
Martingale Long Term vs. Short Term
What
does a Martingale session look like?
These charts are much like the set of charts on long
term vs. short term, except they are for a Martingale player.
That is, a player that doubles the bet after a loss and drops to
the minimum bet after a win. All bets are even money for simplicity.
There are four charts on this page displaying results starting
with the short term (100 hands) and moving through successively
longer terms (up to a million hands). We start with a chart displaying
the total won or lost for a Martingale player playing 100 hands.
What we see is tiny increases — so tiny they barely show up
on the chart. Then we see a large decrease to a total loss of 500
units caused by a long losing streak where the bet kept doubling.
Then a win brought us back to the previous high point plus one unit.

Now we move to 1,000 hands in groups of 10. Here we see the 500
unit negative swing we saw in the previous chart. After that, we
have been fairly lucky without any serious losing streaks for about
8,000 hands. Again we see a large downswing — in this case
to 1,700 units, followed by a recovery.

Let's expand this to 100,000 hands in groups of 1,000. We see the
yaxis has expanded as our results in this section range from 40,000
units behind to 50,000 units ahead. The line is starting to look
smoother. But we see more serious swings.

Finally, 1,000,000 hands in groups of 10,000. Here we start at
zero units won and end up with nearly 500,000 units won. However,
we had one loss of nearly $4,000,000 requiring a $4,000,000 bet
to win it back. That is a bet spread of 1:4,000,000. And that assumes
we have a $1 minimum bet. That would be a $100,000,000 loss betting
green.
Of course this is just one run. Other runs will see the swings
at different points and of different sizes. There is no assurance
that any size bankroll is large enough to withstand a losing streak.
Also, the house edge is still the same as flat betting. At any specific
number of hands, the average expected loss will be the house edge
times the number of bets.

Sim details
 Six decks, S17, 4.8/6 penetration, 4 players, Basic Strategy,
No doubles or splits, 1:1 payouts
 One million rounds


