On the website gamblingwithanedge.com, there are numerous things posted — including my blogs and all of the GWAE podcasts. There are other bloggers on that site as well. One of the features of that site is that there is room for comment.
In a comment to my March 27, 2018 blog, “Liz” wrote, in part:
Many gamblers think they are “advantage players”, meaning they think they have an edge. I see six classes:
1. Gamblers like Dancer who have the edge but won way more than average
2. Gamblers who have the edge but won way less than average or even lost because they didn’t play enough or ran out of money
The remaining categories dealt with those who do not have an edge. When I first read this, I wondered if indeed I was in the first category and, if so, what did it mean. That’s what today’s blog is about.
However you define these things, there’s got to be a category in the middle of these two. The first one says “way more” and the second one says “way less.” Surely there are APs who have won less than “way more” and more than “way less.” This middle category is likely bigger than the other two put together.
How much you win each year is income. How much you’ve won and held onto is gambling bankroll which is a measure of wealth. I assume Liz was speaking about accumulated bankroll.
Accumulated bankroll is a lifetime achievement award. I’ve been doing this since 1994. I have been successful since then and have continued adding to my accumulated wealth. It stands to reason that I would have accumulated more than someone who started in 2015.
How much you started with surely is a factor. I started with $6,000 back in 1994. Many other players have started with more.
How good of a saver you are is important. In the years that I’ve been playing, it’s been both me by myself and me with two wives (at different times.) All three of us are very frugal. For every $100,000 we brought in, we spent perhaps $40,000 and invested the rest. Over decades, that added up.
Without going into details, going through a divorce is detrimental to the bankroll.
Someone with extra income that they deposit into the bankroll account makes that account increase faster than someone without extra income. That income could be from a job, alimony, inheritance, sale of an asset, royalties, or selling your services. Social security or disability payments or retirement income may be added in as well. I’m sure there are other sources of income that I’m leaving out, but those who have some accumulate bankroll faster than those who don’t. And the mix of income sources is different for every player.
Your investment strategy (and results) matter. Timing matters. If you invested $100,000 in the stock market in 2003 you have quite a bit more than if you invested that same amount in 2000. Even so, if you’ve kept that money in until today, in either case you have more than $200,000 today.
How good are you at avoiding taxes? Tax avoidance is legal. Tax evasion isn’t.
If you’ve had “average luck” over your playing career, your results will be average if that average result happened on all of your stakes. But if you’ve been very lucky for quarters and somewhat unlucky for dollars, overall you might be in the hole. In my Million Dollar Video Poker autobiography, I wrote of a six-month period where I was luckier than average on pretty large machines.
There’s always the question of skill versus luck and I don’t know how to come up with an exact number. In drawings, I’ve won more than $1 million over the years. But I’ve participated in a lot of them. I only entered when I thought it was a good deal. I’ve read the rules closely and paid attention to ways to gain an advantage over players who haven’t read the rules. I’ve bent tickets in casinos where that seemed to work. I put physical tickets into full barrels just before the drawing took place, knowing full well that the drum was too full to thoroughly mix the tickets. I’ve played for the drawings when other things were going on as well — such as point multipliers, or additional drawings, or earning annual tier credits, or something. How can anyone say how much luck was involved in my results and how much skill?
There are no records anywhere of exactly how many tickets have been in each barrel and whether my results have been better or worse than average in drawings. There are also players who play $500 a week and enter the same drawings where I play $200,000 a week, and to those people, it appears that I’m the luckiest guy in the world.
Keeping your welcome in casinos is a big part of success. Over time, all successful players lose their welcome at various places. Avoiding or delaying your exodus is valuable, as is talking your way back in.
Belonging to a relevant network of informed players is valuable. There’s a balance between sharing enough information to stay networked and sharing everything. There are people you can swear to secrecy and those you can’t.
Just plain scouting is valuable. In every casino, things are different today than they were a year ago. If you’re not aware of those differences, you can’t make informed decisions.
Players differ in their risk aversion. For a given bankroll, some players will bet bigger than others. Some of these bigger players get wiped out, but most don’t. The smaller players won’t get wiped out, but they won’t earn very much either. There are disadvantages to wherever you position yourself on this.
I’m going to talk about this more next week, including how close to the cheating line you are willing to go. Do you ever cross it? Some players have prospered using techniques that the rest of us consider “foul play.” But they have prospered nonetheless.
Liz’s paradigm has some merit, but it’s impossible to figure out these things exactly. Every AP has a different game plan than every other one, and their results are very hard to compare.
My guess is the folks who are closer to (1) are more willing to put in the effort and hard work than those who are closer to (2). I perceive, even though you stress often, many folks just do not understand how much work it takes to get to (1). We all want to be (1), but few have the work ethic. This column is a good one. Thanks.
The math is actually pretty simple. If you’ve won more than your EV, you’re lucky, if you’ve won less than your EV, you’re unlucky. Don’t make the common mistake of confusing your EV with the computer perfect EV, almost always your true EV in a casino environment will be less than the computer perfect EV and your true EV is the one that counts. The following numbers are totally approximate and are meant as a rule of thumb and assume a normal distribution and so on, feel free to derive the exact numbers: but anyway, plus or minus about a half of the SD is about a third of the possible results, minus about a half of SD or more is about another third and plus about a half of SD or more is about the other third, so there you have it. As Dancer correctly says, there is a middle ground, around a third of gamblers will “experience” (I love that as a marketing term) being within plus or minus a half SD of their EV, while around a third of gamblers will “experience” being screwed with minus a half SD or more below their EV and the other third will “experience” celebrity fame and status with positive a half SD or more over their EV. SD is the square root of variance times the number of hands (sqrt(var x hands)), the more you play, the larger it gets. There is no convergence of SD to EV in the long run, or the short run for that matter. Regardless of number of hands played, about a third of gamblers will be unlucky (results less than EV-SD/2), about a third of gamblers will have about average luck (results within +/-SD/2 of the EV), and the remaining third of gamblers will be lucky (results greater than EV+SD/2).
Correction: there is no convergence of SD to zero. There is convergence of SD to EV, that is Nzero (occurs at variance/EV/EV hands). But SD always increases, it never decreases.
For one hand of breakeven jacks or better (976 royal) using maxEV strategy, the chances of hitting the EV (getting a push) are the same as the chances of hitting a pair of jacks or better, namely 21.27%. The chances of losing your bet are 54.78%. The rest, 23.95%, get lucky and get more than their bet back. Jazbo.com has the curves for 1000, 5000 and 10,000 hands. At 1000 hands, the chances of hitting the EV are 0.65%. At 5000 hands, the chances of hitting the EV are 0.26%. At 10,000 hands the chances of hitting the EV are 0.16%. The more you play, the less likely you are to hit the EV. You are far more likely to get less than the EV (unlucky) or more than the EV (lucky).
So 19.15% fall within half a standard deviation on each side. 38.3% are within a half standard deviation of the mean. So your one third oversimplification is not actually too bad. Take it out to one standard deviation and you capture 68.27%. One standard deviation seems more meaningful. If you are within 1 SD you are neither lucky or unlucky. This is the case Bob is talking about where the group within a SD is larger than those that are lucky and unlucky combined. After a million hands of break-even $1 9/6 JoB (976 Royal) your EV is 5 Million. 1 SD is $22,100. So a player that is 1 SD to the good has $5,022,100 instead of the true EV of $5 million. That 22,000 does not make one boast. A million hands is almost full time for a year. The true AP’s are not playing to break even…nor are they lucky or unlucky. They find a small advantage and exploit it millions of times or even 20 to 50 million times. Possibly a 100 million times in the case of the 100 play full pay deuces that no longer exist.
The coin in would be $5 million, the EV is 0. +1SD would be +$27,459, -1SD would be -$27,459. (Variance of 976 jacks is 30.16).
If you divide the possible results into roughly equal thirds, it looks like this:
Bottom unlucky third loses more than $13,730
Middle third has results somewhere between losing $13,730 to winning $13,730
Top lucky third wins more than $13,730
If you were to increase the number of hands to say 10 million, these numbers would increase, not decrease (SD/2=$43,417@10millionhands). The more hands you play, the bigger the numbers become.
If you want to be slightly more precise, the boundary is closer to SD/2.33
These comments presume a 100% game exactly. What competent player would play an even game? You need an edge to make it worthwhile. If you want to crank out these numbers with a 0.3%, 0.6%, 0.9% or whatever edge, knock yourself out, but a 0% edge is not for winning players.
All these comments infer you can calculate the edge precisely. In the real world that’s simply not the case. You don’t know for sure how many tickets are in the drum. You don’t know for sure how much your mailer is going to be. You don’t know if and when the game will be removed — or you will — or if the slot club will be reduced. All the math skills in the world can’t eliminate these uncertainties.
Nice article Bob. I seen that your buddy Anthony Curtis was mentioned in this article yesterday… http://www.latimes.com/travel/lasvegas/la-tr-las-vegas-fees-may-mean-fewer-visitors-20180501-story.html
Unfortunately, I don’t have the time to contribute in the depth that I would like this time around, but I do want to share the following –
Liz’s second class of player brought to mind a pair of articles Bob wrote in 2003, called “A Different Look at the Difference in Pay Schedules” and “A Continued Look at Bankroll requirements”. My links to these articles are now broken so I can’t share them.
These articles cover a number of points worth discussing in this thread, but what struck me as particularly relevant was how it is quite possible to be a player who plays perfectly and still can run badly over 100,000 hands or more.
Bob wrote: “These comments presume a 100% game exactly. What competent player would play an even game? You need an edge to make it worthwhile.”
Edge is just an offset to the curve, for example on the normal curve, an edge of SD/2.33 would mean about 2/3rd’s of the gamblers are lucky winners while about 1/3rd are unlucky losers:
bottom unlucky third lose
middle lucky third win from 0 to double SD/2.33
top lucky third win more than double SD/2.33
I don’t dispute your math.
The problem is, in my mind, is that nobody can correctly define the edge in real world situations. And the edge for some players is significantly different than the edge for other players ostensibly playing the same game.
For example, different skill levels in the game itself; different knowledge in the way the rules of a particular promotion works; different abilities to extend your welcome when the casino is considering kicking your out; different strategies available to some for reasons of bankroll and/or risk aversion; etc.
Just calling it an “offset to the curve” hides a number of real world considerations. Wallowing in those situations and trying to figure them out is what I’m trying to do. Just knowing that your you’ll be lucky, average, or unlucky each 1/3 of the time isn’t that useful of a predictor. Knowing how to increase your skill level is.
If you can increase your skill level enough, even if you’re in the “unlucky third,” you can possibly still be a lifetime winner.
Ughhhhh. How many times do I have to repeat this. If you need promotions to come out ahead, you are NOT beating the game itself. You’re beating the players club!
You can complain about the wording concerning beating the game over beating the casino all you want, but it’s not going to change my terminology. I consider myself a successful video poker player who utilizes casino promotions as part of the mix.
Bob wrote: “If you can increase your skill level enough, even if you’re in the “unlucky third,” you can possibly still be a lifetime winner.”
I don’t dispute that at all. Mickey Crimm is an example of a gambler who can beat the odds no matter what the gods might throw at him. Of course casinos have enough edge and number of hands that they can effectively beat the odds. The true “Advantage Players” are the casinos.
A couple of days ago, I saw a Bob Dancer blogpost on here on the subject of whether or not APs cheat. I didn’t read the post, leaving it to savor later, since the title seemed especially intriguing. Today when I went to read it, I saw it is no longer there. I found a cached page of the article. I see no reason why it was deleted. I would lke to know the reason that the blogpost was deleted. Thanks for a reply
That’s interesting. You can find it on google cached pages, “Do APs Cheat?” Maybe this website is being hacked?