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.

[DrGutshot]

surprised noone has responded to this yet, awesome and interesting work - thanks for the info Ryno.

Even more data that inspires playing a constant A game.

-DrG

Great post. Maybe you should also add it to the probability forum.

[stigmata]

Nice work. So the basic conclusion is that tilt has a more pronounced effect on multi-tablers (because they have a slightly lower winrate).

I would be interested to see the effect of a more realistic "micro-tilt".

E.g. Fred:
1.5BB/100 Most of the time
1.25BB/100 When on a 50+ drawdown
1.0BB/100 when he's in a 100+ drawdown.

[stoxtrader]

nice work, how would the results differ if you used winrate/hand and sd/hand instead of per 100?

aren't they independent events afterall? why do we use 100 - I think previsouly these calculations were done manually and this was a necessary simplification, but with powerful programs to do this why not use per hand as the standard?

[NYplayer]

it doesn't matter. you just devided the winrate by 100 and the stdev by sqrt(100) or 10 and will get the same results. i think people use per 100 because it's the pokertracker convention.

[stoxtrader]

doesnt it matter because it makes your sample size much larger? This would cause attainable confidence intervals at lower hand counts.

[Ryno]

It came up because I mentioned in another forum that I don't multitable, and I got an interesting response from stoxtrader, so it got me thinking what other benefits there might be. But the study is not necessarily about multi-tabling vs. single-tabling - it's about the sick swings you can experience with a slim winrate, and how much worse they can get if your performance is path-dependant.

Regarding your setup:

Winrate = 1.22BB
Probability of experiencing a 1000BB drawdown over 1000hrs: 3.6%

[Ryno]

Once I define the test period as 1000 hours on the drawdown studies, all of the unit questions are taken care of. If I used per hand, per 100, etc., I would get the same answer. The reason I don't like "per hand" is that the distribution of returns hand-to-hand are very non-normal. Granted, over 1000 hours I'm way into Large Numbers and it won't matter, but sometimes I do small sample size tests.

[ihardlyknowher]

[ QUOTE ]
If I used per hand, per 100, etc., I would get the same answer.

[/ QUOTE ]

I wonder if this is true since it is theoretically possible to have an event with great variation in each individual trial to have very little variation when grouped into sets of 100.