Interesting drawdown study

[Ryno]

{Note - I did this in Excel in like 30 minutes so it's possible I made an error - however, I believe the results to be correct}

Suppose you have the choice of playing 1 table of 30-60 at a winrate of 1.6BB/100, or 4 tables of 15-30 with a winrate of 0.97BB/100 each. Take these winrates as given. In both cases your stdev/100 is 18BB (shorthanded play - I am also assuming 100 hands per hour per table).

If you assume poker hands are iid normally distrubted, then multitabling is the better choice. Your hourly expected earn is 0.97*30*4 = $116.40, with a stdev of $1080. The expected earn playing 1 table is 1.6*60 = $96, with the same $1080 stdev.

How about drawdowns? I define drawdown as the difference between your current bankroll and the highest it's ever been. In the studies below, I used a monte-carlo simulation over 1000 hours, meant to represent 1 years' worth of play.

The chances of experiencing a $30,000 peak-to-trough drawdown under the single-table assumptions is about 7.9%. Under the multi-table assumptions, the chances of a $30,000 drawdown drop to 4.6%.

Now, change the player profiles a little bit.

Sam the single tabler plays better when he's running good. His expected winrate is:

2BB/100 when he's within 50BB of his alltime high.
1.5BB/100 when he's between 50 and 150BB from his alltime high.
1.0BB/100 when he's in a >150BB drawdown.

Marty the multitabler has similar characteristics:

1.5BB/100 when he's within 50BB of his alltime high.
1.0BB/100 when he's between 50 and 150BB from his alltime high.
0.5BB/100 when he's in a >150BB drawdown.

It so happens that Sam's long-run winrate is 1.6BB/100, same as my first example, and Marty's winrate is 0.97BB/100, also same as my multitable example above.

The chances of Sam experiencing a $30,000 peak-to-trough drawdown are 17.8% - more than double the number I got when I assume he plays the same all the time.

The probability of Marty experiencing a $30,000 drawdown is 20.7%, even worse than Sid, and over 4 times worse than someone who can maintain an identical winrate through good times and bad.