September 13th, 2002
|02:57 am - World's first interesting slot machine|
I once interviewed for a job designing games for slot machines. Unfortunately, I didn't get the job; my C++ skills weren't nearly up to what was required and I felt I interviewed quite poorly in a number of ways. (Let's just say that one of the company employees had the first Tamagotchi that I had ever seen.) I don't play slot machines, but today on rec.games.board I read about one which is far more interesting than most.
It's called Cash King Checkers. You can play it at the manufacturer's site online - obviously, neither winning nor losing money. (I dare say that online casinos will add it soon if it takes off.) Now previously I thought that playing no-money Internet slot machines was about as degenerate as gaming experiences got, but this is one actually strangely satisfying.
I think it's fairly generally known how British slot machines work. Effectively, they have a number of different moods. If you can catch one in a generous mood, it is likely to pay out more money than it takes in while it remains in its generous mood. Once it has paid out, it reverts to a less generous mood where it will take in very large amounts of money while seldom, if ever, paying anything out. It's not guaranteed to pay out even in its most generous mood, and I'm not sure that machines can generally get into a mood where they won't pay out at all. Telling what sort of mood a machine is in is deliberately non-trivial. Many/most machines have a mode - not a mood! - by which you can gamble a small win that you have already obtained against a possible larger win; some say that the way to play a machine is to force it into its most generous mood by repeatedly gambling away your wins until it has so much money that it decides to pay the jackpot. If you can start sufficiently close to the jackpot-paying mood then you can release the jackpot at a cost rather less than the jackpot's value. That's the theory, anyhow.
Interestingly, different countries around the world have very different sets of slot machines legislation. I can remember reading that Dutch slot machines must have an equal chance of displaying each combination of symbols every time and must display the reel distibutions on the body of the machine, so they effectively play completely fair and you can work out the expected return of play in advance.
British legislation splits pay-for-play prize machines into two types: Amusement With Prizes (slot machines) and Skill With Prizes. The latter machines typically include quiz machines, but there have been some interesting arcade-game-style machines with cash prizes over the years. Many quiz and game shows have been translated into SWP versions, with varying degrees of success. It's a pretty small market, though, because legislation variations tend to make it relatively impractical to produce machines with international appeal. (I think I remember learning that most SWP machines are made in runs of about 650, which makes pinball machine manufacture look mass-market - and we know what sad state that industry's in.) There is generally fairly little trust of SWP machines among sober players; the prevalent feeling is that of a vicious circle - you'll lose unless you spend considerable time and money mastering the machine, and there already are bigger experts at the machine than you can become. That said, people will evidently pump the cash in when they're drunk, which is why you tend to find the machines in pubs.
There do seem to be more and more bar-top simple machines which frequently offer a wide variety of activities while not paying prizes around the world, though. If they're not paying prizes, then they have worldwide appeal. The state of the art in the UK is the itbox, which offers a variety of ways to
waste spend your money. Even porn, apparently.
Video poker is a well-known form of gambling in the US. Indeed, many of its followers like it because there are specialised situations when sufficiently large progressive jackpots make the expected return positive - that is, if you keep playing until you get the jackpot from a Royal Flush, the size of the jackpot means that it's likely to be worth the effort. This could well take several hours' effort, though, so it's a heck of a way to play. US legislation requires that the games play fair - when they claim something is random, it really must be random - and that the result of any one game is independent of that of any other, so even a machine which has been paying out relatively large amounts recently cannot move itself into a stingier mood, unlike the British machines. There is great effort made, possibly wisely, possibly led by superstition, to find out which machines (if any) are set to be more generous than the rest. Does the old legend that the machines where the players are most likely to be seen tend to pay out the most have any validity to it? I couldn't say.
"Cash King Checkers" is effectively video checkers. We call checkers draughts in the UK. Don't get me started on the issue of related draughts games with confusingly similar names around the world. In Cash King Checkers, you start with three kings (one-space jumps forward and backward, diagonals only) on the near row. A number of enemy checkers are distributed at random about the board. The more checkers that you can take, the more credits you win. You get to choose how many enemy checkers there are to take on the board, paying a credit for each one. (You are also able to multiply the stakes and prizes throughout by up to five.) The game has been designed so that you stand to get the best returns from playing all nine checkers.
The game engenders a pleasant sense of feeling busy in that you have to proactively take draughts when you can, rather than letting the machine do all the work for you. You often have choice over the best way to play, though more often than not (perhaps twice in three) the choice is between two options of exactly equivalent reward. About one game in 15 or one game in 20, though, you really do need to think about how to play in order to maximise the number of draughts to take. The decision is almost always pretty easy, but just about meaty enough to be interesting and not so difficult that the average player won't be able to cope. The old stories about clueless-drunk players sitting down to play poker, leaving everything to the dealer and only saying "How much money do I lose?" are based in reality, after all.
Interestingly, the distribution of the checkers does purport to be completely random and the house edge comes from payment schedules which are, as ever, not commensurate with the true odds. The casino operator can set what sort of percentage the player can expect to achieve - this Strictly Slots Magazine article relates the different payout tables that might be found to the varying expected returns. Interestingly, apparently the machine can be set to pay out 101% of what it takes in over time, subject to perfect play.
A large part of the payback comes from the fact that ocasionally one of the checkers on the board is gold. Taking the gold checker puts you into a bonus game. Apparently the gold checker only appears when you play 5+ checkers at a time and happens most frequently when you play 9 checkers.
The bonus game has twelve rounds. In each one, you pick one of four checkers, each of which conceals a credit bonus or a token which will end the bonus game. There are no "end" tokens in the first three rounds, one in each of rounds four to nine and two in round ten. (Presumably also two in rounds eleven and twelve, though I don't know for sure.) There is no risk involved - if you find an "end" token, you still receive your accumulated bonus winnings to date, it merely concludes the round. Completing all twelve rounds earns the Gold Checker Bonus. Thus you have a 729 in 4096 chance of clearing rounds four to nine and presumably a one-in-eight chance of clearing rounds ten to twelve (possibly 1 in 16 or 1 in 32 - I haven't seen the exact distribution of rounds eleven and twelve) - so it's going to take you many tens of bonus rounds before you crack the Gold Checker Bonus. The expected return of the bonus game is apparently 115 credits (multiplied by your original stake, be it one credit per checker or five credits per checker) so a large part of the return depends on a few good bonus rounds.
The game exhibits some interesting psychological tricks. It encourages you to play nine checkers per game at five credits per checker, 45 credits per deal. Strictly Slots claim that something like 37.8% of deals will result in no checkers at all being available, which is a very quick (two seconds) way to lose 45 credits. That's not the cost of a single play - typically five cents - but forty-five times that much. Taking one checker only returns 10 credits for a 45 credit stake; "You win 10 credits" looks very impressive on-screen, but isn't impressive when you consider that you've had to wager 45 to return 10. (Not to win 10, to return 10; the net result is a loss of 35, not a loss of 45.) Even two checkers matching only gets you your money back, which is infrequent enough. Three checkers returns 15 for 9, which is a very small win; British slots generally don't bother with any prizes less than twice the original stake. Actually, these days, they don't bother with any prizes less than a pound, whether your original stake is 20p, 25p, 30p or 50p. You need to get into the 4+ checker results, or to the bonus game, to get any sort of real result. I've had 5-checker results a few times, but never a 6-timer.
The overall result is a hypnotic and entertaining game. I have managed to blow 10,000 credits on it already - specifically, pumping 2,000 credits in and reinvesting my winnings until everything is gone, five times. My record time for blowing 2,000 credits - which would be $100.00 at five cents per credit - with optimal decisions, as far as I can tell, is under 13 minutes.
Would I do this were it a real machine playing for keeps? No - I haven't played a slot machine for, ooh, fifteen years. I once lost a friend as a child by lending him £1 - which might not even have been my money - to play slot machines, which he then went on to lose. He decided to sever civility towards me rather than face repaying his money. A very interesting guy indeed, but evidently not a resilient character. If you ever read this and recognise yourself, I bear no hard feelings - the incident forgiven, but never forgotten...
That said, I do like the idea of playing every gambling game in a casino once and this is one gambling game that I would quite look forward to playing, especially if I could ever find it set to pay back 101% in the long term. On rec.games.board I said "if I ever wanted to play a slot machine with a negative expected return, this would be the one I'd play". That said, I do occasionally play the National Lottery when there's a multiple rollover; I have convinced myself that my utility function is sufficiently irrational that there are rare times when it's actually in my interest to play the lottery.
Today's discovery leads to two outstanding questions. Firstly, do we necessarily believe "Strictly Slots"? Their figures do seem entirely plausible and consistent with my experience; after all, I haven't yet hit one of the six-checker or more results or the Golden Checker Bonus, which would theoretically be enough to convince anyone to take the money and stop playing. However, I certainly note that I didn't seem to get the Golden Checker turning up at all until I'd lost my first 2,000 credits. There's one hard constraint to a cash-based slot machine; it can never pay out more than what goes in, either from the players or from the operator at the start. (If Cash King Checkers is based on a stored value system where the casino's cashiers deal with the dirty money and the machines themselves never touch it, this objection is purely theoretical.) I'm not sure how wise it is to be sceptical about apparently-impartial industry magazines; they have a lot to lose by not playing fair or by promoting falsehoods.
Secondly, why would Cash King Checkers' manufacturers, Leading Edge Design, let people play the game for free on their site? I suppose the theoretical upside of demonstrating to casino operators what a fun game it really is must exceed the theoretical downside of cheapskates like me finding out what a fun game it is on their web site rather than on a casino. I'm not sure I'd agree with that decision myself, but that's why they're in the business and I am not.
Leading Edge Design's site also links to a number of other articles about the machine - for instance, one about the machine's development and another about the machine from its manufacturer, IGT. (IGT aren't the same company who manufacture the Michael Buffer slot machine, by the way.)
A different area for discussion is that of the general future of slot machines. brakusjs sporadically reports from visits to Atlantic City where he plays new slot machines with game show themes. He generally tends to do pretty well at them, too. (I don't wish to question Jeremy's veracity, but as a general question: does anyone ever admit to having a shocking losing session on fruit machines? It's acceptable - and even macho - to lose at poker if you either learn from the experience or get some good stories out of it, but slot players don't have the same compensations.) They do sound like a lot of fun to play, but I'm sure I would get a good 95% of the fun at 0% of the financial risk by simply watching a friend play them.
When I went for interview with Bell Fruit Manufacturing (no job - no link!) they asked me to prepare a design for a new fruit (slot) machine for discussion. This was quite entertaining to research - I made a useful but short-lived contact in a travelling regional manager of a local chain of arcades and got his perspective. My proposal was for a two-player fruit machine, "Left and Right", designed to be suitable either for solo play or for co-operative play by two friends. Some modes would see the "left half" and the "right half" of the machine interact with each other - a win on one side reflected in a maching win on the other side. I still think it's a good idea, but evidently it wasn't good enough to get me a job. :-)
There's also the question of whether there will be more Skill-With-Prizes-style games in the future. Admittedly, there isn't much skill in video poker or in Cash King Checkers - nothing like the extent that there is in, say, Blackjack. (Stories about blackjack card counters will never stop being cool; this one from Wired promotes this forthcoming book and The Eudaemonic Pie is a classic.) If the casinos decide to go down that route, then hopefully there are many other interesting games to come in the future - not least the tradition of SWP games from the UK. Certainly such games would be far more interesting than the three games most recently introduced into British casinos. Apparently many new casino games are devised by a gentleman called Derek Webb and his company, "Prime Table Games". Nice work if you can get it. Derek sounds like another interesting guy to try to get to know.
However, I suspect that the slot companies will continue to do what they've always done and come up with similar, familiar new machines with slightly different themes. Why, IGT even have a new machine called Enchanted Unicorn. Aww, bless!
Current Mood: pleasantly surprised
Current Music: S. Raab - Wadde Hadde Dudde Da? (c/o ericklendl)
|Date:||September 12th, 2002 11:39 pm (UTC)|| |
Jackpots, crown and anchor
Here in New Zealand, the lottery has a powerball, but it seems that it is rarely won except on the "must be won" draws. This puts us into the unusual situation where (if I have calculated correctly) the total prize pool is likely to exceed the stakes, thereby giving an overall positive expected return. These are the only days I ever play, generally, although theoretical gain has yet to become actual gain.
I also remember expounding my views showing that Lotto is a mug's game, but that didn't stop the guys at work asking me evry Monday 'did you buy a ticket?' and going on about it, as we launched into yet another discussion on statistics and the claim that Lotto is a regressive tax, or a tax on those who are bad at mathematics.
Crown and anchor, a game in itself. Please let me know whether I should post at length about it, or whether you already know about its ingenious psychology.
Re: Jackpots, crown and anchor
I've certainly seen the rules to it - or, at least, to one version of it. It's a fair game when the three dice rolled come up with different numbers, but a game with a big house advantage when two or more dice show the same symbol. Is this the same game as the one you're thinking of?
|Date:||September 14th, 2002 12:07 am (UTC)|| |
Re: Jackpots, crown and anchor
Yes, that's the same game, and you comment on the odds correctly. However, the psych key is that when you get (say) three crowns, everyone playing looks enviously at the "lucky winner" rather than suspiciously at the thieving bank, collecting from five and only paying out on three.
|Date:||September 13th, 2002 02:09 am (UTC)|| |
It's not possible to have an irrational utility function. Rationality (in games) is defined as playing to maximise your own utility payoff.
In the same way that it's possible for someone to be risk averse (such a person would not be happy to receive £10 to accept a 1-in-1000 chance of losing £5000), it is also possible for someone to attach high value to the best-case scenario. Such a person should play the lottery, because even though on average they lose money they also gain utility on average.
Irrational was evidently a poorly-chosen word. I originally had "kinked" there first and changed it to irrational.
The £1 you spend on your lottery ticket goes as follows:
45p is returned in prizes for that draw.
28p is added to the National Lottery Distribution Fund, which is a pool of money allocated to arts, sports and charities that bid for it.
12p is given to the UK government in Lottery Tax (i.e. it goes to Customs and Excise as betting duty).
5p is kept by Camelot Group plc for running costs and profit.
5p is kept by the retailer similarly.
5p is reserved for future Super Draws and Instant Win scratchcard games.
(source: bottom of http://lottery.merseyworld.com/Info/About.html
I think I get 45p of utility from the 45p which goes to the prize fund.
I think I get approaching 28p of utility (say: 25.2p) from the 28p which goes to the National Lottery Development Fund. However, the marginal utility of the 28p for a second lottery ticket is much less - I like to feel that I've done my bit, possibly more than I like doing my bit.
I think I get possibly 8p of utility from paying 12p of Lottery Tax - I'm happy to pay Lottery Tax for the privilege of playing the game. Again, marginal utility of this part of the second lottery ticket's cost feels less than it does for the first, occasional ticket.
Camelot? No utility for me there. Reserve fund? Nope. Retailer? Let's say, ooh, 0.8p of utility from that 5p to make the numbers easier. Running total: 79p so far.
When the lottery rolls over, you get some of last week's prize money distibuted between this draw's players. Let's consider Saturday draws which roll over onto Wednesday, and take the most recent example of this
as a data source; a quick comparison with other recent Sat->Wed single rollovers reveals that it doesn't look atypical. You have, very roughly, £6.3 million of extra prize money split between 28 million tickets - an extra 22.5p per ticket of utility on average. Net result: actual utility obtained exceeds cost, therefore it's a rational purchase.
Now in practice, I don't tend to bother to play single rollovers very frequently, so maybe I don't get as much utility from the non-prize components as I claim to do above. (Indeed, isn't there an economic school of thought that suggests people aren't actually very good at estimating how much utility they get from things?) However, I do think that anyone who doesn't derive any utility from the non-prize components of a lottery entry fee is being a little closed-minded.
Ooh, tomorrow's draw is a Wed->Sat rollover with approximately £3.25 million set to be added to the prize fund, for which we can expect about 45 million entries. Hmm...
(Question: by extension of the above, under what circumstances should I play Lotto Extra?)
There's a flaw in my logic, dear Lisa, dear Lisa,
there's a flaw in my logic, dear Lisa, a flaw.
I may be replying to myself here but this seems to be the best place to store this thought for future reference.
I will not necessarily get 45p of utility from 45p from each pound going to prize money. This isn't because the draw changes the utility from being 45p to being 0/£10/£9 million, it's because the draw that I have entered might itself roll over. In this case, not all the 45p of entry fee is split between the participants - instead, it goes to provide some extra utility for participants in the next draw.
You need this tweak in place to make the utility calculations regarding Lotto Extra work. Now you might get £7 million of rollover money going to a draw in which there are one million tickets entered, but this doesn't necessarily translate to £7 of rolled-over prize money's utility per ticket. It only translates to utility per ticket if someone wins that draw. If, as likely (over 90% likely!) happens, there is no winner in the draw, nobody gets any prize money utility from participation at all.
If you don't have this tweak in place, you start to get very high utility values for relatively low rolled-over jackpots. Now many people say that it's only worth playing Lotto Extra once the jackpot exceeds ~= £14 million because it costs you £1 and you have a 1-in-14-million chance of winning £14 million. This is too simplistic, because you have a 1-in-14-million chance of winning or sharing £14 million. You probably should estimate your expected win, on the assumption you do win, from the number of tickets you estimate will be played and judge your £1 entry fee against that.
Good. That's sorted that out, then.
|Date:||September 14th, 2002 10:53 pm (UTC)|| |
Re: Pedantic Point
I noticed for every pound you buy for a lottery ticket in the UK, only 45p goes back to the players. THAT'S a 55% ADVANTAGE THE HOUSE HAS ON YOU!
Compare that with the slots at Atlantic City, where the slots are programmed to return A MINIMUM of 83% to the players. (Most slots though pay in the neighborhood of 90-95% for every dollar wagered.)
Or a game of blackjack - in Atlantic City, with the rules being Double on any 2 cards, double after splits, dealer stands soft 17 (A,6), the game returns about 99% for every dollar wagered... (The house edge is less than 1%!)
Of course I'm speaking of the long run that these games will come up with these returns. There's no guarantee you'll get that kind of a return in the short run.
That's why the lottery -- especially the daily games like Pick 3 and the twice-weekly games like Lotto and Powerball -- can make so much money -- it keeps a lot more of the dollars wagered than almost any other gambling proposition I can think of...
In most states the top prize in Pick 3 is $500 for picking a three-digit number exactly as drawn on a $1 bet. But the odds of that happenening are 999-1 against you. The proper payout should be $1000 but the lottery only pays out $500. That's a 50% edge they have on you. Not good.
That's why I only play the progressive jackpot games (Lotto, Mega Millions, Powerball) whenever the jackpot justifies the longshot odds of winning the top prize. It's a losing proposition when you play any other time.
I played in today's National Lottery draw for the first time in a while - possibly the first time this year - because a £15,000,000 jackpot was guaranteed. (Or, at least, £15 million of jackpot which would at least roll over.) The detailed stats
are available and interesting as a case study.
A shade under 30,000,000 £1 tickets were sold (ignore the "HotPicks" figures - they're a fixed-odds game based on the main draw's numbers, with a wicked house edge) and well ovee £24,000,000 of prizes were paid out. Some would say "well, that's a 20% house edge". However, this draw will also have generated about £8,000,000 for charity and over £3,000,000 in tax revenue. Taking those latter figures in mind as well as the prize money, was tonight's game worth playing? I would say so and indeed did say so with £1 of my own money, whereas you might not. (This is probably why you're a more successful gambler than me!)
For the record, I got the first and third numbers, so just one out of the fourth, fifth and sixth would have given a result - but they all missed. (The fourth missed by only two.) Close only counts with horseshoes and hand-grenades, as well you know. :-)
Net result for the evening: -1 happy. After all, love (*ding*) + health (*ding*) + wealth (*ding*) = happiness (*chord*)...
|Date:||September 13th, 2002 07:44 am (UTC)|| |
Cash King Checkers
That game is immensely addicting. I spent a whole hour just playing the thing trying to win imaginary nickels. At last, it's a skill-based slot machine that ISN'T video poker.
The big thing about this game is strategy. You have to determine which moves will give you the best return on your money. There have been many times when I jump 2 checkers and say, "Damn! I could have gotten 4!" So it really does require lots of thinking. Best of all, there are no complex strategies to memorize like in video poker, where there are so many different variations on the theme (Jacks or Better, Joker Wild, Deuces Wild, Bonus Poker, etc.).
The top jackpot for clearing all nine checkers is fixed, meaning there's no additional bonus, progressive or fixed, even if you play max coin. The top prize is 10,000 nickels if you play all nine checkers at 1 nickel per checker. That's still $500. The payback percentage will remain constant even if you bet 5 nickels per checker (max coin, 45 nickels, $2.25). There's not really any incentive to play more than 1 nickel per checker, so you don't have to put much money at risk for a good investment. You can increase your bet per checker when you feel like you're winning, and go down to the minimum when you feel like you're not.
Some video slot machines are like that. As long as you bet 1 coin per line, the payback percentage remains the same. I've discovered that games that have 15 or 20 paylines tend to have a straight-multiplier effect for all the payoffs including the top jackpot, so most of the time when I play *those* slots I will just play 1 or 2 nickels at a time.
On games where there is a bonus for getting the top jackpot, whether a fixed or progressive jackpot, it's in your best interest in the long run to play max coin, usually 45 nickels at a time on a nine-line video slot. For example, TPiR Slots offers a 5000 nickel jackpot ($250, multiplied by the line bet) for the top prize - five TPiR logos on an active payline. If you play max coin and get five TPiR logos on the 9th payline, you win $10,000 on the spot, a substantial bonus.
The same is true for reel-spinning slots, and their progressive jackpots (Wheel, Jeopardy!, Elvis, etc.). Even many non-progressive slots pay bonuses for the top award if you play max coin. It's very important to read paytables on a slot machine for this reason. If the top jackpot is a straight multiplier (no bonus for playing max coin), then the best way to play is 1 coin per line. If there is some bonus for the top jackpot by playing max coin, then you should play max coin.
Also on reel-spinning slots, if there is a bonus game, then sometimes you can activate it only by playing max coin. Not all reel-spinning machines require that you play max coin to activate a bonus game, but some -- like Wheel of Fortune and Bonus Times Frenzy -- will require it.
Strictly Slots is a neat magazine -- I subscribe to it faithfully -- that has lots of goings-on in the slot and casino industry. It also contains helpful charts that display which casinos have been offering the best payback on their slots. It's really neat.
Re: Cash King Checkers
I guess it's just general mistrust of the industry which makes me a little sceptical here. Can we really be sure that - say - the chance of the golden checker appearing remains the same when playing one coin per checker rather than five coins per checker? Given that the game's programmers are prepared to change the chance of the golden checker appearing depending upon how many checkers you play, it does seem to be rather a leap of faith that there are no bonuses, announced or otherwise, for playing more checkers per coin. If you know better that legality dictates that manufacturers must reveal when things like this vary, I will of course defer.
It's a historical anomaly that some considerable proportion of slot machines in the UK are to be found in seaside arcades, where slot machines are frequently to be found alongside arcade games - see recent rant. (I understand that this is not generally true in the US - please would you confirm or deny this? - though I believe some of the larger casinos have decent arcades available as part of their entertainment line-ups.)
There was recent discussion about applying age restrictions to playing slot machines in this country; owners of seaside arcades brought considerable weight that putting minimum age restrictions on slot machines would adversely affect their business. From memory, I think the conclusion is that different sets of legislation apply for age restrictions on seaside and inland arcades.
I have much more respect for casino operators when the casinos operate table games than I do for casino operators whose casinos are based around slots. Sorry! :-)