Long Term Discussion

Cogno Scienti

John G. Zaroff


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Cogno Scienti


To: vpFREE@YahooGroups.com
Message: 57829
From: Cogno Scienti
Received: Sun Mar 19, 2006 1:31 AM
Subject: RE:
[vpFREE] Re: Feeling Guilty - Trip Report

>> I understand the long term implications. My point was that by not
>> worrying about it, I won $16,000. It would not have been any more or less
>> if the machines were 100% or 98%.


You would have won exactly 5 coins less for every full house and flush
(if you had played 9/6 DB rather than 10/7 DB).

>> Your math is correct IF one believes in long term. I don't believe that
>> you can add up the sessions and have them become just one long term
>> ratio.


There are many areas of life where people can differ in their beliefs and
still have a great chance of success. Mathematics is not one of them ...

Cogno


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To: vpFREE@YahooGroups.com
Message: 57923
From: Cogno Scienti
Received: Mon Mar 20, 2006 6:49 PM
Subject: RE:
[vpFREE] What is 'Long Term'?

>> I think that no one can truly define 'long term' as it relates to vp .
>> It doesn't seem to be definable in a measurement of time nor in a number
>> of hands . Yet, it is a term that has a lot riding on it for many players.


Very good point. There is really no such thing as 'long term.' There is only
'term.' In other words, every stretch of hands played carries with it a
probability-distribution function exactly predicting the likelihood of being
up or down any particular amount. The longer the stretch, the less likely it
is to be way off the mean (expectation).

On the other hand, for every single stretch of hands played on a full-pay
machine, you will be at or ahead of where you would have been had you had
the same hands on a short-pay machine.

Cogno


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John G. Zaroff


I have been playing video poker for about 15 years, heavily for the last 8 years or so. One of the most frequent and confusing discussions is on long-term results vs. short-term results. Part of the problem is that there is no exact definition for long and short term. As with most statistical measures, you have to define it in terms of a confidence level and percentage change from the expected value. Let's take a look at the definition as given on the VPFREE yahoogroup.

'7. What is the long term?  -   Theoretically speaking, the long term is forever. For video poker purposes, the long term is when you have played a lot of hands (several million at a minimum) and actual results are about the same as expected results. TomSki calculates (with a 95% confidence factor) that the actual results for 10/7 DB, played with perfect strategy, should be within 1.0% of expected results after 1,085,465 hands, and within 0.1% after 108,546,482 hands.'

This definition is a little vague. It says 'actual results are about the same as expected results'. Without putting a number on how close, we don't really 'define' the term.

Furthermore, this definition of long term shouldn't make us think that all is well once we hit the long term. First of all, even though we have played over one million hands, the confidence interval is 95%. That means that 2.5% of the results will be greater than 1% away on the positive side and 2.5% will be greater than 1% away on the negative side. Also, let's take a look at what that 1% means. If we play 1,085,465 hands, we have wagered 5427325 coins. 1% of that is 54273 coins or about 13.5 royal flushes. So even in the 'long run', we can be a long way away from being ahead. Since 10/7 DB is .17% positive, there's a good chance that we have hit this 'long run' and still be behind on the game. Not very encouraging. Also, notice that to decrease this delta from the average value by a factor of 10, we have to play 100 times as many hands. Now my 95% confidence interval is only .1%, but that represents a difference in coins of 542730 coins, or 135 royal flushes. Now I am in a longer, long term yet I can be a bigger loser than I was before. What is going on?

As the number of hands played increases, the percentage deviation from the expected value gets smaller but the absolute deviation in terms of coins gets bigger. .1% of 100 million is more than 1 percent of 1 million.

Read the last paragraph again. Even though we play more hands, we can be down more money than we were in the 'short term'. The long term is not a magical time where everything lines up perfectly and my results are exactly equal to the expected value. Long term refers to how many hands are needed to expect to be within a certain percentage of EV with a certain confidence interval. Depending on how tightly you want your expected results, it can take a huge number of hands. Instead of within .1%, let's say you want to be within 0.01% for the Tomski 10/7 DB example. Now you need to play 10.8 BILLION hands and you are still only 95% confident. If you want 95% to go to 99%, the numbers get even higher. Way, way higher. Also, now that you have played this many hands, 0.01% represents a swing of 5.4 Million coins. We can play 10 Billion hands and still be over 1 Million dollars down. Wow.

What does this mean for most players? Not too much. First of all, you don't magically get to the long run numbers. Let's say I play 950,000 hands of 10/7 DB and am down 1.4%, a very bad result. If I play another 135,000 to get to Tomski's long run number, I don't magically jump to only a 1% deficit. The most likely occurrence for those next 135,000 hands is a return of 100.17% (assuming perfect play). This result will move my -1.4% return to date to about -1.205%. Nothing changes dramatically when you hit this long-term number of hands. I can be ahead after 50,000 and be behind after 250,000 hands or vice versa. The long run gives you boundary on how bad things can get.

Some people use this as an argument to play worse machines. They reason that as long as I can be behind in the long run and I'll probably never play enough hands to get there anyway, it doesn't matter what I play. This is wrong. Playing a good machine vs. a bad machine won't get you to the expected value any quicker but the value you are approaching is higher on a better paying machine. Looking at 9/6 JOB vs. 9/5 JOB, the difference in EV is .9954 vs. .9845 or about 1.11% different. Not a huge number. But what this means in the short term is that every 91 hands, I get $1.25 less than the 9/6 version. Even at a leisurely 400 hands per hour, this is $5.50 per hour. 4 hours a day for 4 days and you have $88. That will almost cover your rental car. If someone tells you to play 9/6 JOB instead of 9/5 JOB and they will pay for your rental car, you'd listen.

Using Jacks or Better as an example, the variance of the game is caused primarily by the royal flush. Over all game variance is about 19. If the royal flush variance is excluded, the game variance goes down to 3.5. The royal flush contributes about 80% of the game variance. This is the single biggest contributor to session results. It absolutely dwarfs any other consideration for a short-term session. It's almost impossible to hit a royal flush in 9/6, quarter, single line JOB and be down for the day. Likewise, it is very difficult to not hit a royal and be up for the day. (I'm taking a day's play as 5000 hands). For most recreational gambler who comes to Las Vegas for 3 days (with 6 hours at 600 hph), we can sum up their results as follows: hit no royals, lose a lot of money. Hit one royal, stay pretty close to even. Hit 2 or more royals and make money.

Going back to Tomski's 10/7 double bonus example and the 1% long-term number. We play 1,085,465 hands, bet 5427325 coins. 1% of that is 54273 coins or about 13.5 royal flushes. The expected number of royal flushes is a little over 23. Now let's look at the chances of actually getting this many royal flushes.

RF cycle = 46727. Hands played = 1,085,465. Expected # of RF = 23.5

Rf p(rf)
10  0.00102814
11  0.002171265
12  0.004203241
13  0.007510925
14  0.01246285
15  0.019300908
16  0.028022635
17  0.038292249
18  0.049418412
19  0.060420624
20  0.07017862
21  0.077630923
22  0.081971123
23  0.082790684
24  0.080134262
25  0.074460484
26  0.066527273
27  0.057237779
28  0.047486609
29  0.038038132
30  0.02945395
31  0.022071257
32  0.016022191
33  0.011278527
34  0.007705795
35  0.005114381
36  0.003300151
37  0.002071929
38  0.001266583

So, 75% of the time we will get between 18 and 28 royal flushes. This is far and away the biggest contributor to how profitable your session is going to be. That's why long term number of hands is so large. You have to play enough hands to where your number of royals approaches the expected value for royal flushes.

That 1% difference from expected value in Tomski's long-term number is mostly comprised of the difference in the number of royal flushes we hit and you just can't predict very closely how many of those you are going to hit.

If you know you will hit 23.5 royal flushes in this million plus hand sample, you will probably be within 0.01% of expected value instead of 1%. The more high paying, infrequent hands are in the pay table, the longer it takes you to get to long-term results.

Each royal flush different from the average value contributes .07% to your delta from the long-term value. Once again, even though RFs are fairly rare, they are a big contributor to the rocky ride of video poker. To me, the short term is where you can still be ahead even if you don't hit a royal.

So, the longer you play, the more your long term results look like your long term royal flush results, at least for Double Bonus. Triple Double will have long term results similar to your long term RF, aces w/kicker and 2-4 w/kicker results.

What this tells you is that the biggest contributor to your spread in play results is the hardest to predict and the most volatile contributor to your results. That's what makes long-term results predictions so imprecise.

Looking at the DB results from Tomski, I don't think most recreational players will be comforted to know that only about 2.5% of the time will they lose more than $13,500 after playing a little over 1,000,000 hands.

Dunbar has a great program that looks at short-term risk of ruin for different video poker games. This program will answer the question ' How much can I lose playing single line, dollar , 9/6 JOB with .3% cashback if I play 600 hph and I play for 12 hours?'. This shows the low end of your results. The one thing no software can show is how well you will do in a given number of hands. You can figure out confidence intervals and expected values but huge swings both negative and positive will happen. If you tell me how many royal flushes you will hit in a given number of hands, I can tell you pretty accurately what your results will be. Without that knowledge, the uncertainty of your results increases.


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