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Tue Feb 17, 2009 12:52 pm
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Eclectico
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Joined: 12 Apr 2008
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Post subject: Relative Monopoly Value Reply with quote

I thought I'd share some pointers for intermediate players regarding the relative value of monopolies. Before reading this, check MagFlag's nice work here: http://www.galacticmag.com/forums/viewtopic.php?t=3138. I believe that a good player must be constantly re-evaluating the value of any monopoly throughout the game.

One very important aspect of monopoly value is opportunity cost. There is a very good reason dark blue stinks in 2p games. Of course, the cost of the upgrades is reimbursed 50% when you sell them. However, the huge upfront outlay means you miss out on other opporunities between the time you upgrade and the time you sell. This means you might miss out on a chance to snag a cheap white or black. It can also kill you because in order to do any damage to your opponent (upgrading blue), you expose yourself to the huge amount of damage he can do to you by getting other properties cheaply. Conversely, dark blue shines in 5p. In 5p you are unlikely to be able to buy more than 1 good monopoly. You don't miss much opportunity by upgrading asap.

Properties like blacks and whites have little associated opporunity costs since they begin to pay out immediately. This is the reason the are worth so much more in the early stages of the game, but decline in value late game. When considering the cost of upgrades it might good to play as if you will only get 10-40% back when you sell them depending on how close EC is.

Another interesting thing is linearity of income increase with upgrades. Of course you rarely have the cash to fully upgrade a monopoly the minute you complete it. Those properties that upgrade linearly in value (brown, red, dark blue, green) are much less risky investments. You can earn a little while you wait for bonuses to fully upgrade. However, those properties that require you to get all 5 upgrades before they pay much (cyan, orange) make it much harder to put any pressure on your opponents. In 4-5P games, properties that increasse linearly in value are strong because every early upgrade allows you to begin collecting from everyone else early.

A third thing worth considering is the affect of bonuses / recession landings. Obviously the more bonuses you hit, the longer you collect money with any monopoly. So, all monopolies increase in value if there are a lot of early bonuses. However, the ones that benefit the most are those normally associated with high opportunity costs. Conversely, if there are a lot of early recessions, everything decreases in value. The monopolies that are hurt the most are those with high opportunity costs. The best monopolies to go for if you expect an early EC are those that have profit potential without many upgrades (pink, black, white).

A tip for aspiring experts: Consider the bluffing potential of monopolies in EVERY decision you make. I won't share all my secrets here, but I can tell you that the bulk of my wins against good opponents involve bluffing. The old adage in Chess that the "threat is often stronger than the execution" defeinitely applies in 2P GM. Experts win games by successfully putting pressure on their opponents (like forcing them to pay a lot to block the 4th utility) or due to their opponent's failure to capitalize on potential bluffing situations.

Cheers
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Thu Feb 19, 2009 1:01 am
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MrCrabbs
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On the subject of the opportunity cost of dark blues, they can in fact be quite useful in 2p games, because if you buy them cheap, then you have in effect spent no money. It is not uncommon to get the first two for under 500 each. Now you only pay 20% if you put them up for auction yourself, so you only pay 400. But they come with 400 worth of credit. So apart from being more likely to have to borrow, and so pay interest (and hence be a touch less inclined to spend), the opportunity cost is very low. Until you buy the third blue and upgrade, you have typically spent nothing, but gained a threat.

Take one of your so-called high opportunity cost properties, the light blue AKA cyan. The opportunity cost of buying them is very high - almost 100%, since they are worth only 10 credit each. You pay money, but can't borrow.

The same is true of the whites and blacks.

So, light blue/cyan - high opportunity cost of purchase, low opportunity cost of full upgrade (it is 2000 well spent).

Dark blue - low opportunity cost of purchase, high opportunity cost of upgrade (it is 700 per 50, up to a max of 3500 for 250, that could have got you a lot more spent on upgrading cyan, pink, green or red).

(Note: the returns from a Euro spent on blue upgrades is in fact higher than the returns from spending that Euro on brown upgrades or orange upgrades, assuming full upgrade of orange and 4x upgrade of brown. This is often something that surprises intermediate players. Adjust your upgrade/downgrade strategy accordingly!)
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Thu Feb 19, 2009 1:21 am
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MrCrabbs
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Post subject: Re: Relative Monopoly Value Reply with quote

Eclectico wrote:
Properties like blacks and whites have little associated opporunity costs since they begin to pay out immediately. This is the reason the are worth so much more in the early stages of the game, but decline in value late game.


Actually, if you have the highest game advantage profit/swing, then the whites actually tend to be especially valuable towards the end of the game, since by giving you income while not hurting your opponent's bank account, they make the game go on longer.

Eclectico wrote:
A third thing worth considering is the affect of bonuses / recession landings. Obviously the more bonuses you hit, the longer you collect money with any monopoly. So, all monopolies increase in value if there are a lot of early bonuses...Conversely, if there are a lot of early recessions, everything decreases in value.


Just to expand on that, if there are quite a few early bonuses, the overall money supply is increase, causing inflation and so higher prices - you should be willing to pay more, just like Eclectico wrote.

BUT, do not do it because you think "oh, this is a high-bonus game, and there will be lots of bonuses throughout the game", since what has happened before has no bearing on what will happen for the remainder of the game. Just coz I flip a coin 5 times and get heads 4 times, it doesn't mean that the next 5 times I will get another 4 heads. Instead, the point Eclectico is making is that the remainder of the game, you assume that bonus will be hit an average amount (that is what we must expect), but you KNOW that it has already been hit more than an average amount, and that ALONE has increased the money supply, and so increased prices.

Lots of bonuses early game + the usual average bonuses for rest of game = more than average bonuses accross the whole game

Therefore, more than average prices accross the whole game.

For those of you who don't understand this, just learn what you can from it and enjoy the game, but for those of you who can understand it but hadn't yet thought about it, iot should be useful.
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Thu Feb 19, 2009 4:38 pm
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Eclectico
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Joined: 12 Apr 2008
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MrCrabbs wrote:
So apart from being more likely to have to borrow, and so pay interest (and hence be a touch less inclined to spend), the opportunity cost is very low. Until you buy the third blue and upgrade, you have typically spent nothing, but gained a threat.


*Edit: After making a post about a hypothetical case, I realized I had left out the auction income. I'm putting together a spreadsheet... will post an HTML version when done.

Agreed, it is the threat that counts with dark blue! However, using that threat correctly requires a good understanding of their bluffing potetnial and the correct timing to execute. I think now that we should consider 2 different things here... the opportunity cost of buying properties and the opportunity cost of upgraded monopolies (the original point of my post).

Your post describes the opportunity cost of buying 2 blues, not a "monopoly" that will be upgraded. While there may be little opportunity cost in buying 2 blues cheaply, you must be carefull not to incurr a high opportunity cost spending too much on the third. Buying a monopoly you can't afford to upgrade is suicide.

It will be interesting to calculate how much your opponent must spend on the 3rd blue to avoid allowing you to gain a credit / cash advantage.

Nice thing about a strategy forum... when you think things through enough to make a detailed post, you learn in the process.


Last edited by Eclectico on Fri Feb 20, 2009 7:26 am; edited 4 times in total
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Thu Feb 19, 2009 4:49 pm
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Eclectico
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Post subject: Re: Relative Monopoly Value Reply with quote

MrCrabbs wrote:

Actually, if you have the highest game advantage profit/swing, then the whites actually tend to be especially valuable towards the end of the game, since by giving you income while not hurting your opponent's bank account, they make the game go on longer.


Can you elaborate here? I'm not sure i get what you are saying. Surely we agree that the earlier you buy a white, the more "hits" you will get. I believe an early game white is worth much much more (in a vacuum). If neither of us own any whites... and EC is looming (late game.. maybee start = +50), I think 1 white is worth significantly less than when start was +280.

By the way, It's a pleasure to talk serious "strategy" in the strat forum! Why haven't you hit top 10 yet? You clearly deserve to!

Cheers mate.
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Fri Feb 20, 2009 10:13 am
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MrCrabbs
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Thanks Eclectico, not sure I do deserve to though.

About the whites making the game go on longer.

Lets' say I have 4 whites. I will get more income per turn. You will get the same income per turn as if the whites were unowned. Since I have unambiguously more income, and you have strictly the same amount of income, the game will last at least as long as if the whites were unowned. They cannot make the game last less time, in and of themsleves.

Now, if I have whites and we both have blocked eachother on the other properties, apart from the blacks which we own equally 2 and 2, then I want the game to go on as long as possible, since I have more income, though I have probably spent more than you. And the whites will make that happen - they will keep me alive long enough to SEE the end of the game, and thus see further benefit of the whites later. This happened in a game I played against Popov where he was the lucky owner of 4 whites, and I the unlucky loser. - Case 1

What if I have whites and I have more income from other properties, whites included, but again I have spent more than you? The whites make the game last longer and again I benefit, because I have more time to let my "swing advantage" come out, as statistically it will with time. - Case 2

What if I have whites and I have more income from other properties, whites excluded? Well, that means I definitely have more swing including the whites, and so again the longer the game lasts, the more likely I win. And the whites stop me going out too early in recession (which is still late in game), so here they definitely are useful towards the end of the game - case 3.

Surely the same would be true of blacks in these 3 cases? Not so much. The whites prevent an early knock-out to their owner by providing twice the income to their bank account, and so preventing an early knock-out. But not being knocked out is not the same as winning. Late in game, they continue to give income, and so assist/allow for the victory. So, whites can be especially useful in early game, since they give you back money faster than blacks, allowing you to make another acquisituon. But they can also be valuable late in game, by extending the game and so CREATING a late-game scenario that would not have otherwise come to pass, since you would already have gone broke. They are their own "no recession for me!" button.

What if I have 4 whites, but you have more "swing" even including the swing I get from the whites? Well, the game will be made to last longer by the whites I own, but typically I will lose, although it will take longer. In this case there is no particular advantage to whites that I can see, though just like any other properties, they might get lucky and see you through.
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Fri Feb 20, 2009 10:46 am
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Eclectico
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Joined: 12 Apr 2008
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You explain what i already belive to be true. Purchasing whites lowers your standard deviation in income fluctuation. Extending the game is good if you have more income. This is also good if you believe your other skills should allow you to "outplay" your opponent more the longer the game lasts. However, the weaker player might chose to spend money (with the same EV) on blacks since the higher fluctuations decrease the skill factor.

However, I don't get how you are showing me that in "general" whites don't decline in value late game. There may be some rare isolated case where buying 1 white for 1200 (that doesn't complete a set) late game may be better than buying a white for 1200 early game. But, in general... surely having that extra income early is better.

Having a set of whites early gives you a safety net. You can take more risks of running slightly cash negative, safe in the knowledge it is highly likely you will "catch up". Thus having whites early is a huge benefit... regardless of the strategy you use for the rest of the game. Buying whites late game (for the same amount you would typically spend early game) is only likely a good idea in rare circumstances imo.
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Fri Feb 20, 2009 10:49 am
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MrCrabbs
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Oh no, I was not arguing that buying the whites for the same price later on could be better. I was never saying that.

I am saying - assuming you buy whites early, then when do they show the most benefit? How does that compare to buying another set early? Those are the questions my post aims to answer.
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Fri Feb 20, 2009 12:55 pm
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Eclectico
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Ah, good to know it was just a semantics issue.

My original statement that whites "decline in value" over time was referring to the opportunity cost of buying them. I gather we are agree that the purchase value of whites does decline over time. Of course this is true of all properties, but I would argue the rate of decline in value for whites is higher than the rate in decline of value of say cyan.

Your comments about the benefits of whites late game are interesting. I might have to think about this more. My inclination is that if player A has 4 whites and player B has 4 blacks... player A has more flexibility in strategies he can employ throughout the game. I guess we all feel this on some level - perhaps it is the main reason whites are always a solid investment.

I have lost many games because i spent too much on 3 whites early, giving my opponent the opportunity to pick up other cheap properties. Perhaps buying whites too early can be dangerous. Perhaps they are a better investment once you know whether or not your opponent's play will benefit from or be hurt from a longer game.
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