Banroll requirements, variance, and shorthanded play
So, I was just playing 6-handed online (not big stakes or anything, just $1-$2). After I finished, I started thinking about variance and win rate, then I started thinking about the recent thread here about bankroll requirements, where you (Dave) mentioned that you play shorthanded $5-$10 online. Anyway so, my question is this:
How do you think that the bankroll requirements for shorthanded play compare to the bankroll requirements for a full game? My first instinct was that you would need a bigger bankroll to play a shorthanded game, because you will tend to play more hands, and play them more aggressively. But now I think that I was wrong. First, the fact that you play more hands seems irrelevant. Also, the pots are smaller and you win a higher percentage of the pots that you play, so it would seem that your variance is lower relative to your win rate, and as a result you would not need as large of a bankroll.
Anyway, I'd like to get your opinion on this, as well as the opinions of others.
Thanks,
Keith
How do you think that the bankroll requirements for shorthanded play compare to the bankroll requirements for a full game? My first instinct was that you would need a bigger bankroll to play a shorthanded game, because you will tend to play more hands, and play them more aggressively. But now I think that I was wrong. First, the fact that you play more hands seems irrelevant. Also, the pots are smaller and you win a higher percentage of the pots that you play, so it would seem that your variance is lower relative to your win rate, and as a result you would not need as large of a bankroll.
Anyway, I'd like to get your opinion on this, as well as the opinions of others.
Thanks,
Keith
Comments
Well... I am in over my head with this answer. I have submitted it to Brian Alspach (he writes "Math and Poker" for CPP) and I will post his reply when I get it.
It may depend how you measure variance. If you measure it "per hour" then the short handed game will have a much higher variance. Probably by simple fact of playing more hands you will increase your variance over such a short time. If you are talking "per hand" it may be less since you will tend to have less opponents and they will, therefore, draw out on your less often.
Although your opponents may not draw out on you as often (because there are fewer of them), you have to call your opponents down way more often than in a full game, sometimes with second pair, sometimes with bottom pair, and sometimes with no pair.
Also, the average pot in this game was not smaller than at the full table. Like I said, although it wasn't 'show 'em hold 'em', a lot of pots went to showdown heads-up, not unlike a full table that is playing tight. Also, as has been pointed out, there are more hands/hr shorthanded.
My bankroll system in dealing with this game was no system at all for a while. I think I got up to 3K, freaked out because I made 3K in profit, and cashed 2K. Then returned to play 25/50 shorthanded with 1K. At this point I could have easily lost it, in less than ten minutes. Luckily, that's not what happened, and I eventually developed the not optimal but more reasonable system of making it to 12K, then cashing 5K, then making it to 12K, then cashing 5K, etc....
Regards,
all_aces
Right. This is what I was thinking. But hourly variance is not what matters for bankroll requirements. I mean, if your game moves twice as fast (say, online as opposed to B&M) your hourly EV is doubled and your hourly variance is multiplied by the square root of 2, but your bankroll requirements remain the same.
I am guessing that the important numbers here are EV per hand and variance per hand, although I'm not exactly sure how these numbers are used. I guess you could do "risk of ruin" calculations but I'm not 100% sure how these are done (I'm no statistician.. in fact I hate stats). Does Mason Malmuth talk about this in any of his books or essays?
Keith
That was a good and informative post. I don't mean to just pick on one point but I was to point this out. The fact that there are more hands per hour is irrelevant in terms of bankroll requirements. If you go broke after 1000 hands, it makes no difference if it takes 8 hours or 30 hours to play these 1000 hands. Certainly, the fact that you play the hands quicker does not increase your chances of going broke over those 1000 hands.
Keith
Thanks! Every now and again I post something useful...
Totally agree, good point. However, in those 1000 hands--which can take all the time in the world or no time at all--if you find that you have to call your opponents down with sub-optimal hands on a regular basis, you'll find that your variance goes way up. As a result, you'll need a bigger bankroll to handle it. What happens if, during those 1000 hands, you call down people who are notorious bluffers, and they happen to have the goods, time and time again?
You know that calling these people down with just about anything has been a profitable move for you in the past. Raising's no good--they'll fold. The best way to make money from the hyper-aggros is to simply call them down the whole way while they try to knock you off your hand. So, for 1000 hands, you use this strategy that's been working well for you in the past, but they happen to be hitting like the maniacs they are, and a chunk of your bankroll consequently disappears in the blink of an eye. Sure, you'll get it back from them... their style of play combined with the laws of probability say that it's pretty much inevitable. But for the time being, if you don't have the stake, you're broke.
I guess what I'm saying is that while the hands/hour don't directly have an impact on what the size of your bankroll should be, the way you are forced to play against super-aggressive opponents in a shorthanded game will certainly have an impact, and a big one at that.
Regards,
all_aces
It is not necessarily irrelevant. It depends what your ruination goal (or rather, your anti-ruination goal) is, and there are certain ruination goals where speed at which the game is dealt matters.
Bankroll requirements are typically stated in the form:
"What bankroll do I require so that I have probability P of losing my entire bankroll before Condition X is met?"
Condition X could be a lot of different things. Often people by default think of Condition X as "the end of the universe" or some other such long-term criterion. In that case, it doesn't really matter what interval you use to measure variance (nor does it matter whether it's hand based, ot time based) as long as:
1. Win rate and Varaince are measured using the same interval.
and
2. Your interval is small enough to make the data you have useful, meaning that your sample size is large enough (i.e. measuring Win Rate and Variance per year is probably not the right choice).
I get your point about it making a difference whether you play twice as many hands per hour. The way I think of it is that your Win Rate at a 30 hand/hr game is not a good estimator of your Win Rate at a 60 hand/hour game. But if the game is otherwise the same, you just have to make the adjustment of multiplying your 30 Hand/hr Win Rate by 2 and Variance by 2 (not sqrt(2)... you might be thinking of Standard Deviation which would be multiplied by sqrt(2)) and the resulting estimate would be fine. Without this kind of adjustment, an analysis using hourly data will be quite innacurate.
There *are* some ruination goals where the speed at which the game is dealt matters. For example, someone on a trip to Vegas bringing $1,000 may want to figure out what the best game to play would be so that he has less than a 1% chance of going broke during the 60 hours he plans to play poker there. Variance (and Win Rate) per hour will surely be considerations for this particular ruination condition, and this person's goal will cause a $5-$10 full ring game to be treated differently than a similar $5-$10 shorthanded game in the ruination analysis.
Though, as Guest/all_aces points out... good luck even finding a $5-$10 full game which is "similar" to a $5-$10 shorthanded game. 8)
ScottyZ
Ok, then maybe my original post wasn't specific enough. When I asked how the bankroll requirements from the two types of game would compare (ie, short vs full games) I was referring to the amount of bankroll that you should have in order to be able to play arbitrarily long without going broke. I think that this is what is usually meant by the term "bankroll requirements", at least if it is not stated to be otherwise.
You know, I always say variance, and I always mean standard deviation. I don't know WHY I do this. Although, when you start talking to people about dollars squared, they look at you kind of funny.
On a side note, this is my 200th post, so you may now refer to me as "Poker God". 8) Does this mean that it's my fault when people get rivered?
Keith
No, but it does mean that every time that *you* get rivered, you may demand the sacrifice of some sort of animal on your behalf.
I usually go grab a Big Mac.
Don't forget, you're also now entitled to a free subscription to Canadian Nude Poker Monthly Magazine.
ScottyZ
I would be interested in unsubscribing to this....
Regards,
all_aces
Are you sure? You'll miss out on the free cologne sample inserts!
Next month's: "Eau d'14 hour poker stink"
ScottyZ
First, I have serious doubts as to the amount of actual animal in a big mac. Second, if I ate a Big Mac every time I got rivered, I could star in "Super Size Me 2". Finally, as for the magazine, I'm out (unless Annie Duke is on the cover)
Keith