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Calculating the maximum expected gain from food club?


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#1 darktank

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Posted 21 November 2012 - 06:28 AM

Hi guys, a while ago I read a guide on an old guide about the food club: http://www.neopets.com/~windagame

Basically the idea is that, because the odds on the pirates are capped, you can make bets that have a higher expected value than 0. Normally someone with 1:2 odds should have a 50% chance of winning, so if you bet 1000 np:

(0.5)(1000) + (0.5)(-1000) = 0
You have a 50% chance of winning and a 50% chance of losing, so the expected gain is 0 if you do this bet a lot of times.

But food club is different because someone with a 70% chance of winning is still listed as 1:2 odds, meaning that you can make bets that will still return double your winnings even though the odds of that pirate winning is higher than 50%.

(0.7)(1000) + (0.3)(-1000) = 400
When you bet 1000 np, you now have a 0.7 chance to win 1000 and 0.3 chance to lose 1000, making your expected gain positive.

To me, what's interesting is how you deal with multiple races where you can find these situations. Like the author of the guide proposed making hedge bets in which you can increase the expected gains you get. I was wondering if anyone had insights on how an algorithm might go about finding the best combination of bets to maximize expected gains in a given day. Food club isn't really profitable, but I think it's kind of an interesting problem. It reminds me a lot of the MIT blackjack team (or if you've seen the movie 21).

#2 RitzWin

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Posted 21 November 2012 - 08:44 AM

Look into the 'dutch book'. I heard about what you're talking about in my rational decision making course- they called it a 'dutch book', a situation where you can always win.

I was thinking of writing a guide on it, but never ended up doing it (or looking to see if there already is one). Finding out if there is a possibility for a dutch book is pretty easy:
Check http://foodclub.daqtools.info/
If the ratio is lower than 0, there's a dutch book to be had! I don't feel like typing it out- but I'll post the email I sent to my friend about it:

But it seems to me I can always win a moderate sum if I do my maths right depending on the heap I'm betting on.
So there's 4 participants in each race, each with a ratio of winning (ignoring this ratio in my analysis as it's useless in my scheme), and each with a payout ratio.
Some of the races have payout ratios of each participant that add up to less than 1:
eg: p1 = payout ratio 2:1
p2 = payout ratio 13:1
p3 = payout ratio 13:1
p4 = payout ratio 9:1
1/2 + 1/13 + 1/13 + 1/9 = 0.76
So if I bet 2NP on p2/3/4 and 10NP on p1 (16NP spent total), I'd always win (a small amount) right? (do the maths for each outcome in your head)
I guess if the ratios don't add up to < 1 then it's not worth doing the above scheme.


I've looked online for a good dutch book calculator- but they seem confusing, at least more confusing than my above example, so I gave up on it for now. Hope this was helpful!

Edited by RitzWin, 21 November 2012 - 08:46 AM.


#3 MissSunshine

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Posted 21 November 2012 - 08:57 AM

Food club isn't really profitable, but I think it's kind of an interesting problem. It reminds me a lot of the MIT blackjack team (or if you've seen the movie 21).


If you have an old account, it is quite profitable. I make on average 50k a day (70%) return. Which is a nice little boost to my daily income, I admit it isn't huge but it is still very good for an easy and legit means of making neopoints. Though that return is only considering the days on which I actually follow my system, I generally bet MUCH more riskily near the end of the month in the hopes of gaining a nice trophy (and therefore usually end up losing NP). On those days I sacrifice high long term percentage return for higher (but likely more spread out) daily returns.

Basically what you need to do is add up the total odds (so 2:1=50%, 3:1=33%, etc) in each arena. If the number is less than 100% that means that that arena will likely pay out 'better' than what the odds say. When this is the case I place 6-10 bets on the 2:1 pirate in that arena, with 0-4 bets on the next likely winner(s).

If multiple arenas have less than 100% total odds, you have a better chance of winning big(ger) that day :D. In this case I place bets on all the 2:1 pirates in all the arenas with less than 100% odds. (because (<100%)*(<100%)=(<<100%))

You see, if the odds in an arena add up to 80% while the actual odds must add up to 100%, that means the 20% difference must be there because some pirates have better odds than shown. In arenas where the total odds are less than 100%, generally the 2:1 pirates will have better odds than 2:1 (because 2:1 is the lowest payout shown) and the 13:1 pirates will have worse odds than 13:1 (because 13:1 is the highest payout shown). However there is no easy way of seeing whether the pirates with intermediate bets have better or worse odds than shown. To do so you need to look up the pirate to see what foods he likes/dislikes and check how many of his favourite foods are on the menu, as well as how many foods he dislikes. And unfortunately I have not yet found out how this converts into a change in the pirate's odds. I am too lazy too check this everytime I bet so the easiest solution is to pretend that each pirate with intermediate odds has exactly the odds shown.

For example if two arenas open with less than 100% odds. Say, arena 1 open with 90.4% with a 2:1 (pirate A), 4:1 (B), 13:1 ( C), 13:1 (D). And arena 2 opens with 73.1% and odds 2:1 (E), 13:1 (F), 13:1 (G), 13:1(H), while all the other arenas open with >100% odds.

You would want to bet on pirate A and E (because (<100%)*(<100%)=(<<100%)=66% meaning there is a larger discrepancy (44%) between the odds shown and the actual odds, and A and E are most likely to have better odds than shown. In fact if we assume that the other 6 pirates odds in those 2 arenas are ON AVERAGE equal to their stated odds, AxE gives a 44% higher payout than the actual odds say they should. So you should bet with A and E for almost all your bets with one additional pirate from other arenas (starting from the arena with the lowest total odds). Generally it is best to avoid 13:1 pirates, but you can choose to include them if you want to cover all the pirates in one arena. (This will DECREASE your overall percentage return, but will also DECREASE your chances of not winning at all that day. So it is good if you want short term returns, but bad if you plan on playing food club for a long time). Also in this case you would probably want to place one bet on B and E (8:1) so that you don't lose ALL your money if A and E do not win.

So lets say arena 3 has the next lowest total odds and has a 2:1 pirates (X), a 3:1 pirate (Y), a 4:1 pirate (Z) and a 13:1 pirate (W).
You would be AEX and AEY and AEZ but you would NOT bet AEW.

By betting on all the viable pirates in arenas with slightly higher than 100% average you increase your payout. because this allows you to use all 10 of your bets instead of just 1. Because betting on AE would give you a 44% payout, but only on one bet. Now if A and E win you are ALMOST certain to win your bet on A+E+One pirate from arena 3, so you get a 44% payout on larger odds (8:1 to 16:1). By also doing this on a second/third arena you can get 44% on two/three larger bets.

(Note the 44% represents how much more often you will win the bets than what the odds show.)

If more arenas open with (well) under 100% average, you are likely to win more. But the calculations are a little different for each number of available arenas (I also simplified them a bit so they are more understandable). I may post my full/actual calculations in the future, but I do not have the time to fully explain them now.

Edit: Or you could use the chart at http://foodclub.daqtools.info/ if you don't feel like calculating the values yourself, because apparently they HAVE (kinda) figured out how strength/food adjustment affects the odds. From what I can tell they use past data to predict the actual chances of each pirate... which is a great substitute for experience (Because that's kinda how I choose between two pirates, once you play for a long time you get a 'feel' for which pirate will win :p). Thank you RitzWin, for reminding me that this exists!

Edited by Sunshine1994, 21 November 2012 - 09:14 AM.


#4 RitzWin

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Posted 21 November 2012 - 09:53 AM

Heh, thank you for going more in depth. You kind of pointed it out, but with my scheme (where you bet a certain amount on each contestant if the ratio is negative), the amount of negative % is the amount you stand to win if you calculate the dutch book correctly.
In most cases, (like today for example), there's 3x -20%s. Meaning you really could (if you calculated the correct amount to bet on each contestant), be absolutely sure to win 3x ~20% of the max amount of bet you're able to throw down...
Can be very profitable, since it's no-lose, if you figure out the proper ratios- you might as well bet on all the heats where there's a dutch book.

#5 darktank

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Posted 21 November 2012 - 10:02 AM

Look into the 'dutch book'. I heard about what you're talking about in my rational decision making course- they called it a 'dutch book', a situation where you can always win.

I was thinking of writing a guide on it, but never ended up doing it (or looking to see if there already is one). Finding out if there is a possibility for a dutch book is pretty easy:
Check http://foodclub.daqtools.info/


Wow, that is a really useful tool! The food adjustments they make are really interesting too, but the calculations on their odds is really helpful. Now I wonder if there is something else that we can do with the data collected by the database. Like studying past trends or something. I'm sure there are some sorts of biases in the rounds. I also wish I could understand the statistics that they collected. But I guess following the dutch book strategy is probably the most surefire thing to do though.

So lets say arena 3 has the next lowest total odds and has a 2:1 pirates (X), a 3:1 pirate (Y), a 4:1 pirate (Z) and a 13:1 pirate (W).
You would be AEX and AEY and AEZ but you would NOT bet AEW.

By betting on all the viable pirates in arenas with slightly higher than 100% average you increase your payout. because this allows you to use all 10 of your bets instead of just 1. Because betting on AE would give you a 44% payout, but only on one bet. Now if A and E win you are ALMOST certain to win your bet on A+E+One pirate from arena 3, so you get a 44% payout on larger odds (8:1 to 16:1). By also doing this on a second/third arena you can get 44% on two/three larger bets.

(Note the 44% represents how much more often you will win the bets than what the odds show.)

If more arenas open with (well) under 100% average, you are likely to win more. But the calculations are a little different for each number of available arenas (I also simplified them a bit so they are more understandable). I may post my full/actual calculations in the future, but I do not have the time to fully explain them now.


I see what you are saying. Thanks for clarifying a lot! I guess it makes sense to view the odds of a pirate as a range rather than an actual number? I am still a little confused about how you would use all your bets though. Suppose there is a fourth arena with slightly above 100% odds that are similar to arena 3. Would you do the same thing you did with the third arena? Like if G, H, I, and J were pirates from the fourth, you'd bet: AEG, AEH, AEI? Or suppose AE didn't win; would that be really bad? I guess I am going to have to do the math out because there's too much to think about lol.

#6 RitzWin

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Posted 21 November 2012 - 10:21 AM

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There, you can see that you should always win if you bet with the ratios (individual stake) indicated by the above calculator ( http://www.betcalc.c...qprofitcalc.php )
edit: fixed the problem.
Tell me if there's a way to lose in the above scenario ;)
In every outcome, you will win more than 100NP.

Should I make a guide on this... seems like I have everything we'd need lol

Bump, fixed my post

Edited by RitzWin, 21 November 2012 - 10:32 AM.


#7 darktank

darktank
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Posted 21 November 2012 - 10:38 AM

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There, you can see that you should always win if you bet with the ratios (individual stake) indicated by the above calculator ( http://www.betcalc.c...qprofitcalc.php )
edit: fixed the problem.
Tell me if there's a way to lose in the above scenario ;)

Should I make a guide on this... seems like I have everything we'd need lol

Bump, fixed my post


Haha, well i'd certainly like to learn more about the math behind it. But I think what sunshine was saying was that you could earn more over the long run if you maximize expected gains rather than just go for the immediate dutch book solution because the bets are capped and limited. Like you would win more over the long run but you could lose a lot in the short run.

Also, in that food club tools link you posted, i discovered there is a bet optimizer application in there which gives the set of 10 bets that would be optimal for that day. That takes the fun out of things lol. I would still like to learn the math behind it though, like how you would calculate expected values and how you would find the 10 optimal bets, so I definitely read more into that.

#8 RitzWin

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Posted 21 November 2012 - 10:44 AM

I'm sure that you can win more over the long run like what sunshine was saying too, just might as well place this sure-thing bet among your other bets.

Edit: Just made a guide instead lolz:
http://www.neocodex....ime-dutch-book/

Edited by RitzWin, 21 November 2012 - 11:31 AM.



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