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 y-axis 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