assuming something is wrong with my assumptions/gameplay, but so far an interesting experiment.

[Edited for clarity on betting strategy]

[nullflux]

That same site has an interesting article on Martingale betting systems: http://wizardofodds.com/gambling/betting-systems/

IIRC, a martingale strategy will eventually destroy you because it requires an exponentially sustainable bankroll to maintain the same risk of ruin.

Also, 3,650 hands is far too small of a sample size for a game with such a small edge and you are probably just witnessing positive variance. See where the law of large numbers leads you and run your simulation for 500,000 hands.

[mckilljoy]

Yes, Martingale's doesn't raise your expected value above zero/negative for any games of chance. Towards infinity, it won't change your outcome -- you will still eventually loose all your money.

If you factor in the times the player went bankrupt, your win percent probably won't look so hot.

[noal]

I'll clean up my code a bit and post it on pastebin, there's probably a mistake in my logic somewhere.

Overall; I agree [and having played my share of a variety of strategies] I found the data to be confusing, hence my peaked curiosity. :-)

[noal]

Though it did (in the simulation). The accumulated winnings with the limits on bankrupt and cashing out at 1500 created a over time win percentage in a otherwise negative-biased game?

[mckilljoy]

By definition, if there is negative expected value, simply changing your betting strategy won't help. Any short term fluctuations would be from "luck".

The famous MIT black jack team was able to 'take down the casino' by counting cards and waiting for expected value to swing positive, and then placing large bets at that time. If the game is truly random and negative (like all well-constructed casino games should be) then there should never been an opportunity for positive expected value.

[noal]

Note that's 3,650 decks / 28,470 hands (not counting "War" hands).

As it was run twice, it's closer to 56,940. (using two different alg.)

Rerunning it (now) produces minimal differences, even at a 1,000 year setup. (3-5% variation)