Speculus,
First, this sequence-is-so-important stuff has simply not been my experience with HMI. I would suggest that you are looking at too small samples if sequence is
appearing so important. However, you and I can spend some time priavtely if you like and go over your results more specifically.
Have you ever heard of "Oscar's system?" In Alan Wilson's
Casino Gambler's Guide (which I have mentioned a number of times in the past and should be in every serious gambler's collection) he talked about it.
In preparing to dsicuss "Oscar," one must first be familiar with the
D'Alembert system, also called the
seesaw or pyramid.
In the D'Alembert, one starts with a 1-unit wager. After each loss, the bet is increased by 1 unit and after a win it is decreased by 1 unit. The concept behind the system is that every loss has a corresponding win that is for 1 unit higher than the loss. Thus, in a perfect sequence, LWLWLW one's result is:
-1 +2 -1 +2 -1 +2
... and a 3-unit profit is realized - one unit for every "LW." Thus, in (say) a 100-bet session where there are 51 losses and 49 wins, 49 of the losses and wins produce a profit of $49 and the remaining 2 losses determine profit or loss. If the player had to go deeply into his sequence (say 10 units) then these two "extra" losses would be $9 + $10, for a loss of $19, resulting in a net of +30.
There are two questions: 1) "How bad is the downward swing?" and 2) "How many extra losses are there?"
I wrote a craps simulation of this system and tested it against
millions of craps hands. It lost money.
The reason it lost is that, when one plays a losing proposition, the player falls ever more and more units behind - the longer he bets,
theoretically, the more units behind he goes.
Back to "Oscar."
"Oscar's System" was actually quite simple... it is similar to D'Alembert but different. Start with a 1-unit wager. After a loss the bet remains the same as the previous bet. After a win, increase the wager 1 unit, but at no point wager more than is needed to show a 1-unit profit.
From Wilson's book:
Code:
Result - L W L W W
Bet Size - 1 1 1 1 1
Net Gain - -1 0 -1 0 +1
Result - L L L L L W W W
Bet Size - 1 1 1 1 1 1 2 3
Net Gain - -1 -2 -3 -4 -5 -4 -2 +1
Result - L L W L W L L W W L L W W
Bet Size - 1 1 1 2 2 2 2 2 3 1 1 1 2
Net Gain - -1 -2 -1 -3 -1 -3 -5 -3 0 -1 -2 -1 +1
Anyway, in the simulation studied in Wilson's book he ran 280,000 series of craps hands through a computer simulation. At the end of it all, he found a solid loss, of course because of the table limits.
He did say that games "with a memory" such as black jack might have merit
Enter, Ron Thacker. Ron worked at the old Gambler's Book Club in Las Vegas back in the '70s. He would fall today into the realm of "egghead nerd." (I am a nerd, but not an "egghead," as I do not have the math background for it. Ron had
serious math skills - M.I.T. serious.)
Ron did an Oscar-craps simulation of some magnitude back in the early '80s. I believe he published it as a paper. I know I actually had a copy of it about 25 years ago.
He made one tweak in Oscar. As I recall, he put in a stop-loss of sorts. That is, he played a finite session maximum rather than depending upon the table limit to end the session.
The long and the short of it is that after millions of dice hands, he netted one unit. I am not kidding -
one unit.
Now, this is no small feat in and of itself. Even if he had
lost one unit - or I should actually say lost
only one unit.
Personally, I have just never taken the possibility of beating a negative expectancy seriously.
There are two sides to every proposition. For our example, it is best to call these two sides
player and
casino. What we have been discussing doing in this thread is "player-beating-casino."
Instead, I want to play "casino-beating-player" and I want to be the casino.
IMHO, the goal of all players who truly care about winning should be to gain
any advantage because that thrusts them into the role of "casino" with an added positive: you get to tell the "player" what to bet.
Regards,
Dave Schwartz
