Harry Porter wrote:
snipped link and other comments re how a casino's "hold" is calculated
... an earlier article by the author provided a very basic
definition of how a casino calculates it's actual hold for a game:
Total chips held at the tables / Total chips purchased
In other words, for a given player if they purchase $500 of chips
during their play and cash in $400 (having lost $100), the casino hold
is 20%.
snip
There are two definitions that actually come into play:
The first is the more stringent one and is analogous to the table
calculation above:
--> Total cash,coin,tokens,tickets held at the machines / total
tokens,tickets inserted
The second is much simpler and frequently is what is referenced is
very common discussion:
--> 1 - (Total Player Coin Out / Total Coin In)
The first equation meets the technical definition. If a player's
total insertions into the machines during their visit is $1000 and
total cashout is $600 (leaving $400 behind at the casino), then the
hold is $200/$1000 = 40%.
But obviously in the course of their play, that $1000 buy-in is
extended to a much larger total coin in (where the total wager of each
play is added to coin in) ... let's say $10000. Having ended play
with a $400 loss, their coin out will be $9600.
Under the second defintion, "machine hold" will be equal to:
1 - (9600 / 10000) = 4%.
The difference between these two definitions explains the disparity
referenced earlier in this thread. It was cited that an article
provided numbers for Louisiana "truck stop" machines that translated
to a 65% hold.
"EEcounter" flagged this as questionable, noting that his
understanding was that these machines typically had around a 10% hold.
The explanation is that the two separate definitions above are at work.
snip
That was my gut reaction as soon as I read the 'truck stop' post; however, I'm having a hard time grasping how the casino or anyone else would be able to determine this figure other than by coin-in vs. coin-out, or slot-club records, or by a mere estimate, which might or might not be very accurate. If anyone can come up with another source, please post it; meanwhile, let's look at the three methods I've mentioned, although I'll cover 'coin-in vs. coin-out' last because I have the greatest concerns with it:
1.) slot-club records -- from which the casino can determine how much of a player's money was played versus how much winnings were re-played; however, this figure is not completely accurate because not all player's use slot-club cards all the time, and I especially doubt that truck stops have such a thing, or that truck drivers just passing through would necessarily bother with getting one; does anyone know if the machines in truck stops even have a card 'slot'? If not, then this completely eliminates what might have been the most reliable source of data that could have been used. And the problem is that without such reliable data, we have no idea where the "... $114 million was wagered ..."-figure comes from, or what "wagered" means. Does "wagered" include re-played winnings from the machine (simply coin-in), or is it just session stakes (what gamblers brought into the truck stops with them)? For sake of illustration, let me proportionately reduce the figures from the original post; let $114 million = $114.00 "wagered" by a single player, and let the $73.8 million in winnings be $73.80 the player had remaining when he left the casino. The player is playing 20 nickels = full coin (a dollar bet per game). If the $114.00 was total coin-in at the end of the session, and $73.80 was coin-out, meaning that only 114 games were played, then the player did, indeed, have an AR of only 65%. But if, on the other hand, the player put $114.00 into the machine, played 10,000 hands (equal to a coin-in of $10,000), and then cashed out with $73.80, then his loss was only $40.20 on $10,000 of play, and so his AR was really 99.58%. Well, the figure keeps changing; if he put $114.00 in, played only 5,000 games, and still cashed out with $73.80, then he lost $40.20 on just $5,000 of play, and his AR was only 99.16%. If he only got to play 1,000 games, his $40.20 loss on just $1,000 of play was an AR of just 95.88%. If he played 250 games, his $40.20 loss yields a pitiful AR of 83.92%. More importantly, since AR depends upon how much replay a gambler gets, how do the truck stops know what that figure is _IF_ then don't happen to have a slot-club card of some sort to track it? How would the machine know if the quarter being inserted into the machine comes from my last winning hand or from a brand new player? If can't and doesn't, and as can be seen from above, the shorter the sessions become, i.e., the fewer the games played in proportion to the money lost (which might be likely for truck stops), the lower the AR.
2.) an estimate -- which could be way off, especially when we wonder what info it is based upon, and who made the estimate. Was it a reporter who doesn't know anything about math or gambling? Was it some public interest group that is trying to expose the evil of VP machines in order to have them banned? Without further info, I don't know that I want to trust an "estimate" too much, and if we happen to not have 'slot-club records', then that pretty much brings us back to 'coin-in vs. coin-out'.
3.) coin-in vs. coin-out -- this is the figure that all of us are familiar with, but as Harry pointed out, it _should_ (based on all of our sensibilities and experiences) reflect a much more conservative figure, and so the 65% _just_doesn't_seem_right_ by this method; i.e., coin-out divided by coin-in equals the actual return of the machine, and so 65% was approximately the percentage of ACTUAL return reported in the original post. I think we can all agree that $114 million pays for enough games to represent long-term play, and that a 65% AR (actual return) on machines with a _supposed_ ER (expected return) of about 90% is more than a statistical anomaly or likely to be explained merely by pathetically poor play with complete lack of strategy. It would be interesting to see what sort of AR a monkey would get just randomly hitting buttons on machines that have an ER of 90% - and this is not to suggest in the least that truck drivers are no more skillful, but just that monkeys would at least give us a bottom line below which we could very reasonably begin to suspect that the machines are rigged. I could work up some math on monkeys, but I don't want to waste my time speculating without at least some idea of what sort of paytables the truck stops have; does anyone here know? Just for the hell of it, I ran this JoB paytable -- 1,1,2,3,4,5,10,20,200 -- through WinPoker and it analyzed it as having an ER of just 66% (perfect strategy), so obviously it is quite possible to create VP which will result in a 65% return, or even lower; the question remains whether anyone would ever play such a game, but folks who don't know squat about VP might actually do so.
Now, the problem with concluding that a 65% return (when that figure is determined by coin-in vs. coin-out) _MUST_ be wrong simply because it is too low for us to imagine, is that it assumes that the machines are honest, and it also assumes that the aforementioned _presumed_ 90% ER is accurate. But I have to wonder, with the government being a player (receiving a cut of the profits as taxes), whether the ER is necessarily as high as the aforementioned 90%. To begin with, states have no qualms about using lotteries which have deplorable returns of only about 50%, so unless someone can show me a written state law that requires the VP in truck stops to pay at least 90%, I'm inclined to suspect that the machines really do have a horribly low ER, and possibly as low as 65 or 70%. Second, does anyone know how closely Louisiana gaming control monitors truck stops? It sounds like there are lots of them, and gaming control could be turning a blind eye for any number of reasons, such as being under-staffed, bribed, threatened, lazy, indifferent, or whatever. I'm not stating that the latter is true, but why should we _assume_ that it is not?
I know that this has been a long post, but once I got into it ... well ... I just hope that someone finds it helpful or interesting.
Cheers.
Bill Velek
