Small Edges and Bankroll Growth

[Toffler]

I am relatively new to poker. I am a former BJ player. Until a few years ago, it was thought that a good BJ player should push small edges like splitting TT vs 5 or 6 and doubling down with T v T or T v A when the count is such that the play is correct. A smart fellow, Karl Janacek, showed that such plays actually slow bankroll growth because of increased variance. He showed the plays were only correct when the edge was higher (that is, make the plays at higher counts) and your bankroll would actually double sooner even though you were giving up EV. He even showed that some negative EV plays like insuring a 20 when the count was not quite high enough would result is faster bankroll growth by decreasing variance.

Now to Hold'em poker. I think the same might be true for certain plays in poker. Examples would be going for a gut shot with slightly more than break even odds. Playing small pairs in a loose aggressive game against 5-6 limpers. Playing marginal holding on the button in unraised pots. It might even be incorrect to call a raise or reraise with certain holdings like TT or 99 against certain oppenents even with slightly positive EV. I suspect giving up some small EV in these situations might actually result in faster bankroll growth. Has this been studied with computer sims for poker? Is this concept wrong for poker?

[K C]

I'm no expert in blackjack but assuming a negative expectation, anything that would increase variance would have to increase losses. Then again, maybe you count cards or something and get an edge that way.

With a positive expectation though, you're adding equity to the account each time you take advantage of an edge in the odds. And variance is a zero sum game, as long as you don't have to drop down to a lower playing level. So without that consideration, it is indeed advantageous to push any edge that arises.

Now on the other hand, this is going to depend on your bankroll strategy. The goal for most players is to move up of course. So, the closer the distance is between your levels, the more variance is a concern. And with the more aggressive bankroll management that I teach, which looks to put you up levels much faster than normal, it's not only dropping down that concerns you, it's delays in moving up that you need to worry about as well.

So indeed this may be something you need to look at, depending on your strategy here, and what effect variance has on it. This goes beyond the situations you suggest though, and extends to managing variance in general. You may even want to switch to a different type of game - for instance, from cash games to single table tournaments, if your variance is enough of an issue.

Good insight though. This is pretty advanced stuff for a new player, and if you keep this up, your opponents are going to be paying a big price [img]/images/graemlins/smile.gif[/img]

KC
kingcobrapoker.com

[Cheeseweasel]

First of all, thank you very much for your thought-provoking post.

I am also a former blackjack player. I used to use the Uston Advanced Point Count, primarily for its very high betting efficiency. Of course, as you know, betting proficiency is the most important element of playing blackjack, much more important than playing efficiency.

When I play no-limit and pot-limit poker, I calculate the optimum Kelly Criterion percentage of bankroll for bet-sizing. As I'm sure you know, this insures the optimum geometric bankroll growth. However, it has never occured to me to do an analysis of limit poker games.

Are you familiar with Don Schlesinger's "World's Greatest Blackjack Simulation"? I'm sure you know the SCORE. (By the way it was done using Karl Janacek's Statistical Blackjack Analyzer). It seems that a project like that should be done for limit holdem.

I'm sure that you won't find that it's been done already. The great majority of poker "theoreticians" (Sklansky and Malmuth excepted) seem to be more comfortable with hand-waving arguments and vague, ephemeral assertions than their blackjack counterparts.

You have some good examples of plays that may be EV+ but bankroll-draining because of their relatively high variance. I think that the number of marginal poker plays may well be far greater than those in blackjack.

Is this concept wrong for poker? In my humble opinion, a resounding NO. I'm surprised that it hasn't been addressed before now. If I could find a decent poker simulator, I would undertake the project myself.

Best of Luck

[stigmata]

Thought provoking post, although I'm not sure I quite get it yet. Could you explain further, or point me to somewhere I could read more. As far as I understand it, what you are saying is that some minor +EV plays have a major increase on variance. This is fine and understood.

I'm just not sure why this will be detrimental to bankroll growth. E.g. say, for example, I decide to cut out all these minor +EV, large variance plays, but my clone (who plays identical poker) decides to carry on using them. In 6 months time, averaged over all universes:

My bankroll: 10000 +/- 1000
Clones bankroll: 11000 +/- 3000

So my clone is of course doing better, on average. So why are these detrimental to bankroll growth... is it the day-to-day variance that is the problem? E.g. on one give day my clone is at 8000, the next at 14000? So that his bankroll is unstable, with its lowest point being below the lowest point of my bankroll?

Is it this volatility that limits me from moving up stakes quicker? E.g. if I was to sacrafice perhaps 0.25 BB/100 on high-variance plays (basically play a bit weak-tighter), my variance would be reduced such that I would not have as many -50BB downswings. This way I would not need a 500BB bankroll to move up to 10/20, but perhaps 300BB would do?

If this is correct, then it's really how you want to play it. To move up stakes quickly, playing weak-tight might be better. To extract the maximum from your limit, chipping away at every little +EV situation is obviously the way to do it, but you need a bigger bankroll.

Basically adjusting between variance/EV according to your bankroll.


Please correct me if I am wrong, but this is the way I understand it.

[axioma]

one thing i would point out is that bankroll groth is FAR more important in BJ than in poker.

In BJ, the game is exactly the same at high stakes, as it is at lower stakes - this is not at all the case with poker.

therefore the notion to pass up small edges in BJ in order to grow bankroll more smoothly might be profitable in order to assure advancement to higher stakes ASAP, whereas in poker you would want to push those small edges, because you dont have as much riding on your moving up.

just a thought.

[SunOfBeach]

2-tabling 5/10 requires less bank.

at 1BB/hr on each, but with SD(10/20) = 2* SD(5/10), then
2 5/10 tables gives expected hrly rate of 20 with sd = 1.41SD (sqrt of 2), which is obviously less than 2SD.

[stigmata]

OK I think I've confused the point somewhat.... I'm not sure thats what I was getting at. Clearly 5/10 requires smaller BR than 10/20.

I meant could you get away with smaller bankroll at, say, 5/10 if you reduced the number of high variance plays.

Unless your just confusing me even further..... doh

[yoshi_yoshi]

I think the reason this applies more to Blackjack and less to poker is that you have more freedom to choose how much you bet in Blackjack. In fact (I think), if you are using something like the Kelly criterion you always have a mathematically correct amount to bet at each count, depending on your bankroll. So having a steadily increasing bankroll would be useful in BJ because you can bet more in the future.

Contrast this to poker, where, if you have a 300BB bankroll, you are likely to be staying at the exact same stakes for a lengthy period of time, only moving down in cases of very bad luck, and moving up when appropriate. In most of our poker lifetimes, we are only going to be moving throughout 10 or so limits, so the variance issue is not as important as in BJ.

However, I think your theory has more and more relevance to poker as players decrease their necessary bankroll. For example, if a very disciplined player decided to move up to the next level when he has 40BB, and move down when he has 30BB, variance will matter a lot more to him, because he can use the extra bankroll more judiciously than the 300BB player. A 300BB player who wins or loses 20BB can shrug it off as it usually does not affect how much he can bet it the near future, while a 40BB player who wins/loses that much is going to have to change his next bet drastically.

Just my two cents.

[Ed Miller]

Is this concept wrong for poker?

In my opinion, it IS WRONG for poker... at least limit hold 'em. In fact, this concept you've stumbled upon is actually a very popular one among poker "theorists," and it's one of my major pet peeves. Wanna know why it's my pet peeve?

[ QUOTE ]
Playing small pairs in a loose aggressive game against 5-6 limpers.

[/ QUOTE ]

Because a pocket pair after five or six limpers is an incredibly +EV situation, and if you skip it to reduce variance, you are shooting yourself in the foot. Now I know you are new to poker, and you were just throwing out possible examples, but this represents a problem almost everyone who tries to implement this concept has:

They try to use it in completely inappropriate situations. They like the concept.. think it's sexy or what not.. and they try to use it in all sorts of scenarios where it doesn't belong.

In blackjack, you can quantify everything. You can say, "For these three specific plays, lowering your EV actually grows your bankroll faster." There's no temptation to make the play in any other situation.

Not so in poker. Poker isn't blackjack. Simulating doesn't work: The game is too complicated to simulate to any accuracy even remotely near necessary to make these sorts of hair-splitting CV distinctions. At least there's nothing available now that simulates that accurately, and don't hold your breath for something either.

I'm not familiar with the numbers, but I can basically guarantee you that the effect on bankroll growth of splitting versus not splitting tens versus a six at a +6 or +7 count (or whatever the index is) is negligible. That is, you can show mathematically that it ever so slightly grows your bankroll faster to make the -EV play. But if you never made that adjustment, you wouldn't begin to actually appreciate the difference in real bankroll-size terms for centuries, probably.

Now think about what would happen to your bankroll if you liked this "I'm gonna lower my variance by not doubling and splitting in +EV situations" concept and had to figure out the appropriate situations on your own without computer aid. You'd start doing it all over the place. I'm not gonna double soft-15 against a 5 anymore. I always catch a ten when I do that. Bleh.

Maybe I won't split sixes anymore against a three. After all, I don't like having two sixes as hands. That just seems like it's gotta be the right spot to make the adjustment. In fact, I think I'm just gonna stop splitting sixes entirely. Sure it's theoretically +EV, but it just jacks my variance up, and I'd prefer to lower my variance.

Maybe you, personally, wouldn't say that stuff, but a whole lot of people would. I know gamblers. [img]/images/graemlins/tongue.gif[/img]

Think about what that would do to your bankroll. SUICIDE. Well, that's what poker players do ALL THE TIME to themselves when they try these "I'm gonna lower my EV and variance" plays. They pick all sorts of inappropriate spots that "seem" right, and they end up playing like douchebags.

99.9% of all limit hold 'em players would make more money, grow their bankroll faster, and have more fun playing if they just forgot about this lowering variance crap and made the highest EV play they could. Because of that, I feel this discussion is totally unhelpful, and I wish it would just die.

EDIT: BTW, you guys who link my posts in discussions when appropriate, please start linking this post. This "let's all lower our variance" nonsense is really beginning to piss me off. [img]/images/graemlins/smile.gif[/img]

[colgin]

[ QUOTE ]
BTW, you guys who link my posts in discussions when appropriate, please start linking this post. This "let's all lower our variance" nonsense is really beginning to piss me off. [img]/images/graemlins/laugh.gif[/img]

[/ QUOTE ]

Consider it done.