05-27-2006, 10:41 PM
im afraid i got way too technical here. perhaps if i had mroe than one white russian i wouldnt have felt so up to doing so much math at 1 am...... ugh
cranberry i might be taking you up on this editing thing.
Chapter 4: Multi Race Optimal Bet Strategies and Parlays.
So now you see which races are profitable, which will ultimately make you a winner in this game. The question becomes: How do you make some serious money.
And again, it goes back to the risk-reward question. To make it clear, we are all about maximizing expected reward. You could put together a crazy strategy that could net you millions if it hits, but if the bets are bad it?s not worth it. You could go buy 5 powerball tickets, that would seemingly maximize the risk-reward ratio too, but again, we are only interested in increasing risk, if our EXPECTED gain increases.
To make it a little easier to understand, lets take some non-foodclub scenarios.
Bag A has 5000 neopoints
Bag B has a 50% chance of 10000 neopoints, and a 50% chance of 0 neopoints.
Which bag is better?
Effectively their expected value is equal, so if this sum of money is not important to our daily activities, we can safely pick either bag and not worry about the consequences.
Lets redo the scenario.
Bag A has 5000 Neopoints
Bag B has a 40% chance of containing 15,000 neopoints, and a 60% chance of containing 0.
Which bag is better?
Now, even though were more likely to walk away with NOTHING, bag b is better, again assuming we don?t need these neopoints desperately. On average, we will make 6000 by choosing bag b over the long run. Since the food club is all about the long run, playing many times over the year, we should clearly choose bag b even though it is a ?riskier? strategy.
At the same time, we clearly want to avoid THIS mistake:
Bag A has 5,000 Neopoints
Bag B has a 10% chance of 45,000 neopoints, otherwise it has 500 neopoints.
Bag B looks enticing, a chance at a big payoff, and at least a consolation prize if it fails. But on average, bag B will only have 4,950 neopoints (45000 * .10 + 500 * .9 if you cant do the math)
Bag B is the mistake though, and therefore is usually NOT worth betting on. (the scenario that it is will be discussed later)
So our goal, always, is to maximize our AVERAGE gain, and I am not worried about the prospect of losing, or even losing big on any race. If you are worried, or are poor, I suggest you take your guaranteed arbitrages when they are there, and just let it go.
So how do we get there?
Great Question. I will lay out my strategies that have made me money. You can use them or modify them to your own liking. Picking the right races is most of the trick anyway, I feel I have tailored my strategies to get that extra bit of profit but its up to you.
Lets start out with some scenarios:
----------------------------------------
Scenario 1: There are no arbitrages on race day?.
Solution 1: Don?t think of betting, unless you are chasing a trophy (and the chasing the trophy section will address this in more detail), or are sufficiently addicted to gambling that you want to take a shot at something and don?t mind throwing the money away. Just take a pass on today, and do other activities.
As a quick guide, here are some ways you can eyeball a race and immediately know its not bettable.
Two pirates have 2:1 odds. The arbitrage rule tells us this is at least -10 points of arbitrage. AVOID THESE AT ALL COSTS. Sometimes you?ll see amazingly bad races of 2 pirates at 2:1 and a third at 3 or 4 to 1. These are even worse than what real life bookies would offer you on an actual horse race. The reality is that the 2:1 pirates are probably about 36% to win. Too juicy for 3:1, but not good enough for 2:1. AVOID AVOID AVOID!!!
No pirates have 2:1 odds. AVOID THIS RACE TOO! The way the math works, again, you never get the benefit of the doubt from the bookie. So something at 26%, even though its real close to 4:1, and should be 3.9:1, only gives you 3:1. As a result, anytime you see no pirates at 2:1, it?s a situation where all 4 pirates are getting a raw deal from the bookie. AVOID.
2 Pirates have 3:1 odds, or 2 Pirates have 4:1 odds in any race. Wont do out the math here, but you can avoid these too?. Trust me.
---------------------------------------------------------------------------------------------------------------
Scenario 2: There is one arbitrage on race day:
Solution 2: Again, if you are looking to maximize profit, only bet on that race. I never touch the 13-1s. Perhaps if you studied garmfay?s method, there might be a spot where a 13-1 seems like a good bet. I don?t study garmfays method though, and usually 13-1 to me means its really about 20-1, so I just stay away. If the race is only marginally profitable, you have a tough call. For example:
Eater A: 2:1
Eater B: 5:1
Eater C: 5:1
Eater D: 13:1
This is about a 5% point arbitrage if you use the analysis I gave you earlier. We think A is 50% to win, B is 20% to win, C is 20% to win, and D is 5% to win.
Again, in these situations I give the 5 points of arbitrage to Eater A, because of the cap at 2:1. We can reasonably assume that if neopets had their way the true value on Eater A would be about 1.9 to 1.
This then leaves us this difficult question, and 2 possible bet strategies. Is it better to just dump your whole load on Eater A, or maybe a big bet on Eater A, followed up with about half sized Bets on Eater B and Eater C?
Meaning we could to the following:
2000 NP Eater A
OR
2000 NP Eater A
800 NP Eater B
800 NP Eater C
The first way, gives us a 55% chance of winning 2000, and a 45% chance of LOSING 2000. The expected value is only 200 neopoints.
The second race gives us a 95% chance of winning 400 neopoints, and a 5% chance of LOSING 3600 neopoints. The expected value is exactly the same. Which strategy do I choose?
I choose the first one. I don?t want to waste my time with 3 bets. I don?t want to only make 400 neopoints. The expected values are the same, but more importantly, Eater B and Eater C are probably also slightly negative expectation bets. Meaning if TNT gives them 5-1 odds, they are definitely better than 6-1, but definitely not better than 5-1. They could be 5.3 to 1, or even 5.5 to 1. Either way, I?ll stick with my single bet and be done with it. Not much of a moneymaker unless it?s a big arbitrage, in which case I feel good about winning my maximum bet back.
Scenario 3: Two races are profitable
Solution 3: Let?s do some talking now!
This is probably the most common scenario you?ll see on a day to day basis. It isn?t your biggest moneymaker, but the skill in doing these right will be a decent and solid bit of profit.
Lets start out with what I call the Two Race Monty
Race 1 has the following pirates
Eater A: 2:1
Eater B: 6:1
Eater C: 9:1
Eater D: 13:1
Race 2 offers us this scenario:
Eater E: 2:1
Eater F: 10:1
Eater G: 11:1
Eater H: 12:1
Both races are decent sized arbitrages, and both are clearly profitable.
The main bet I want to make, again is as follows:
2000 on A at 2:1
2000 on E at 2:1
2000 on AE at 4:1
We?ve talked about this before. This is the basic two race monty, and you will make this bet every time when it comes up.
There are two more bets I want to make. In the one race monty, I didn?t want to hedge, and I had reasons why. Here I will make one hedge bet, and it is a very important bet to make.
2000 on BE at 12 to 1
Why this bet? Isn?t B still a losing expectation pirate?
Yes. B is a loser. But B-E is a big winner. The second race outlined is a big arbitrage situation, 20 full points. Racer E has about a 73% chance of winning in my book.
While Racer B probably isn?t even 16.6% good to win, its going to be above 14% to win, and it is pretty darn close to an even money bet. More importantly, Racer/Eater A has a 32% chance of wrecking us and ensuring we have a losing bet on our two race monty.
Overall, if I just do the two race monty, here?s what I can expect:
50% of the time I win 10,000 (If A and E win)
41% of the time I lose 2,000 (If A or E but not both win)
9% of the time I lose 6,000 (If A and E lose)
All told that?s a net profit of about 3600 per race.
That hedge bet though changes the odds a bit. Here are the new odds
50% of the time I win 8,000 (if A and E win, I win less this time in profit)
12% of the time I win 20,000 (if E and B hit, I get the payoff on E & EB)
29% of the time I lose 4,000
9% of the time I lose 8,000 (again a disaster A and E both miss)
This changes the odds a little bit for me. The potential loss is bigger, but I actually win a little bit more often, and more importantly, my average profit per race is now about 4400 per race!
The hedge bet here is clearly good, because betting on EB by itself is a winning proposition. I could make other hedges, or even change the value of my hedges. I could just bet 1000 on EB, and maybe 1000 on EC. I could even bet 500 or 1000 on AF. Whatever. There is some creativity here that you can tailor to your bet. But this is a spot where the two race monty is good, but a well timed hedge can be even better. 7/8 times you are just throwing away an extra 2000, but that 8th time you are making 22,000 neopoints you never would have had otherwise. And that is a valuable insight.
To conclude: when two races are profitable, bet the two race monty, and possibly hedge, especially if the hedge involves the 2nd pirate having decent odds (I define decent as 7:1 or better, you can define this as you wish)
Scenario 4: 3 Races are proitable
Solution 4: It?s 3 race monty time! (with 3 hedges behind it)
This is actually similar to the two race monty.
Lets set up our races, and go over what the 3 race monty looks like.
Race 1:
Eater A: 2:1
Eater B: 13:1
Eater C: 13:1
Eater D: 13:1
Race 2:
Eater E: 2:1
Eater F: 5:1
Eater G: 6:1
Eater H: 9:1
Race 3:
Eater I: 2:1
Eater J: 4:1
Eater K: 12:1
Eater L: 13:1
3 arbitrages? what to do what to do?.
Race 1 is a monster race. Race 2 and 3 will help make race 1 even more profitable. First the 3 race monty.
Bet 2000 on A at 2 to 1
Bet 2000 on E at 2 to 1
Bet 2000 on I at 2 to 1
Bet 2000 on AE at 4 to 1
Bet 2000 on AI at 4 to 1
Bet 2000 on EI at 4 to 1
Bet 2000 on AEI at 8 to 1
Whew!
For the record, for this particular format, the expected profit breakdowns look like the following:
If all 3 pirates win: 14000 NP turns into 52000, for a profit of 38000
If 2 of the 3 pirates win: 14,000 NP turns into 16,000 for a profit of 2,000 np (ouch!)
If 1 of the 3 pirates win: 14,000 NP turns into 2,000 np for a LOSS of 12,000
If 0 of the 3 pirates win: it is perfectly acceptable at this point to say your favorite expletive as loudly as you wish and spike whatever you are holding at the moment against the floor. Please try not to hold anything in your hand too fragile when checking your winnings.
The odds of course vary, but if your races looked like this, here are my best estimates:
Odds of all 3 pirates winning: .85 * .53 * .62 = 28%
Odds of 2 pirates winning: (.53 * .15 * .62) + (.47 * .85 * .62) + (.85 * .38 * .53) = 47%
Odds of 1 pirate winning = 22%
Odds of 0 pirates winning = .15 *.47 * .38 = 3%
The two pirates winning is basically a push. All your bets cashing in is a little more likely than losing in this case, but its kind of close. Of course the payoff if you win is monstrous. I estimate the total expected value to be 8500 neopoints.
This is a big payday potentially. But now lets make it bigger.
If Eater A loses, we can count ourselves in trouble here, because I want to put in 3 hedges.
They are as follows:
Bet 2000 on AFI at 20 to 1
Bet 2000 on AGI at 24 to 1
Bet 2000 on AEJ at 16 to 1
This isn?t so much for insurance, as we already win if 2 out of our 3 pirates win, but since its quite likely that we will have 2 of our main 3 win, we might as well bet on the scenarios that could provide a big payoff if this does happen. Here are the 3 most likely scenarios with their affiliated payoffs. It is 1:30 in the morning and I don?t want to hit you or myself over the head with any more numbers tonight, but this makes the expected payoff much bigger. Just trust me please.
Anyway? More to come later. I did a lot today, and hopefully can continue the pace
cranberry i might be taking you up on this editing thing.
Chapter 4: Multi Race Optimal Bet Strategies and Parlays.
So now you see which races are profitable, which will ultimately make you a winner in this game. The question becomes: How do you make some serious money.
And again, it goes back to the risk-reward question. To make it clear, we are all about maximizing expected reward. You could put together a crazy strategy that could net you millions if it hits, but if the bets are bad it?s not worth it. You could go buy 5 powerball tickets, that would seemingly maximize the risk-reward ratio too, but again, we are only interested in increasing risk, if our EXPECTED gain increases.
To make it a little easier to understand, lets take some non-foodclub scenarios.
Bag A has 5000 neopoints
Bag B has a 50% chance of 10000 neopoints, and a 50% chance of 0 neopoints.
Which bag is better?
Effectively their expected value is equal, so if this sum of money is not important to our daily activities, we can safely pick either bag and not worry about the consequences.
Lets redo the scenario.
Bag A has 5000 Neopoints
Bag B has a 40% chance of containing 15,000 neopoints, and a 60% chance of containing 0.
Which bag is better?
Now, even though were more likely to walk away with NOTHING, bag b is better, again assuming we don?t need these neopoints desperately. On average, we will make 6000 by choosing bag b over the long run. Since the food club is all about the long run, playing many times over the year, we should clearly choose bag b even though it is a ?riskier? strategy.
At the same time, we clearly want to avoid THIS mistake:
Bag A has 5,000 Neopoints
Bag B has a 10% chance of 45,000 neopoints, otherwise it has 500 neopoints.
Bag B looks enticing, a chance at a big payoff, and at least a consolation prize if it fails. But on average, bag B will only have 4,950 neopoints (45000 * .10 + 500 * .9 if you cant do the math)
Bag B is the mistake though, and therefore is usually NOT worth betting on. (the scenario that it is will be discussed later)
So our goal, always, is to maximize our AVERAGE gain, and I am not worried about the prospect of losing, or even losing big on any race. If you are worried, or are poor, I suggest you take your guaranteed arbitrages when they are there, and just let it go.
So how do we get there?
Great Question. I will lay out my strategies that have made me money. You can use them or modify them to your own liking. Picking the right races is most of the trick anyway, I feel I have tailored my strategies to get that extra bit of profit but its up to you.
Lets start out with some scenarios:
----------------------------------------
Scenario 1: There are no arbitrages on race day?.
Solution 1: Don?t think of betting, unless you are chasing a trophy (and the chasing the trophy section will address this in more detail), or are sufficiently addicted to gambling that you want to take a shot at something and don?t mind throwing the money away. Just take a pass on today, and do other activities.
As a quick guide, here are some ways you can eyeball a race and immediately know its not bettable.
Two pirates have 2:1 odds. The arbitrage rule tells us this is at least -10 points of arbitrage. AVOID THESE AT ALL COSTS. Sometimes you?ll see amazingly bad races of 2 pirates at 2:1 and a third at 3 or 4 to 1. These are even worse than what real life bookies would offer you on an actual horse race. The reality is that the 2:1 pirates are probably about 36% to win. Too juicy for 3:1, but not good enough for 2:1. AVOID AVOID AVOID!!!
No pirates have 2:1 odds. AVOID THIS RACE TOO! The way the math works, again, you never get the benefit of the doubt from the bookie. So something at 26%, even though its real close to 4:1, and should be 3.9:1, only gives you 3:1. As a result, anytime you see no pirates at 2:1, it?s a situation where all 4 pirates are getting a raw deal from the bookie. AVOID.
2 Pirates have 3:1 odds, or 2 Pirates have 4:1 odds in any race. Wont do out the math here, but you can avoid these too?. Trust me.
---------------------------------------------------------------------------------------------------------------
Scenario 2: There is one arbitrage on race day:
Solution 2: Again, if you are looking to maximize profit, only bet on that race. I never touch the 13-1s. Perhaps if you studied garmfay?s method, there might be a spot where a 13-1 seems like a good bet. I don?t study garmfays method though, and usually 13-1 to me means its really about 20-1, so I just stay away. If the race is only marginally profitable, you have a tough call. For example:
Eater A: 2:1
Eater B: 5:1
Eater C: 5:1
Eater D: 13:1
This is about a 5% point arbitrage if you use the analysis I gave you earlier. We think A is 50% to win, B is 20% to win, C is 20% to win, and D is 5% to win.
Again, in these situations I give the 5 points of arbitrage to Eater A, because of the cap at 2:1. We can reasonably assume that if neopets had their way the true value on Eater A would be about 1.9 to 1.
This then leaves us this difficult question, and 2 possible bet strategies. Is it better to just dump your whole load on Eater A, or maybe a big bet on Eater A, followed up with about half sized Bets on Eater B and Eater C?
Meaning we could to the following:
2000 NP Eater A
OR
2000 NP Eater A
800 NP Eater B
800 NP Eater C
The first way, gives us a 55% chance of winning 2000, and a 45% chance of LOSING 2000. The expected value is only 200 neopoints.
The second race gives us a 95% chance of winning 400 neopoints, and a 5% chance of LOSING 3600 neopoints. The expected value is exactly the same. Which strategy do I choose?
I choose the first one. I don?t want to waste my time with 3 bets. I don?t want to only make 400 neopoints. The expected values are the same, but more importantly, Eater B and Eater C are probably also slightly negative expectation bets. Meaning if TNT gives them 5-1 odds, they are definitely better than 6-1, but definitely not better than 5-1. They could be 5.3 to 1, or even 5.5 to 1. Either way, I?ll stick with my single bet and be done with it. Not much of a moneymaker unless it?s a big arbitrage, in which case I feel good about winning my maximum bet back.
Scenario 3: Two races are profitable
Solution 3: Let?s do some talking now!
This is probably the most common scenario you?ll see on a day to day basis. It isn?t your biggest moneymaker, but the skill in doing these right will be a decent and solid bit of profit.
Lets start out with what I call the Two Race Monty
Race 1 has the following pirates
Eater A: 2:1
Eater B: 6:1
Eater C: 9:1
Eater D: 13:1
Race 2 offers us this scenario:
Eater E: 2:1
Eater F: 10:1
Eater G: 11:1
Eater H: 12:1
Both races are decent sized arbitrages, and both are clearly profitable.
The main bet I want to make, again is as follows:
2000 on A at 2:1
2000 on E at 2:1
2000 on AE at 4:1
We?ve talked about this before. This is the basic two race monty, and you will make this bet every time when it comes up.
There are two more bets I want to make. In the one race monty, I didn?t want to hedge, and I had reasons why. Here I will make one hedge bet, and it is a very important bet to make.
2000 on BE at 12 to 1
Why this bet? Isn?t B still a losing expectation pirate?
Yes. B is a loser. But B-E is a big winner. The second race outlined is a big arbitrage situation, 20 full points. Racer E has about a 73% chance of winning in my book.
While Racer B probably isn?t even 16.6% good to win, its going to be above 14% to win, and it is pretty darn close to an even money bet. More importantly, Racer/Eater A has a 32% chance of wrecking us and ensuring we have a losing bet on our two race monty.
Overall, if I just do the two race monty, here?s what I can expect:
50% of the time I win 10,000 (If A and E win)
41% of the time I lose 2,000 (If A or E but not both win)
9% of the time I lose 6,000 (If A and E lose)
All told that?s a net profit of about 3600 per race.
That hedge bet though changes the odds a bit. Here are the new odds
50% of the time I win 8,000 (if A and E win, I win less this time in profit)
12% of the time I win 20,000 (if E and B hit, I get the payoff on E & EB)
29% of the time I lose 4,000
9% of the time I lose 8,000 (again a disaster A and E both miss)
This changes the odds a little bit for me. The potential loss is bigger, but I actually win a little bit more often, and more importantly, my average profit per race is now about 4400 per race!
The hedge bet here is clearly good, because betting on EB by itself is a winning proposition. I could make other hedges, or even change the value of my hedges. I could just bet 1000 on EB, and maybe 1000 on EC. I could even bet 500 or 1000 on AF. Whatever. There is some creativity here that you can tailor to your bet. But this is a spot where the two race monty is good, but a well timed hedge can be even better. 7/8 times you are just throwing away an extra 2000, but that 8th time you are making 22,000 neopoints you never would have had otherwise. And that is a valuable insight.
To conclude: when two races are profitable, bet the two race monty, and possibly hedge, especially if the hedge involves the 2nd pirate having decent odds (I define decent as 7:1 or better, you can define this as you wish)
Scenario 4: 3 Races are proitable
Solution 4: It?s 3 race monty time! (with 3 hedges behind it)
This is actually similar to the two race monty.
Lets set up our races, and go over what the 3 race monty looks like.
Race 1:
Eater A: 2:1
Eater B: 13:1
Eater C: 13:1
Eater D: 13:1
Race 2:
Eater E: 2:1
Eater F: 5:1
Eater G: 6:1
Eater H: 9:1
Race 3:
Eater I: 2:1
Eater J: 4:1
Eater K: 12:1
Eater L: 13:1
3 arbitrages? what to do what to do?.
Race 1 is a monster race. Race 2 and 3 will help make race 1 even more profitable. First the 3 race monty.
Bet 2000 on A at 2 to 1
Bet 2000 on E at 2 to 1
Bet 2000 on I at 2 to 1
Bet 2000 on AE at 4 to 1
Bet 2000 on AI at 4 to 1
Bet 2000 on EI at 4 to 1
Bet 2000 on AEI at 8 to 1
Whew!
For the record, for this particular format, the expected profit breakdowns look like the following:
If all 3 pirates win: 14000 NP turns into 52000, for a profit of 38000
If 2 of the 3 pirates win: 14,000 NP turns into 16,000 for a profit of 2,000 np (ouch!)
If 1 of the 3 pirates win: 14,000 NP turns into 2,000 np for a LOSS of 12,000
If 0 of the 3 pirates win: it is perfectly acceptable at this point to say your favorite expletive as loudly as you wish and spike whatever you are holding at the moment against the floor. Please try not to hold anything in your hand too fragile when checking your winnings.
The odds of course vary, but if your races looked like this, here are my best estimates:
Odds of all 3 pirates winning: .85 * .53 * .62 = 28%
Odds of 2 pirates winning: (.53 * .15 * .62) + (.47 * .85 * .62) + (.85 * .38 * .53) = 47%
Odds of 1 pirate winning = 22%
Odds of 0 pirates winning = .15 *.47 * .38 = 3%
The two pirates winning is basically a push. All your bets cashing in is a little more likely than losing in this case, but its kind of close. Of course the payoff if you win is monstrous. I estimate the total expected value to be 8500 neopoints.
This is a big payday potentially. But now lets make it bigger.
If Eater A loses, we can count ourselves in trouble here, because I want to put in 3 hedges.
They are as follows:
Bet 2000 on AFI at 20 to 1
Bet 2000 on AGI at 24 to 1
Bet 2000 on AEJ at 16 to 1
This isn?t so much for insurance, as we already win if 2 out of our 3 pirates win, but since its quite likely that we will have 2 of our main 3 win, we might as well bet on the scenarios that could provide a big payoff if this does happen. Here are the 3 most likely scenarios with their affiliated payoffs. It is 1:30 in the morning and I don?t want to hit you or myself over the head with any more numbers tonight, but this makes the expected payoff much bigger. Just trust me please.
Anyway? More to come later. I did a lot today, and hopefully can continue the pace
My friends always get together to play an assortment of poker games during weekends.
gj the onlysaneone and thanks again to sirhatter, for revealing one of the greatest secrets since RSing