Recently I posted an article concerning winning a Louis Vuitton handbag at an invited-guest event at the M casino. I said that I had played $100,000 in coin-in before the drawing so that I would continue to receive invitations to such events in the future.
Nobody told me that $100,000 in play was required. There is no magic formula that tells me how much to play in such circumstances. It’s done by feel. The better the invitation, EV-wise, the more I play. The nicer the casino, the more I play. If I’ve been winning at a place recently, I tend to play more. If I “have time,” meaning I’m not trying to squeeze several events (including non-casino activities) into a short period of time, I play more. Possibly no other player came up with the $100,000 figure for that event. This doesn’t mean that any of us are necessarily right or wrong. Each player has to work it out for himself.
It also depends on the available games, slot club, and other promotions. If my play will earn entries to one or two additional drawings in which I think I will have decent equity, I’ll tend to play more.
If I lose a lot early in a promotion like this, I tend to quit. Why? Because a major purpose of the play is to keep the invitations coming. If I lose $3,000 for an event with an estimated EV of $500, the casino marketing department is happy. They got what they wanted. Clearly, I’m a desirable customer in their opinion. (If there were other promotions going on in that casino, as is usually the case, I might continue to play because I’m getting equity elsewhere. Being behind $3,000 or any other number is not a particularly meaningful event.)
Against this background, I received a question on the gamblingwithanedge.com forum that asked how much bankroll would it take to play $100,000 coin-in in Jacks or Better or Deuces Wild? I was vacationing at the time, so I didn’t respond immediately. I’m going to address this now.
This is an important thing to address before you start to play. You don’t want to tell your wife, “They gave us a $150 Dooney and Bourke handbag. We didn’t win the Louis Vuitton bag. Worse, other than the handbag, we’re flat broke now.”
Important though it is, the question isn’t anywhere near specific enough to be able to answer. What pay schedule are you talking about, what denomination, and what kind of game are you playing? That casino has 9/6 Jacks or Better and NSU Deuces Wild for dollar single line. Fairly fast players would take 25 hours to play $100,000 on such machines. These are not appropriate machines to play for such an event.
To get credit for “playing for an event,” pretty much you have to play that day. For a high-roller event where you intend to play $100,000, that probably means on $5 or $10 machines, or maybe $1 Ten Play, or 25¢ Fifty Play. Something like that. Each casino has its own mix of games. You have to check out each one before you decide what game to play. To be invited to this event, you needed to have played $800,000 coin-in over the previous January – June or July – December period. There are a few players who earned that status by grinding it out on dollar single-line games, but not too many. Most of us played larger games.
For a given game and pay schedule, playing it in the $5 version, $10 version, $1 Ten Play, and 25¢ Fifty Play versions required four different bankroll calculations. 9/6 Jacks or Better or NSU Deuces Wild don’t exist for these stakes at this casino. 9/6 Double Double Bonus does. Is that the game you want to know about? That game requires a significantly bigger bankroll than Jacks or Better — for a number of reasons.
The best tools to figure out bankroll are Video Poker for Winners and Dunbar’s Risk Analyzer for Video Poker. They each have their strengths. I use both.
Use them and you’ll see that the bankroll required is a probabilistic number. That is, if you are willing to accept a 10% risk of ruin, you need half the bankroll as if you are only willing to accept a 1% risk of ruin. What level of risk are you comfortable with?
You’ll also see that playing $5 machines is less risky than playing $10 machines. So what denomination do you want to play? On VPW, you’ll see that playing $1 Ten Play requires significantly less bankroll than playing $10 single line.
One person posted on the forum in response to the bankroll question that if you assume you’re not going to get royals, straight flushes, or 4-of-a-kinds, playing 9/6 Jacks will cost you about 9%. Although we might quibble whether it’s closer to 8.5% or 9%, this is basically correct. And, to me, essentially irrelevant.
This looks at bankroll calculations as a worst-case scenario. Assuming you’re talking about a $5 game, you’ll typically get around 9.5 quads per $100,000 coin-in, almost a half of a straight flush, and a tenth of a royal. Assuming you’re going to strike out on all of these is a very small number — on the order of 1/20,000. Could it happen? Sure. Will it happen this weekend? Almost certainly not. Will it ever happen to you? Probably not that either. If you had one of these promotions every week, this would happen once every 400 years. Good chance you’re not going to live that long.
And if you have some sort of a stop loss figure (for me, I indicated that if I lost $3,000 and this was the only promotion I was playing for, I would probably quit for the day) you’re not going to lose 9% of the entire amount.
So, my suggestion is to get one or more of the software products and wallow in the numbers. Over time, you’ll get a sense of what each game costs to play. You can tweak the parameters so that they are appropriate to the actual games you are playing at any particular casino.
I know that wallowing in the numbers is tougher for some than others. Still, that’s what it takes to become proficient in this game. If you can’t, or won’t, do this, getting good at video poker is a pretty difficult goal for you.
Being difficult doesn’t mean impossible. Richard Munchkin has said on the podcast that since he wasn’t particularly good with math, he teamed with others, some of whom were very good with numbers. Richard had a considerable number other strengths.
This is a LOT more useful information than coming up with a specific number and saying THAT’S the amount of bankroll you need. Any such number would need to be qualified twelve ways from Thursday and would be meaningless in real life situations.
Finally, whatever the bankroll calculators say, you need some experience to make sense of them. For example, the M has a senior drawing every Tuesday. (Obviously some of my readers aren’t eligible for a drawing where you must be 50 years of age or older.) Playing $100,000 coin-in improved my equity in that drawing. By how much? Who knows for sure? Possibly $50 or $100 more? Probably more than that, but I don’t have enough information to calculate it exactly. And even if I did, it would only be an average amount. I COULD end up with first prize of $1,500 or strike out altogether. If I calculated an average win of, say, $263.42, it will NEVER come out to be exactly that. And the casino had a couple of other promotions going on as well that are also hard to analyze accurately but playing an extra $100,000 helped my chances in those promotions as well.
And I like the benefits that come from having ICON status there. If I haven’t reached the $800,000 threshold for this six-month period, playing $100,000 is worth more to me than if I’ve already qualified. Things like this aren’t covered by the software analysis but are nonetheless important considerations in the winning process.
I think the rule: bankroll equals 4 times royal flush payout is a good rule. It has worked for me. I have played for 20 years and have never run out of money.
4 royals seems excessive for a session bankroll, that would fuel one hell of a bender. I can’t see Bob taking out a marker for $80,000 to play single line $5 jacks. Besides, he stated above that he had a $3000 loss limit, so the safe thing to do is to bring just $3000 into the casino, and to stick to that loss limit. If you gamble without a loss limit, or can’t stick to a loss limit, that’s one of the signs of gambling addiction. The question then is how long would that last on average and what are the odds of making $100,000 coin in. These questions and more can be answered with the above mentioned software. The prepared gambler should know these answers before starting, and if the are unacceptable, the gambler should find another gamble to risk their money on.
For what it’s worth, since March, I am minus five royals on .25 single-line FPDW. This is not the first time I have sustained losses of that size–it’s about the twelfth. I think you actually need more bankroll than the math gurus say you do.
For instance, suppose you feel that four royals is enough of a bankroll. Well, fine, but in the short term, you could lose 25%, 50% of that bankroll–and all of a sudden, your RoR is high enough that you’ll have to either lower your standards or quit. So you actually need whatever bankroll you ostensibly require PLUS enough of a cushion to weather an initial bad run.
There’s even more to consider. Say you have a $10,000 bankroll. You lose $4,000 of it. Will you have the “faith” to soldier on? Would you keep playing if your roll dropped to $3,000? $1,000? If there’s a point at which you would throw your hands in the air and quit, then your REAL bankroll was the difference between $10,000 and that number. What I’m getting at is that bankroll is as much a psychological construct as a mathematical one.
There’s a difference between session bankroll and total bankroll, my understanding was that this was a discussion of session bankroll. Also, if you find your results are different than those predicted by statistics, chances are your error rate is higher than you think it is. You hear people saying the EV for FPDW is +0.76% or whatever, but this is only the computer perfect EV which probably no one actually achieves in a casino environment, even Bob Dancer has admitted to making play mistakes, so the real EV might be only +0.5% or even negative. Most players probably lose money on FPDW.
I certainly don’t think I play FPDW perfectly, but I also doubt that I make very many mistakes at this point, as I’ve been playing the game for 20 years and yes, I do practice on the computer from time to time. Probably the vast majority of errors I make are missed penalty card situations, which cost me maybe a penny each when I make them. That doesn’t BEGIN to explain results that are continually three or more standard deviations south of expectation.
Also, I dispute your contention that most players lose money on FPDW (or at least, do so due to errors). Most of the people I watch seem pretty competent at the game. And it would take some pretty egregious errors–like always holding two pair–to wipe out an 0.76% edge.
The larger question of whether casino video poker is honest is one that is still open IMHO. Evan a relatively unsophisticated computer algorithm could reduce the player win rate by 1 or 2 percent and be completely undetectable simply from analyzing results. Then, there’s always skepticism and bias. I recorded over 1,000,000 flush draws on triple play 10/7 DB many years ago and found that the flushes were being filled once in every 6.5 hands–far less often than they should have been. I tried reporting this on various internet forums but got shouted down. So do we, as players, have any defense against being cheated? Can we even TELL when we’re being cheated? Especially when the VP cognoscenti tell us that our huge losses are meaningless because they’re just “negative fluctuations”? At what point are bad results something other than just bad luck or bad play?
I took another look at your 5 royals down in FPDW. Assuming you are playing at +0.76% or have enough freeplay to cover your error rate: the risk of losing one bet by my reckoning is 0.9993527 so the risk of losing 5 royals or 4000 bets is 0.9993527^4000 = 7.5%, so it would be unfortunate to lose that amount but sadly not all that rare. Certainly, the more you play, the more you will see 5 royal down losses. Personally, I’d go with the Kelly system which features zero risk of bankruptcy and is the only system that works, for what it’s worth the Kelly number is 2925. As far as things being fixed, it’s been done before, I see no reason for it not to happen again plus these days seems like basically everything is fixed, so …
On error rate, the issue isn’t your knowledge of strategy, anyone can get that with a smartphone app, the issue is your ability to perform in the casino environment. You can get a rough estimate of that with most of the trainer software, they have a “log errors” mode, so it doesn’t tell you right away you made an error, instead it logs errors to a file that you look at later, you play say a thousand hands as fast as possible, then check your results for errors. Also, you need to simulate the casino environment: spotlights aimed at the screen which causes eye strain, two sources of high volume high distortion teeny bopper music which causes long term ear damage, some video distraction like a stripper movie or youtube cat videos or something, and so on. Now you could wear noise cancelling headphones and polarized glasses, try that and see what happens to your error rate, and so on.
Liz wrote, “I took another look at your 5 royals down in FPDW. Assuming you are playing at +0.76% or have enough freeplay to cover your error rate: the risk of losing one bet by my reckoning is 0.9993527 so the risk of losing 5 royals or 4000 bets is 0.9993527^4000 = 7.5%, so it would be unfortunate to lose that amount but sadly not all that rare. ”
That’s a very sharp comment, Liz! It might have been clearer if you’d written “the risk of losing a one-bet bankroll” instead of “the risk of losing one bet”, but, regardless, it shows a real understanding of how long term risk of ruin is calculated.
What Liz is saying is that if you try to play $1 FPDW with a $5 bankroll (that is, one bet), you will go broke 99.3527% of the time. Obviously no one will try to play with a $5 bankroll. But, once you know that number, you can get the chance of losing any bankroll from 99.3527%^Z, where Z is the number of bets in your bankroll.
Liz’s 7.5% figure is the long term risk of ruin for playing with a 4000-bet bankroll. (ie, 5 RF’s). It assumes that the game is being played endlessly, until the player is either unbelievably rich or broke. Even though Kevin said he was 5 RF’s behind since March, that’s not a “long term risk of ruin” question. His risk of being so far behind can be calculated with other methods if we know how much he played. If we assume that he plays a huge amount, say 20 hours a week at about 500 hands/hr, and say it’s been 30 weeks, than the chance of him at some point being 5 RF’s behind is closer to 2% than 7.5%.
As Liz pointed out, it’s unlikely that Kevin is playing the game with a 0.76% edge. Most serious players I know subtract at least 0.1% from the theoretical return to account for errors, Using a modest 0.15% error rate, then the chance of Kevin being 5 RF’s behind at some point since March (under the previous assumptions about the amount of play) rises to almost 4%. As Liz suggested, not a rare event at all.
I want to add a note of appreciation to Bob who, in this blog post, mentioned my software along with his own as “the best tools for figuring out bankroll” questions. I’ve never met Bob and we’ve never worked together on anything. His including my software in the blog post was quite a generous act.
–Dunbar
“The larger question of whether casino video poker is honest is one that is still open IMHO. Evan a relatively unsophisticated computer algorithm could reduce the player win rate by 1 or 2 percent and be completely undetectable simply from analyzing results.”
Kevin has talked about this before and I appreciate his posts. Especially because nobody wants to talk about it. Are the chips gaffed? Is there a way to gaff the chips and still get approval from the Nevada Gaming Commission?
Oh well. Let’s talk about trucks! I like trucks!
Almost always, when stuff like this gets settled, there’s a gag order included, so it doesn’t get talked about. I’m sure Bob Nersesian and his pals could tell you stories, oh but wait, there’s a gag order, so he can’t. You might think there is freedom of speach, but actually, there isn’t. It’s important to separate reality from propaganda.
Regarding gaffing, you can purchase a simple tally counter for around $4 from Big 5, Walmart, Office Max, etc and then use it to count the number of hands (delta) between some premium hand occurring (it’s a non-electronic device and is perfectly legal to use in a casino). For example, using the 4K in OEJ. I’ve found that when betting $.05/hand versus $1/hand (20 coin $.05 denomination 97.95% payback OEJ is used, 1 unit versus 20 units) and then doing a T-test for the .05 delta sample and the $1 delta sample with 100 deltas being recorded in each of the two samples, that the two sample populations are different at the 0.001 significance level, with the average delta for the $1 delta 4K being ~40% higher than the $.05 delta (73.8 hands until a $1 4K versus 52.7 until a $.05 4K). Try it with your favorite game (on the same IGT machine) and two much different denominations and see what happens.
Posting this probably leaves me open to a nail gun incident.
Do not worry Nail Gun. Everybody understands exactly what you are posting and appreciates your hard work.
I have a couple of clicker lap counters for when I run laps. My wife has a clicker counter she attaches to her golf glove for when she plays golf to keep track of her strokes.
What you are talking about is tantamount important. Why?
Ticket in ticket out.
Back in the old days of coins, you could look in your tray at the machine and have some idea of how your play was going. Ticket in ticket out destroyed this.
Ticket in ticket out was originally touted as a labor saving idea, a way for players to play without getting black stains on their hands, a way for players to play without waiting for a hand pay (under $1,000), a way for players to play without having to wait for a slot tech to clear a bent coin out of a jammed machine, and other positive casino baloney. (I remember old women playing coin slots with white cotton gloves on.)
But the real benefit for the casinos with ticket in ticket out is that you could not put $20 through a machine and have any idea of how you were doing.
What you are talking about is absolutely true. You put $20 into a $1.00 machine. You play a hand or hit spin. Each time, you click your little plastic counter. After 20 clicks on your counter, you look at the credit meter. If you have 19 credits, that’s not so bad. If you have 30 credits, woo hoo! If you have 5 credits, get up and leave quickly.
You are right, sitting at a slot machine or a video poker machine and clicking away on a plastic counter sounds kinda dumb, but what you are talking about is smarter than most can ever understand.
Ticket in ticket out took away more than most players will ever know.