I was totally right about Federismo yesterday.
Unfortunately, the out-of-system safety I placed on him combined him with Lucky, who I felt to be totally safe - and that's where I was wrong.
No wins for me today.

Really crazy odds today.
If I'd follow my system, I would have to 10-bet Gooblah (as Harpoon Harry's is the only positive arena), and I'd combine him with all four pirates in Shipwreck, and the six single-digit pirates in Lagoon and Treasure Island. These are the bets I'll be using for my statistical section, as they are what my system recommends.
My actual bets are different, because I really don't understand the starting odds in Hidden Cove. Lucky has strength 82 and a +3 food adjustment; Sir Edmund has strength 79 and a -1 food adjustment. So why are they both opening at 2:1? In my opinion, Sir Edmund should open at 4:1 or so.
So I decided to place bets as if this was the case, using the two-arena system on Hidden Cove and Harpoon Harry's. Standard safeties (the 4:1 on Sir Edmund + Gooblah looks odd, but is really a safety!), and booster bets on all pirates in Lagoon and the non-13:1 pirates in Treasure Island.

Don't like my bets? Try one of these: (note that not all are updated daily)
Banano87's bets
Betty's bets
Boringg's bets
Canon's bets
Christie's bets
Dutch's bets
Gmdaddy's bets
Gooddevil's bets (Note: Page is in French)
Greylorn's bets
Harry's bets
Leafboyza's bets
Lucas' bets
Lukas' bets
Neoguy's bets
Osprey's bets
Paige's bets
Riley's bets
Sachi's bets
Sidney's bets
Stac93's bets
Tracey's bets
Vicki's bets
Vicky's bets

These are all the Food Club pages I could find, listed in alphabetical order. I have not tried to assess the risks and chances of the various betters.
See a page missing from this list? Please mail me.

Some other Food Club related links:
Food Club main page
Revenge's Food Club guide
Greylorn's Food Club review
Sirhatter's betting guide
Christie's chart of Food Club Winners
Food Club Monthly Competition

My betting system

The bets I made are based on a method I started using in september 2010. This method has proved itself to be better than the method I used before, and lots better than my first attempts to outsmart the system.
Many thanks go to sirhatter. His betting guide has helped me make lots of neopoints, until I found a way to improve upon his method.
Without sirhatter, this guide would never have existed.

What odds to use?

The odds for the various pirates change throughout the day. Many people have different theories about the relevance of opening odds, movements, and closing odds.
My theory is that the opening odds are determined by the Neopets computer, based on their actual chances of winning, and that movements throughout the day are caused by players' actions: if a lot of players bet a pirate his odds go up; if almost noone includes him, his odds go down.
Since I consider the opening odds to best reflect the actual chances, these are the odds I always use when picking my bets.

Calculating value

The first step in my betting system is to calculate the value for each of the five arenas. The value is found by converting the listed odds to percentage values, adding those percentage values, and subtracting the total from 100%.
For example, suppose the pirates in an arena are listed as 2:1, 6:1, 8:1 and 13:1. Converting to percentages yields 50%, 16.67%, 12.5%, and 7.69%; a total of 86.86%.
The value of this arena is 13.14% (100% - 86.86%).

Choosing bets

The next step is to count the number of arenas with a positive value, since the bets to be made depend on the number of positive values.

If there are no arenas with a positive value:

In this case, I don't bet at all.
There are people who will bet, and some will even make nice wins. But in my experience, you'll lose more neopoints than you win in the long run, so the winning strategy is not to bet if no arenas have a positive value.

If there is one arena with a positive value:

In the positive value arena, find the pirate with the 2:1 odds. (There should always be exactly one). I will make ten bets (the maximum), all on this pirate + one other pirate.

The rules for finding the ten pirates to include in these bets are:

1. Start with the remaining arena with the highest value. (Since the remaining arenas have negative values, remember that -2.5% is higher then -14.8%!).
   Use all pirates from this arena, except those that have 13:1 odds. (The reason why I omit 13:1 pirates is that their real odds might be much worse. The Food Club never goes below 13:1, but the actual odds may be worse - and an actual win chance of (for instance) 25:1 with a payout of only 13:1 is terrible value. Sometimes, the strength and food adjustments of pirates indicate that it might be a "real" 13:1; in those cases, I do include the 13:1 pirate in these bets).
   
2. Repeat the previous step until you have exhausted the ten bets.
   

Note that you must include all pirates from at least one arena. If all the arenas with "high" negative value have one or two 13:1 pirates, then you must either use a different arena, or include the 13:1 pirates from one arena (check strength and food adjustment to find one that is at least close to a "real" 13:1).

If there are two arenas with a positive value:

Let's call the arenas with a positive value X and Y.
You place ten bets, as follows:

1. One bet on two pirates: the 2:1 pirate from X combined with the 2:1 pirate from Y;
   
2. Zero or more safety bets on two pirates: the 2:1 pirate from X combined with each of the 3:1 to 7:1 pirates from Y;
   
3. Zero or more safety bets on two pirates: the 2:1 pirate from Y combined with each of the 3:1 to 7:1 pirates from X;
   
4. All remaining bets are "booster bets" on three pirates: the two 2:1 pirates from X and Y plus one pirate from one of the three remaining arenas.
   The rules for finding the third pirate in the booster bets are similar to the rules for finding the second pirate in the section for one positive value above.
   One extra rule is that the single 4:1 bet on the two 2:1 pirates may be replaced by a booster bet if at least one arena has all its pirates included in booster bets. To make this happen, I sometimes include a 13:1 pirate in my set of booster bets.
   

If there are three arenas with a positive value:

If one of the three arenas has a very small positive value, you can opt to use the strategy for two arenas with a positive value (using the two arenas with the highest values).
If all three arenas have at least a decent positive value, or if you decide to take a bit more risk (and maybe win a bit more), then you can play the full three arenas.
Let's call the arenas with a positive value X, Y, and Z.
You place ten bets, as follows:

1. Three bets on two pirates: the 2:1 pirates from X and Y, from X and Z, and from Y and Z;
   
2. One bet on three pirates: the 2:1 pirates from X, Y, and Z;
   
3. Zero or more safety bets on three pirates: the 2:1 pirates from X and Y combined with each of the 3:1 to 7:1 pirates from Z;
   
4. Zero or more safety bets on three pirates: the 2:1 pirates from X and Z combined with each of the 3:1 to 7:1 pirates from Y;
   
5. Zero or more safety bets on three pirates: the 2:1 pirates from Y and Z combined with each of the 3:1 to 7:1 pirates from X;
   
6. All remaining bets (if there are any) are "booster bets" on four pirates: the three 2:1 pirates from X, Y, and Z, combined with one pirate from one of the two remaining arenas.
   The rules for finding the fourth pirate in the remaining bets are similar to the rules for finding the third pirate in the section for two positive values above. This also includes the option to replace the single 8:1 bets on the three 2:1 pirates with an extra booster bet if at least one arena has all its pirates included in booster bets.
   

If there are four arenas with a positive value:

This is extremely rare - and offers a very good chance to make lots of neopoints!

If two of the four arenas have an extremely small positive value, you can opt to use the strategy for two arenas with a positive value (using the two arenas with the highest values).
If one of the four arenas has smallish positive value, you can opt to use the strategy for three arenas with a positive value (using the three arenas with the highest values).
If all four arenas have a very high value (20% or better), you can choose to go "all in" on the 2:1 pirates from these arenas:

1. Four bets on three pirates: the 2:1 pirates from each possible combination of three of the positive value arenas;
   
2. Six bets on two pirates: the 2:1 pirates each possible combination of two of the positive value arenas.
   

If all five arenas have a positive value:

This is an extremely rare scenario. I have seen it happen - but only once or twice in more than a year of playing almost every day!
Anyway, if it does happen, then the method is similar to the four-arena scenario above.
There are two alternative strategies, though. The first one can be used if all five arenas have an extremely high value:

1. Five bets on four 2:1 pirates (using every possible combination of four arenas).
   
2. Five bets on three 2:1 pirates (using every arena in three of these five bets, or using the highest value arenas more often).
   
3. Optionally, replace one of the five bets on three pirates with a five-way bet on all pirates.
   

The second one can be used if all five arenas have a moderately high value, and all of them are about as likely to upset (so no easy choice of which arenas to leave out when you want to fallback on the two-, three- or four-arena game):

1. Ten bets on three 2:1 pirates (using every possible combination of three arenas).
   
2. Alternatively, make this ten bets on two 2:1 pirates (using every possible combination of two arenas).
   

Final note

I consider the above system as a guideline.
I usually end up betting according to this system, but I also always check strength and food adjustment of the pirates in each arena.
Sometimes I end up deviating from the method described above. In some cases, this has made me more money, or reduced my loss. In other cases, it has cost me money.

And remember, Food Club is a gambling game. No matter how smart your system, you will always have days, sometimes even weeks, where you win nothing. Don't worry, just keep on playing. My statistics (see below) prove that in the long run, I come out ahead.

Statistics

The tables below list my results. These reflect the bets I made since I started to use the method described above.

Notes:
¹ In round 4769, I decided to play a set of bets that was more risky than the set that my system advised me to play. Since these statistics are supposed to track the value of my system, I have included the 14:10 that the advised bets would have won, instead of the 26:10 result I actually had.
² In round 4770, I decided to play a set of bets that was more risky than the set that my system advised me to play. Since these statistics are supposed to track the value of my system, I have included the 14:10 that the advised bets would have won, instead of the 10:10 result I actually had.
³ In round 4777, I decided to play a set of bets that was more risky than the set that my system advised me to play. Since these statistics are supposed to track the value of my system, I have included the 34:10 that the advised bets would have won, instead of the 26:10 result I actually had.

Recently collected winnings: