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12AX7
10-04-2005, 08:15 AM
Hi Everyone,
I'm sure this has been done elsewhere. But here goes.

Suppose a player is breakever, how often should he expect a 10 BB downswing? 20BB? etc.

Suppose the player is the hypothetical "expert" at 1BB/hr (or what ever the equivalent is for 100 hands per hour, the online measure).

What I'm trying to figure out, is how much of a downswing is typical for a session of say 4 hours, 8 hours etc. so I can gauge how much is just the inherent variablity of the game vrs. how much of it is the "I suck a HE" factor. LOL!

AaronBrown
10-04-2005, 07:54 PM
The key missing information in your post is standard deviation. Suppose you have a standard deviation of 20 BB per hour. Then 1 hour in 6 will be a 20 BB downswing. The chances of being down by 20BB at some point in the hour is roughly twice that value, or 1 in 3. Over 1 hour, the 1 BB positive expectation is negligible.

Standard deviation goes up with the square root of time or hands, so after 100 hours your standard deviation is 200 BB. But now your +100 BB expectation is significant.

12AX7
10-05-2005, 08:23 AM
Hi Aaron,
I'll admit my ignorance here, where standard deviation is concerned.

However, suppose we know a player is breakeven, what is the inherent fluctuation of the game itself?

Is there anyway to quantify that?

Or suppose we know nothing of the player at all? What is the inherent "streaky-ness" of the game itself?

As a side thought/example, consider craps. If you play "Any 7" you would expect 5 loses for every win. So an idealized graph would look like "5 steps down, 1 step up".

With the payoffs as they are in craps, the 1 step up would always be a little shorter than the 5 steps down. By about 15%.

On the other hand, if you played the no pass line, I think you might have several tiny steps up and then a bigger down draft (not sure this statement is true, been years since I gave up on -EV games and analyzing them.)

Anyway, you get the idea, two betting situtions could have identical EV's but differing fluction characteristics.

Perhaps a germaine example is the difference between betting on Options Spreads like a Bull Put Spread where you expect to have a profit some 90% of the time... but lose 10%.

As everyone in here knows, you're EV for that situation would require you to know the expected profit and losses.

But this would be a case with "9 steps up, 1 step down". Irrespective of thier size.

So I'm trying to figure out the character of poker itself. The EV, of course depends on how good our betting is.

But to illustrate the question in a poker context.... you expect to lose most flushes you start chasing. So it's a "many steps down, 1 step up" graph. On the other hand, playing AA against 1 opponent is what, about 80% to your favor? So it's and just the opposite character-wise.

To use a Black Jack example. I once read that 98% of the time you should expect your BJ bankroll to be below your last highwater mark. That author (Snyder I think) was trying to point out that card counting wasn't for you if that characteristic bothers you.

So same basic question as I started with. "What's the inherent win loss ratio in the game itself?"

10-05-2005, 10:51 AM
There is no... "standard" standard deviation of poker.

The degree to which the outcome fluctuates is dependant on how you play and the type of opponents you face. In contrast, craps or any table game will (in general) have a fixed standard deviation that is dependant on the nature of the game.

A tight aggressive player against weak/tight opponents will have a standard deviation that is relatively stable over a large sample. The outcomes are volatile (and the degree to which it is volatile is explained by the standard deviation), but the degree to which it is volatile is constant. That is to say, the standard deviation derived from one player's sample of 10k hands is likely to be nearly identical to the standard deviation derived of another player's sample of 10k hands if the conditions of the table and the style of the player are similar.

Of course, if you put that same player up against a field of loose aggressive players, the standard deviation will almost certainly go up relative to what it was against weak/tight opponents.

Because of that, you can't generalize a single standard deviation. The volatility of your outcomes will depend on who you play against and how you play.

10-05-2005, 10:58 AM
[ QUOTE ]
To use a Black Jack example. I once read that 98% of the time you should expect your BJ bankroll to be below your last highwater mark. That author (Snyder I think) was trying to point out that card counting wasn't for you if that characteristic bothers you.

[/ QUOTE ]

I'm not sure that's true. If he's trying to explain why card counting with a positive expectation still has high volatility, one would expect that over a given sample you would expect to be up only marginally more than 50% of the time for a single trial, not down marginally less than 100% of the time. For a sample of trials, the probability of being "up" increases, not decreases (supposing you can count effective enough to make it a positive expectation).

It doesn't make intuitive sense. Blackjack isn't a high payout / low probability game (like, say, lotto tickets).

That figure would be true if you were talking about a (hypothetical) game that paid out only 2/100 outcomes (the other 98 lose), and the 2 that do win get paid 51 times the wager... for a single trial. The expectation would be positive, but (for a single trial), you would expect to be down 98% of the time. You can see though, that as the sample increases, you expect to be "down" less often. If you were to repeat it 100 times, you would expect to be down significantly less than 98% of the time and as N approaches infinity, that percentage figure approaches zero.

AaronBrown
10-05-2005, 06:01 PM
I think you misunderstand what he means. Say you're just flipping a fair coin for \$1, betting on heads each time at even money. Call your stake after the Nth flip, S(N).

Half the time, S(N) &lt; S(N-1) because the Nth flip was tails. If that's not true, one time in four, S(N) &lt; S(N-3) because the Nth flip was heads, but the two flips before it were both tails. If that's not true, one time in six S(N) &lt; S(N - 5).

If you keep going forever, eventually you get to certainty that you are below your high-water mark. The probabilities add up to 1.

However, with Blackjack you have a positive expectation, so the probabilities add up to slightly less than one. It's only slightly less, because the expectation matters only in the long run; for the last 100 hands or so the probability is not much different from coin flipping.

BillC
10-05-2005, 10:41 PM
It might be a bit hasty to be using normal probabilites here. I mean in some B&amp;M games you only get 30 hands/hr and maybe only play a few hands. Of course whether or not the results from an hour of poker is approximately normal is the eternal question of poker. But you are doing more than assuming normality for the hour. You are using a random walk model throughout the hour to get the factor of 2 (unless you are doing it a different way).

Btw it was Peter Griffin in "Other Stuff" that argued that your chances of being at you all-time high is sthg like 1-advantage.

12AX7
10-05-2005, 11:13 PM
OK, I originally asked the question in BB terms. But I think that has everyone on the wrong track.

Suppose there were no money in the game...

Now consider a coil flip. The idealized average is one win, one loss... back and forth, back and forth. But in reality it has a bell curve.

Taking the dice example again, the "any 7" bet, idealized is 5 losses, 1 win. So you see 5 downs and 1 up.

So what is the nature of poker in this sort of way, and then how does that translate when the money is added in?

Should I expect long down drafts with a few big pots bringing me back a profit? Should I expect to grind upwards slowly and then have an occasional massive down draft? Is it 50/50?

Getting back to poker, chasing only flushes would have a several down, one up character. True?

So what character does the game as a whole have?

See what I mean?

Surely some math wizard has looked at this the same as the coin tosses and dice have been?

And beyond that, has it been quantified in some way that makes it possible to grasp what to expect?

Clearly a "many up, few down" character is better for paying the bills as you're more likely to be in the black at any given moment. LOL!

10-06-2005, 01:51 PM
There really is no standard "ups and downs" proportion though.

A standard deviation for a session of poker is a product of the standard deviation of a HUGE variety of chance outcomes.

How the game is being played changes the nature of how volatile the typical events of chance will be.

In multi way pots, a small pair may be a long shot to win preflop, but pay out big time for sets. In loose games then, you have a high standard deviation. In heads up pots, small pairs are far more likely to win, but the amounts that they do win are small. That means in tight games, small pairs have lower standard deviations. Every situation your in will be more or less volatile depending on how many people see a flop on average, how aggressive they are, and a variety of other characteristics. Generally speaking, looser games have higher standard deviations (i believe).

[ QUOTE ]
If you keep going forever, eventually you get to certainty that you are below your high-water mark. The probabilities add up to 1.

However, with Blackjack you have a positive expectation, so the probabilities add up to slightly less than one. It's only slightly less, because the expectation matters only in the long run; for the last 100 hands or so the probability is not much different from coin flipping.

[/ QUOTE ]

I took "high water mark" to be where you start prior to the session. Oops.

12AX7
10-07-2005, 10:21 PM
Good Points.

Oddly it dawned on me though that theoretically your "up/down" ratio for the cards themselves is (1/number of players).

In other words you're dealt your fair share of winners over time.

However, the "bunching factor" isn't apparent in such a simple analysis. But I suspect it really does mean that this is a "many down, few up" game. Granted that's somewhat of a bozo-ish way to describe it.

I mean consider that every draw you start fails to complete significantly more often than it completes. So at any given time you may be in the "fails" part of any type of hand you play. (Not sure if that's clear at all.)

So that leads me to wonder if it is typically to see your bankroll slowly decline and then on occasion, when all your hands hit it quickly spikes up? Assuming you are a winning player then the upspikes would have to average being slightly more than the declines (obviously). But it still seems the characteristic of the game itself then, is to be bleeding chips over long periods, followed by a few big wins here and there.

On the other hand, my personal experience has been that I tend to make small gains over time, the suffer horrendous downdrafts.

Of course, that may mean I'm just -EV.

Not sure yet.