Salutations Senors, Senoras, Senoritas, Statisticians & Strategists,
(Today’s post is sponsored by the letter ‘S’)
Hi, I’m Super Safi and you may remember me from such stats and strategy posts as KEM Farming and the advanced losing-to-win Superheroes battle strategy.
After a stressful week of work or school, the weekend is finally here. And what better way to spend the weekend than talking math. So every few Saturday’s, I’ll come to you with a post that delves into the wonderful world of numbers, stats, and/or strategies.
This week we look at Springfield Downs.
Springfield Downs Odds Table
| Odds | Payout | XP | % Chance |
| 2-1 | $6,000 | 75XP | 50.51% |
| 5-1 | $12,000 | 100XP | 25.25% |
| 9-1 | $20,000 | 150XP | 15.15% |
| 19-1 | $40,000 | 250XP | 7.58% |
| 99-1 | $200,000 | 500XP | 1.52% |
| Consolation Prize | $0 | 50XP |
So what is your best bet? Let’s take a look at what happens over 1,000 spins (roughly a years worth of tapping for the hardcore Addict who’ll play the downs almost the maximum three times per day).
2-1:
50.51% of the time, you spend $2,000 and get $6,000 and 75XP.
49.49% of the time, you spend $2,000 and get just 50XP
$ Formula = 505.1 x (-2,000 + 6,000) + 494.9 x (-2,000) = $1,030,600
XP Formula = 505.1 x (75) + 494.9 x (50) = 62,627.5XP
So after 1,000 bets at 2-1 odds, you would walk away with $1,030,600 in-game cash and 62,627.5XP.
5-1:
25.25% of the time, you spend $2,000 and get $12,000 and 100XP.
74.75% of the time, you spend $2,000 and get just 50XP
$ Formula = 252.5 x (-2,000 + 12,000) + 747.5 x (-2,000) = $1,030,000
XP Formula = 252.5 x (100) + 747.5 x (50) = 62,625XP
So after 1,000 bets at 5-1 odds, you would walk away with $1,030,000 in-game cash and 62,625XP.
9-1:
15.15% of the time, you spend $2,000 and get $20,000 and 150XP.
84.85% of the time, you spend $2,000 and get just 50XP
$ Formula = 151.5 x (-2,000 + 20,000) + 848.5 x (-2,000) = $1,030,000
XP Formula = 151.5 x (150) + 848.5 x (50) = 65,150XP
So after 1,000 bets at 9-1 odds, you would walk away with $1,030,000 in-game cash and 65,150XP.
19-1:
7.58% of the time, you spend $2,000 and get $40,000 and 250XP.
92.42% of the time, you spend $2,000 and get just 50XP
$ Formula = 75.8 x (-2,000 + 40,000) + 924.2 x (-2,000) = $1,032,000
XP Formula = 75.8 x (250) + 924.2 x (50) = 65,160XP
So after 1,000 bets at 19-1 odds, you would walk away with $1,032,000 in-game cash and 65,160XP.
99-1:
1.52% of the time, you spend $2,000 and get $200,000 and 500XP.
98.48% of the time, you spend $2,000 and get just 50XP
$ Formula = 15.2 x (-2,000 + 200,000) + 984.8 x (-2,000) = $1,040,000
XP Formula = 15.2 x (500) + 984.8 x (50) = 56,840XP
So after 1,000 bets at 99-1 odds, you would walk away with $1,040,000 in-game cash and 56,840XP.
Springfield Downs Net Table after 1,000 bets
| Odds | Net Cash | Net XP | % Chance |
| 2-1 | $1,030,600 | 62,627.5XP | 50.51% |
| 5-1 | $1,030,000 | 62,625XP | 25.25% |
| 9-1 | $1,030,000 | 65,150XP | 15.15% |
| 19-1 | $1,032,000 | 65,160XP | 7.58% |
| 99-1 | $1,040,000 | 56,840XP | 1.52% |
So if you’re into in-game cash, your best bet is to stick to 99-1. But if you prefer XP, your best bet is to stick to 19-1.
How do you bet at the track? Will you change your betting ways after this post? Would you prefer in-game cash via 99-1 or XP via 19-1? What aspect of the game’s stats and strategies would you like me to discuss next? Share your thoughts. You know we love hearing from you.
Minigames:
Springfield Downs, Go Kart Tracks, Insanity Mode, Sideshow You, Rocket Launch Pad, Claw Machine, Scratch-R, The Eliminator, Bigclaw, Excavation Site, Drone Scan, Sci-Fighter, Where’s Maggie
In the beginning of me regularly playing Springfield Downs—back when they dropped the price from 5k to 2k and changed the odds—it seemed like one dog kept winning. I knew this was preposterous, and being a mathematician I knew the that the fact it appeared the same dog kept winning was due to chance, but the emotional feel of the same dog winning sent me betting this one dog time after time. I win more than half the races, which keeps me coming back. Not for the money or the XP, just for the heck of it.
So if you play a straight line (or even jump around a get lucky). You will spend 2,000,000 to get 1,040,000 back max theoretically.Sounds like i’m done playing the downs then. As for the XP, A couple of KEM’s and i surpass the XP easily.
Just to clarify, you spend $2,000,000 to get $3,040,000 for a net profit of $1,040,000.
I just learned that I receive more xp (170) from visiting a neighbor’s Krustyland than from visiting their town (155). Any explanation for this? Is it worth it? I usually cash in my tickets when I get over 30,000. Has anyone done the math?
Do you have a higher bonus multiplier in Krustyland than in Springfield?
Definitely not! Over 200% in Springfield. Only 5% in Krustyland.
I choose based on the last winner (usually the 2:1) so I pick the 2nd or third option (5 or 9) frequently and do fairly well. I almost always pick the top cart (2:1).
Awesome! Congrats to a analysts approach to a long game
Indeed makes a benefit to our fellas and beautifuls girls from TSTO Community
Cheers to Safi! 🆙
4lvinos from 🇧🇷
Thanks for putting in the odds and expected payouts based on 1,000 plays. That is a great way to look at this in the long run.
Pushing this a bit further though, an additional factor to consider is the time value of the in-game cash at different parts of the game. For example – I have only been playing the game for about a month and just hit level 40. For me, the 50/50 odds of turning a $2,000 bet into $6,000, is impactful at this point in the game because the risk of losing $2,000 versus the opportunity to generate an additional $4,000 often makes a short-term difference in my ability to do things like buying the next available building and/or the next boardwalk piece for Squidport, etc.
For example, the difference between losing $2,000 versus gaining an additional $4,000 can sometimes make or break my plans at the moment. I can think of several times when I had enough money to buy a new building + an additional Squidport piece, but then I will go and lose $2,000 – thus causing me to have to delay making the Squidport piece.
I can definitely see the logic though in going to 99-1 races though if/when I get to the point that I have way more in game cash than I need (like many of the people on here who have been playing for a long time). In the short run though, I will stick to the 50/50 chance of getting an additional $4,000, since I constantly need to keep generating in-game cash
On that note,
why not target the 9-1
More XP and a ~15% (~1/7) chance
✓ a more conservative choice
At your stage of play, I wouldn’t play the racetrack at all….there are much better uses of your cash at this point. I think I only played once until I had lots of cash to burn (and I still rarely ever play it, tbh).
I just always bet on the same dog, Not A Chance. It works out pretty well for me.
So do I. I choosed it because of it’s name 🙂 The same way I choosed one (actualy the white one) car.
Same here! Always Not A Chance. I’m very loyal. But with the car races I always go for the largest payout, even though it seems like I hardly ever win. It’s just awesome when I do!
Same here. I was born in London, so it’s Drool Britannia FTW! (Every so often, anyway ;-)) But, as mentioned above, I’m a veteran now, so have millions to burn!
LOL! I always bet on Not A Chance also & do pretty well. I may have to try choosing the high $ winner once in a while. I always choose the max $ winner in the go-cart game; not sure why I always pick the same dog! 🐶 RachelS
“So if you’re into in-game cash, your best bet is to stick to 99-1”
The difference is less than $10,000 of over $1,000,000. That’s hardly much of a difference. And I’m willing to bet (no pun intended) that people who often play 99-1 eventually stop playing as often since they rarely win, so over time they would win less. (Yes, I realize your models assume 1000 games for all options.)
So some of it comes down to the person’s style. Are they likely to get really frustrated when they go many many races without a win (and is that frustration worth $8,000 or so)? Would they “feel better” if they won a race 50% of the time (even though earning/race are less)? You can’t totally discount the human element.
I’m curious about your theory that players who only pick the 99:1 dog eventually stop playing as often – why wouldn’t they just start betting on the 2:1 dog instead?
For what it’s worth, I always play the 99:1 dog because I have enough in-game cash to not miss it when I lose, and the thrill of getting a 99:1 win is fun. (Also, I hate the idea of seeing the 99:1 dog win when I bet on a lower-stakes dog!) I have no interest in giving up. I’d like to hear if anybody actually does, though.
Also, from my experience, after 2+ years of playing twice daily (so, around 1,500 races), the 99:1 dog wins more often than once every 100 races. I’ve found that it actually wins about once every 50-60 races, on average. (So, once a month.) True, I’ve had dry spells of 2-3 months (100-150 races) with no wins, but I’ve also had it come in twice in the same week. I think it’s a good bet.
I was hoping you would cover the idea of betting on a particular dog. Thanks
Splaguet level I32
The math here is completely wrong. You misunderstand odds. 2 to 1 odds against means you lose 2 times for every 1 win. Therefore, you win 33% of the time and lose 67% of the time with 2:1 odds. Applying this correction to your math, the money payout turns out to be a wash for all 5 options. You net $0 regardless of the option you choose in the long run. The XP is different, although minor differences. I calculate XP payouts of 58,333; 58,333; 60,000; 60,000; and 54,500 for 2:1, 5:1, 9:1, 19:1, and 99:1 options, respectively. Using these correct probabilities, I also ran a probabilistic simulation, using 1,000 trials, and using both a truly random Monte Carlo sampling methodology and a stratified Latin hypercube sampling methodology, I get similar results of roughly no net dollar win or loss for each option (due to whole numbers of trials with fractional probabilities, there are sometimes a non-zero net).
The math in your comment is completely wrong. You misunderstand the first table. The first table shows he actual win percentage coded into the game.
2-1 odds in a casino may mean 33% win, 67% loss. But as programmed into the code, 2-1 means you win 50.51% of the time.
Why on Earth would TSTO/EA intentionally code wrong statistics into the game?!? Smh at STEM ed these days…
I agree. Considering how educated and bright the people behind the show are, you’d think they would hire people behind the game who know the difference between 1-1 odds and 2-1 odds.
To quote one Homer Jay Simpson: “How is education supposed to make me feel smarter? Besides, every time I learn something new, it pushes some of the old stuff out of my brain. Remember when I took that home wine making course, and I forgot how to drive?”
Marge: That’s because you were drunk.
Homer: And how.
looking for more details on your observation
very interesting approach on the Probability!
May I suggest you to go over
KEM Farming
because KEMCycle%boost with Mistery Box
should be more fun for you
look the math there it’s exciting !
For example
.there is a curve on % per day gained
against the # Bonuts per 4hCycle
if we go over Time and acumulate %.
With my first KEM farming
I had 3Bonut 〰 1~2% per 4hCycle
4Bonut 〰 jump to 2,12% per 4hCycle
5Bonut 〰 jump to 2,43%
6Bonut 〰 to 3,4%
7Bonut 〰 to 4,23% ( 105~123 donuts per day )
8 still moving to this level of farming
The game in cash per 4h Cash
in the beginning was 290000Xp
now reached more them 800000Xp
I play 2:1 on cars and always Dog Biscuit.
Never paid attention to bonus percentages and the track. Just played and lost. The 50 XP consolation prize was multiplied by 5 to 250, but not by my XP bonus percentage. I assume, then, that dollar winnings don’t participate in bonus percentage either.
I’m glad I’m not the only one who says math be damned and just plays the same dog every time. Go Dogbiscuit! (And Red Racer)
Thanks Safi! Love these posts.
Nice post! I’ve usually done the 99:1 race hoping for the big $$ – maybe now I’ll alternate between the 99:1 and 19:1 to try and get an XP boost in there too!
For years I have nearly always played 99-1 and still haven’t won.
Wow,I used to play 99-1 all the time and won several times, including twice in one week once.
Some people are luckier than others with some of these things…still playing the rocket at least once a day (and often twice) and have yet to get even one mini-nuke!
Yeah, I play it religiously twice a day and only have two nukes to show for it.
Honestly, I’d settle for one. Then is probably just stop launching the damned thing (or not…I have gotten a few alien topiaries out if it…).
Found the comment I was looking for, Addicts Open Thread July 10th 2016:
http://tstoaddicts.com/2016/07/10/addicts-open-thread-39/comment-page-2/#comment-477845
I won at 99-1 twice in one day.
Haha! The math nerd in me loves this! A little expected value calculations made my Sunday morning. The little things….
Great post very interesting. Thanks.
Cannot fault the logic, and argue with the maths, the way that I have been playing it was alway betting on the same dog/racer every race, was winning more times and money over a 3 maths period than just betting on longshots.
Thanks for this Safi….I think🤔🤣. I only ever bet on Dogbiscuit because he’s my favourite and reminds me of one of my favourite episodes in which SLH features heavily. Sometimes I win, sometimes I lose. I usually get lucky if I go for the smaller two payouts. I just play for fun……💜X
……ps. play very seldom too. Usually just to get the ‘ready’ symbol out of the way when I’m tapping🙊😂……Have a lovely Sunday…..💜X
Drool Britannia every time. And the blue go kart.
I always bet 99:1 but Drool Britannia seems to win every race… unless he’s the 99:1 dog!
Safi you are awesome, I’ve wondered for so long what was the best strategy for betting and now I know! Think I’ll bet on the long shot from now on.
The problem is, you kinda have to be all in to really benefit from playing the ponies at the higher odds. If you only pay occasionally, it’s highly unlikely that you’ll make that long shot. It’s only when you do play a high number of times that you’re more likely to get the actual mathematical benefit.
I’ve got to agree with Sandra. The difference in payout is so small, I’ll just stick with the 2:1 odds. Then again, I’m a Penny Slot machine sort of gambler.
Like everything else it’s for people who play this one and care. Just like donut farming posts are detailed for those donut farming and should i buy posts are for those who want help deciding. If you’ve already made up your mind not to play the dog track regularly, or only bet a certain way, then this post likely isn’t for you.
Sorry…I didn’t mean to imply that I didn’t find this post interesting because, whether I pay the track or not, I still find this kind of post very interesting! And I actually enjoyed the fact that I actually could follow the math, which was elegantly simple. 🙂
My math degree can’t let that one go…. probability doesn’t behave like that…. each trial is independent. In other words, it’s like a 100-sided die where “winner” is on one of the sides. Every time you play, your odds of getting the win is the same- even if you just won the last time. So the value is commiserate with the risk…. in fact, as Safi is showing you, it actually pays out higher with that win (which happens rarely) than a tons of wins from the 2:1 (which win half the time).
So while expected value payouts (which could have been an equivalent way to analyze these payouts) rely on “in the long run” as a defining concept, the average payout per play considering the probability works on each independent trial.
So yes, you are less likely to see a win if you play the longer odds once or twice a month… but Safi is cleverly showing you the risk/reward ratio.
Oh, I totally get the independence thing and it was in my mind thewhole time iI was writing the post (i knew someone would bring it up, lol!). I’m usually the one taking people’s logic this task when they talk about being “due.” But it’s also true that, if your “n” is small enough, then the odds are less likely to play out as they should. It wouldn’t be that odd to flip a coin five times and get heads all five times, but it would be a lot odder if you flipped a coin a thousand times and got heads all one thousand times. Possible, yes, but likely, no. (Although I do realize that the 1,101th flip is still just as likely to be heads as tails.)
Agreed all the way up to the five in a row part… that’s a different event- there’s a geometric distribution for the probability of how many trials before you get the first, say, tail on the 6th or 1001th event. But that’s neither heads nor tails… 😄
I just asked my husband (who doesn’t play) to pick a name. He chose Drool Britannia and that is what I have bet on for the past 3-4 years.
I also always bet on the red car at the race track because I have a red car.
I prefer the 9:1 simply because I don’t want to take the time to scroll down….
Had to let the ‘ol pre-frontal cortex cool down a bit before I could reply, although not as intense as some of your previous math😉. I think I’ll stick with the 2:1 odds as there doesn’t seem to be significant difference in payout. Besides, I like to see “YOU WON!”. thanks Safi for another great post. Looking forward to that S.H. math
Same here – I just like a win, even if it is an easy one. 🙂
2-1 odds continues to sound just fine to me. Same with the race cars.
Wow. Umm thanks for that. Not a Chance has been my guy since day one and always will be. I honestly don’t pay attention to whether I win or not. Just a fun aspect to the game.
Do I understand this correctly…if you play 1000 times, spending $2000 per play, you have spent $2,000,000 …for a potential win of $1,040,000 at best? Why would anyone do that? I have placed mine so that the Rich Texan has a place to hang out, but I never actually bet on the dogs…I mean “woof”…that is crazy!
So if you spend $2,000,000 on bets, you’ll win $3,040,000, for a net profit of $1,040,000.
That makes so much more sense…thanks Safi, it was totally inconceivable the other way.😬
Wow! Thanks math genious! I will now play 19-1. I am speechless! Thanks for your work!