Given the rules of the game, players want to pursue the objective to keep money for as long as possible, not spend it all in one turn. When there is a majority going against the grain in such a fashion, the only factor of relevance is cooperation.

That is the definition of cooperation.

EdTrice: It is always possible, although statistically unlikely that every other player will bet their entire amount of the first round. In that case, you will fall in regardless of your wager. Thus there is no way you can 100% guarantee that you will win.

Answer: If there is NO COOPERATION among the other players, and the OBJECTIVE is to last for as long as possible, you can say with 100% certainty a bet of $19,999 will keep you around until the next turn.

Why is this so?

The only way to "lose" would be if everyone bet $20,000 (I am not sure if this would mean they all zero out anyway) which would imply massive cooperation, which would mean criterion #3 for unravelling the strategy has been evoked.

Granted, this is a ridiculous example, but you can go through a RETROGRADE ANALYSIS of survival through N rounds, then determine a bound you need never cross, then work your way back, then come up with a betting plan.

It is easier than you think, just play with it on paper (or in Excel) and you will see what I mean.

Let me not give away the system but still try and answer your question.

Is there a bet I can place on round 1 that will 100% guarantee that I do not fall into the pond? say $20,000 is the max, what is the most I can bet and still have me around for turn 2?

EdTrice: Ok, so throw us a bone. I assume your bet for the first round is a function of the number of players in the pond. Pick a number of players close (or even not close) to the 50 currently entered in the pond you are going to play in, say 47 (or 447). What would your first bet be?

Do you have a link to a copy of Nash's paper?

The bet is a function of the number of players, the round, the average money per player, the standard deviation of the money, and your rank.

Plug all these into an equation, it spits out the bet you should make.

By the way, I have been signed up for a pond game for quite some time Walter. I am just waiting for it to start.

Thad:

1) Like a WWII pilot, you learn about them after the fact.

2) You can know with 100% certainty that you will not fall into the pond. The only way there is a CHANCE you DEFINITELY will fall into the pond is if everyone works together against you. Read Nash's paper. It deals with cooperationg and competition.

It's a simple question. Are you, or are you not going to play? Who cares about your spreadsheet. Just play the game. If you win, you win. If you lose, I'll give you a hard time about it, but atleast you can say you played the game.

Who's in denial. May I quote yourself?
"I don't understand why there is denial over this simple fact."

OK, I'm through. I think I've made my point. I will let the game speak for me on this subject now. Thank you all for your indulgence. We'll see you on the shore testing the waters Ed.

EdTrice: Oh, and is the minimum number of players this will work with two or do you need more initially for it to work?

EdTrice: I also do not understand how there can be a system for this, and would also love to take a look at the spreedsheet.

For example, start with 20,000 points - 20 players - first bet - what does your system tell you what to bet? What factors are in place to decided what to bet?

On first bets, I have seen some fall into the pond with a bet of 3, others with a bet of 18 (and as the game goes on - I would think first low bets will be 100+ or even 1,000+)

On first bet, i have seen some people get the 500 bonus with bets in the 200's - giving them OVER 20,000 points to start the second round. But I have seen some bet over 1,000+ on the first round also - leaving them over 500 down.

I just don't see how a system can help - but i'm interested in learning.

EdTrice: I am still unconvinced.

1) How do you distinguish a "kamakaze" from someone who has just made a few bets that work against your method?

2) How do you know what to bet in the first round? There is no mathematical way to know for certain that you will not fall into the pond on the first round.

I will disclose the method to Pedro after filtering out the high level math, but there is nothing in the spreadsheet that is not in Nash's paper.

Nash's paper deals with things far more complex than the pond game. It deals with a wide range of applicability such as Nuclear Arms Race negotiations, trying to get a better raise from your boss, deciding which girl to ask to dance in a crowded room, and plea bargaining a federal conviction.

It works for Pond games too, unless, as previously stated:

1. Some other person also derives the strategy.

2. A "kamikaze" id enters the pond with the sole objective to disrupt your strategy, even though they will lose sooner in doing so.

3. Everyone else messages what they will play, so it is you vs. the pond-dwellers rather than everyone for themself.

Maybe even a group can pool together and cooperate and thereby influence their own self preservation longer than they could if operating alone.

The point is:

This is a mathematics game, which means it can be modeled. It is "small enough" so that every permutation can be plotted.

I don't understand why there is denial over this simple fact.

EdTrice: We, and until now, you were talking about the Pond game. You change the subject as you wish. Bragging again about games that you will play, but not ones that you won't. What's the point? Who's going to take you seriously. I'm not. Now go back to your machines and programs. Hey Ed. Mr. Chess champion, let's play some Dark Chess. I might be number one in the ratings, but I'm easy to beat. A couple of newcomers beat just this week. How's 'bout a series of games, say 7 of them. You expect you to win every one of them. I'll be happy if I win four. Or do you only play games were the outcome is certain to be a victory for you?

Yeah, suddenly you say your Pond system is now worthless. Why'd you rub it in our noses then?

You know what, I can win 100% of all my Pond games if all my opponents make predictable bets too!

it's nonsense. There cannot be such a strategy. Once again, produce the math, not just a vague reference to an old mathematician.

EdTrice: Oh, ok. It seemed like you were talking about Ponds (here). In that case, let's play a game of Pente. ;-)

As far as your strategy goes, you're saying that it works as long as another player does not employ the same stragegy or intentionally make a "kamakaze" bet. Is that right?

Thad, your profile says:

235 wins, 17 draws, 97 losses.

You have lost 97 times. I was not just talking about the pond.

I said earlier, once someone rederives the strategy, it is of no use anymore, so what is the point?

EdTrice: What happened to your proposal for a wager? The post seems to have been edited or deleted. Does that mean you don't want to wager? If so, why not?

PS: My hand is up too.

Walter Montego: His arguments are getting weaker. Next it will be tea leaves.

EdTrice: And you are currently entered in how many pond games?

I still running in one and have lost one, you?

Walter Montego:

OK, everybody who has not lost a game on here, raise their hand.

(looks around) My hand is up.

Don't let my tone fool you. What Ed is alluding to in the study of games of this nature is a very complicated type of game theory. I just want to see it put into practice. If he can win all the games, perhaps the game will stop being played. Or, maybe we don't want fencer posting all the bets or what order they were placed in and just leave how it is now. After Ed has played a few games, we'll see the results of his spreadsheet system. Though I'm willing to bet that Ed won't even enter three pond games, let alone enough of them to prove that his system works. Wining every game seems preposterous on the face of it. Winning just a little more than your share of the amount of people entered would make you a pretty good player in my eyes. Say you enter 16 different games and each of those games has 16 people in it. If you're able to win more than four of them consistantly, you must be on to something and know how to play good. That's better then luck alone would explain after enough games have been played.

Looks like Pedro Martínez will be the first pond winner of his own pond! - http://brainking.com/game/Pond?g=69&trnst=10

Shortly after that, zockerdotcom should be our second pond winner - http://brainking.com/game/Pond?g=26&trnst=10

EdTrice: Yeah, right. Stop the hot air, enter a few games and put theory to test.
I'm willing to bet he loses more than half the games he enters. That's assuming he enters more than ten of them. Any takers?
As they say of system players at the roulette table. "System players go broke systematically."
It fails on the logic of it. Suppose we all used this "Strategy". Someone has to lose. So play the game and make us believers.

ditto

I'll believe it when I see you win every pond you join, EdTrice

EdTrice: OHhhhh that was such a gooooooooooooodd Movie!

EdTrice: If ANYONE can win this game by employing mathematics...Mr.Nash is the Man

The winning strategy, by the way, was the subject of the mathematical paper written by John Nash which was the subject of the movie A Beautiful Mind with Russel Crowe playing Nash.

There, now I revealed my strategy.

ScarletRose: I'm not saying that there are no strategies to employ that may or may not improve your chances, only that there is clearly no way to force a win from the outset.

This is OBVIOUS and frankly frustrating to listen to. Let anyone place the mathematics attempting to prove otherwise here and I'll show you why it's bunk.

This pond kinda shows my point:

http://brainking.com/game/Pond?g=108&trnst=2

Grenv bid 511 but was outbid by 523. There were others who bid 500+ as well, so they show the example of what happens when several people aggressively pursue the bonus.

But there are two things a player can do:

1. Minimize losses
2. Maximize gains

I am pretty sure some of you are well on the path to the right track, but you are using intuition (how else you can explain the "511") rather than deduction (a formula that will let you outperform the field.)

I joined a pond of 50, so now I know there is a target on my back

grenv: No grenv, his examples he showed me that the bids can force people in a "defensive" mode, betting higher to keep one player from winning the bonus, when in fact, they become self defeating, and many people run out of money sooner. I seemed to remember that if you play too cautiously and don't win any bonuses, you can end up with your bankroll being doubled or tripled or even more by his bidding winning bonuses. If you try to get bonuses after you fall behind, it costs you too much to earn them, and you lose that way. I think.

grenv: you don't have to bet higher than everyone else to "win" a round. Your objective is not to be lower than everyone else, correct?

EdTrice: No amount of obfuscation will change the fact that you cannot guarantee a win in a game like this. What number is your first?

e.g if you bet 100, it might be a losing bet (everyone else bets between 1 and 20, and one person bets 101), it might be a winning bet (by being the highest). How would you know? impossible! Stop the tomfoolery and play.

EdTrice: Yes.. at the end of the round.. since we have certain time limits set to place our bids.. we can also edit them up to the deadline..

Czuch Chuckers:

You hit the nail on the head, Mr. Formerly UpchuckKing.

But when will "everyone" do this? Will everyone bid the sum of their money on the first run? How about the second run? Will they bid half of their money?

The idea is to force as many people as possible to bid as high as possible, and still be able to bankrupt them.

Like entering the Final Round of Jeopardy with more than twice as much money as everyone else. It does not matter what they bid, you can't lose.

Now use retrograde analysis and keep working your way back from a proven win.

You will see an interesting pattern emerge, independent of what other people bet.

And, since I generated all of the betting scenarios, I discarded the ones that lose, and the ranges of lost bets, and guess what

I do have one question though.

At what point can you see what everyone else has bet. At the end of each round?

Czuch Chuckers: Exactly! Smells like a horse racing system to me!

I dont think there can be any fl proof way to win a pond game, no matter what any computer says. There is always a possibility that everyone will bid higher than you and knock you out.

Ed - I'd like to see your spreadsheet-based strategy in practice. You can use it in my Run Around the Jacuzzi pond, if you want to.

what distribution do you assume for the bets of all players in 1 round ?

EdTrice: I believe your claim to be in error due to the fact that no matter what bet you make, I can make a better one (or at least equally good). Certainly there are good and bad bets in certain situations, but it's more about understanding the opposition.

Ed, can you e-mail me the spreadsheet so I can have a look ? or is it top secret...

I'd take part as an honest independent player in a test run.

Stevie: SIMULATION SIMULATION

Hello! I have not played in a pond before, this was just running numbers to show there is a way to:

a) secure the top point position
b) bankrupt "n" people below you in the long run, where "n" = the round number + 1, or splash the only person who can catch you with boni.

... and luckly Pawns can not play in the ponds!

EdTrice: Of course we both know it won't mathematically prove your claim, but I sure would like to see it! And, ok, I'm up for a small wager. What do you propose? Also, I suppose we would have to create a special pond (or ponds) with the rule stipulation that spreadsheets are allowed so Stevie won't complain. ;-)

There are three ways to circumvent this method.

1. Discover it for yourself prior to the start of the pond, and move before the other person who knows the strategy.

2. Enter "kamikaze" pawn ids and have them screw everything up.

3. Somehow get access to everyone else's numbers, through messaging one another or bribing Liquid

So yes, there is still a way to lose, so I guess it is pointless to argue.

EdTrice: what does that say?

Looks to me like the macro's and formula's etc etc are making the choices..not you


A spreadsheet that is not helping is like the bad biiishop one...its just a reference chart