Trip Report, part II (still long)

No sense writing a program...

...because the playing venue under a program never changes substantially.

IMHO, this is far different from actual playing conditions, where actual venues do differ substantially, even under identical rules, even from table to table in the same casino.

Unfortunately, these observations are purely emperical; and cannot be mathematically proven or disproven.

But, since I've been playing this silly game since 1970 -- I have THIRTY-FIVE YEARS of such observations, and that's a LOT of data -- provable or not .

Justification for stop loss

There's this nasty thing called dealer cheating. It's not common, but it exists. Say you have a one in a hundred chance of being cheated when you sit down to play. Then say you have a really bad session. So bad you use up all cash on hand before you're ready to go home. Bayes' law says the chance you are being cheated has greatly increased. Without knowing your game etc., 10% is a reasonable estimate. So now there's a 10% chance you're getting shafted but good.

Now, if the dealer is a competent mechanic, you're playing to something like a 30-60% disadvantage, whereas if you're a competent counter, you're getting about a 1% advantage. Maybe you have no idea you're being cheated. Should you observe your stop loss, or should you jog over to the cash machine?

ETF

Of course it works

Of course a stop loss works in the real world, OCfVA! It works for a multitude of reasons; cheating dealers (little chance of a publicly traded corporations cheating systematically, but a dealer that takes a dislike to you could easily do so), cheating houses (mainly a problem in some overseas locales), or you could just be having a bad day (I've heard that even Einstein had 'em.)

I wasn't even appealing to those reasons - I was hoping someone could prove or disprove the statistical proposition that the distribution of a sum of biased distributions is itself a biased distribution. It would be easy to simulate (I was being modest before, I could program it, but I don't have the code for a simulator that would allow me to take the 5 minutes to add the "simulation of simulations" shell, and it would takes weeks/months to program the simulator itself in my spare time. I know some people have them, though.)

It's possible that I am thinking about the statistics incorrectly, but no one has offered any reasoning that I hadn't already considered. If someone could just point an error in assumptions, that would work too (i.e., I can convince people of the truth to the Monty Hall paradox in seconds by pointing out the implicit assumption - if someone could do the same for me here I would be convinced of the theoretical math (although I'd still use stop losses for the reasons discussed above.))

Asked and answered, no?

"I was hoping someone could prove or disprove the statistical proposition that the distribution of a sum of biased distributions is itself a biased distribution."

It isn't. I thought I had answered you already. You may not have liked the answer, but that doesn't mean that it was wrong! :-)

The Central Limit Theorem (ask MathProf for further clarifications) will demonstrate that if you take enough truncated distributions and lump them together, the result will be normally distributed.

You can't "save money" by quitting early. If you simply devote some thought to the notion, you will see that it is absurd. Quitting early limits your larger wins just as much as your larger losses. If you have the edge and you play less, you win less. What could be simpler to understand than that?

Don

In other words.........

The less you play when you have the advantage, the more you lose when you win! LOL

Some Numbers for You

Here is a very simple example that will illustrate stop losses. Suppose that you have a chance to bet on biased coind, which will win with p=60% of the time and lose q=40% of the time. You bet $100 each time. Note that your EV per bet is $20.

For simplicity suppose that you have time for exactly 2 bets. Your distribution consists of 3 possible results: Win both best (result +$200), lose both bets (result -$200) or win 1 lose 1 (result 0).

The probabilities are respectively, p^2 (36%), q^2 (16%), 2 p*q (48%). That is

 

+200   35% 

   0   48% 

-200   16%  

You can compute the EV of this and se that it is $40. This is precisely 2*$20; you have 2 bets with $20 EV each. EV is linear.
Now suppose that you decide to employ a stop-loss of $100. If you lose the first bet, you don�t make the second. Again there are three possible results: lose the first (40%), win the first lose the second (60%*40%=24%), or win both (36%). The distribution is

 

-200  40% 

   0  25% 

+400  36%  

If you compute the EV of this, you will see that it is $32. Note that you stop-loss strategy has cot you $8.

There is another way to look at this. With the stop loss strategy we will make, on average 1.6 bets. We always make the first bet, and 60% of the time we make a second bet. Our overall EV = ( 1.6 bets ) * ($20 a bet) = $32.

Your stop loss strategy has decreased your action by 40% of a bet, and therefore decreased the EV proptionally.

This is a very general principle: Total EV = (Ev per Bet ) * (Expected Number of Bets). Anything which reduces you Expected Number of Bets reduces your Total EV.

You might object that this example is unrealistically simple. You can do more complicated examples if you like, it will be more work. If you want, try 3 bets with a stop loss of either 1 or 2. Or try even more complicated things, like 10 bets with a stop loss of 5 bets, etc.

The principle will be the same.

Harrah's Cut

> I saw this somewhere in Vegas this past Summer but don't remember where.

I saw it at Fitzgerald's -- the dealer would cut off about 10 cards.

Milo

pretty good...

That was pretty good. I could almost hear the chalk screeching on the blackboard during the lecture. :)

It may have decreased your EV, but it increased your bankroll

MathProf: I understand the coin example, but setting aside the mathematical probabilities for a moment and looking solely at the profit/loss accounting, there is a positive, both from a psychological and accounting standard, for using stop loss.

If after 3 tosses I am up $100 (2-1), despite the probabilities of winning, I can only either win or lose my bet on the next toss. If I choose to walk away, at that point, with a $100 profit and not risk my capital on another toss, I increase my bankroll, for that session.

You can't play forever, at some point, by choice or force; you have to end a session. A favorable count and EV does not guarantee a profit for any session. My preference is to stop playing when I've reached my exit (profit or loss) goal, instead of plowing ahead and losing more of my bankroll or risk losing what I worked hard to gain.

No: Bankroll and EV move in the same directionq (nt)

Correction to EV vs. Stop Loss Post Title

MathProf: I reread your post and saw where I misread the following: �Your stop loss strategy has decreased your action by 40% of a bet, and therefore decreased the EV proptionally.�

The content of my post wasn�t effected by the mistake in the title.

Other numbers

I once ran a program, in which tracked a player, counting hi-low using the I18, sitting at first base on a DD table with 2 other players, DAS, S17.

The purpose of the program was to learn the average, mean, and std. dev. of the depth needed for the player to win 20 holding bets (i.e., 20 x the table minimum).

The depth was rather less than I had always assumed it would be (although the std. dev. was quite large).

The mean is the number I now use for my trailing stop loss.

My philosophy on this is a follows:

Either it is true that we are only in one "session" which lasts the full length of our playing lives or it is not.

If it is, then triggering the trailing stop loss does no harm -- it merely inserts a break for our own mental/personal needs/benefit.

If it is not, then triggering the trailing stop loss helps by limiting losses (or the amount of a win given back before stopping play); and the process begins anew with a clean slate after the break.

Either way, there is no downside and, at minimum, a positive psychological upside.

Excellent Idea M-P!

I had been thinking that I needed an engine that had all of the count-based strategy bets and plays and that I could put a macro around this to have it run the simulation of simulations, but reading your post I realized that I could get a reasonable idea of the effect of a stop loss on a much simpler simulation.

I simulated 256 hands/session (because excel has 256 columns, and because this seems like a reasonable number for a good day of AP) for 20 days a month for 40 years. This is my idea of approximately a full career of full time play (assuming you could take it for that long.) I gave the player a 1% advantage on each hand, and then simulated 20 careers both with a stop loss and without. (This works out to slightly less than a billion "hands".)

As advertised, the macro took about 5 minutes to write. I got very nice convergence.

And the answer is...... under those conditions, the stop loss cost about 0.56% of my expected monthly win rate. In other words, if I expected to win $100, I would expect the stop loss to cost me 56 cents.

In my book, that's pretty cheap insurance against dealers who decide they don't like me, cheating houses (probably overseas), or the occasional bad day (when I say this, I don't mean bad luck; I mean a day when I am not playing well.)

Since it is unlikely that I would be able to get a sustained 1% advantage on every hand, I would regard this as an upper limit on the cost. (I know, I know, you can get a better average advantage by wonging, but can you get it for 256 hands per day?) It would be interesting to repeat the simulations with a prior distribution for an element of each hand's advantage in a session; one that would reflect external factors such as those described above. This would be added to the player advantage determined by whatever counting system you are using to give the practical, as opposed to theoretical, player advantage by hand.

Anyone have any thoughts on the form of the prior distribution? It's not hard to say it would vary based upon whether you play locally or travel a lot, and on the amount you play, but I'd be interested in other constructive thoughts.