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jonts26

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A Primer on Luck
« on: February 27, 2012, 10:40:22 pm »
+14

Luck. Who needs it? amirite?

Weíve all had games where weíre just need to buy that last province to bring home the win only to look down at $7. Twice. In a game with as much shuffling as Dominion, there is understandably a lot of luck involved.

So what exactly is luck? It is everything outside of the control of the players involved. In my definition, anything that canít be attributed to skill, is attributed to luck. And vice versa. It is often said that good players create their own luck. Well, a more technically accurate way of saying this is that skilled play often looks like luck to the unskilled. I say skilled play and not skilled players, because skilled players are often capable of incredible feats of incompetence from time to time. Also saying skilled players wouldnít make grammatical sense. Anyway, over a large enough sample, every single person has exactly the same, neutral, luck. If you think others tend to get luckier than you, either you just arenít as good as you think or you are bad at recognizing luck. Speaking of which...

You Are Bad at Recognizing Luck

The human psyche is wrought with cognitive biases. The important ones for right now though are the self serving bias, outcome bias, and negativity bias. Additionally, you are generally quite poor when it comes to assessing randomness. When taken together this means that you tend to attribute positive results to your own skill and negative results to opponent's good luck. And you will have a tendency to remember the Ďbad beatsí (either real or perceived) more than your own good fortune. And the really cool part, knowing that you have a tendency to do this doesnít stop you from doing it. Also knowing that knowing this doesnít stop you from doing this. And knowing that knowing that knowing Ö you get the idea. Youíre still going to do this.

Discerning Luck from Skill

So how do we decide where in the luck/skill dichotomy a result falls? Well, the primary way is through experience. The more familiar you are with the game, the better you get at separating the two. For instance, a new player might complain that their treasure maps didnít collide. But an experienced player knows that the odds of treasure maps colliding any time soon without support arenít all that great. However, for a good number of example cases we have basic probability on our side. So we can more accurately assess the chances of certain events succeeding and get an objective feel for some measure of luck. More on that in a bit. First, how do we deal with our fortunes.

Deal With It

If you find yourself in the enviable position of favor with the Luck Gods, how do you press your advantage? For the most part, you donít actually need to do anything special. Keep an eye on your opponent but keep using your better deck to attack more, build economy faster, and grab more points in the end game. Early good luck tends to snowball into wins. Late good luck tends to just end the game with a win. There are however, times when particularly good fortune presents an interesting opportunity. An unexpected 5 copper hand in the midgame? Buy that Mint and do your happy dance. Turn 3 $7 hand? Expand or Forge could be your friend even if you wouldnít normally buy them later. Indeed, good fortune can enable strategies and engines which would never be viable normally, but become amazing when just the right conditions are met. Keep an eye out for these.

Conversely, if you find yourself in probabilistic deep water, maybe even before youíve made a single decision, what do you do? Well, you have a few options. Though keep in mind, if you find yourself in a hole, you probably arenít winning anyway. Have Fun!

Curse the Fates: Sometimes helps, though often the Fates just decide to screw with you even more. This option is not mutually exclusive with the following ones.

Hope for the best: Especially when there is a clearly dominant strategy, you really just have to hope luck swings to your side. Or maybe that your opponent makes a mistake. Maybe you opponent's Mountebank and Chapel will fall to turn 5? Probably not though.

Try a different strategy: Sometimes there are competing strategies which are viable. This might be a good time to experiment. You could also try a higher variance, high risk, high reward strategy.

Assume Good Luck:
This applies mostly to late game. Figure out what you need to win and assume your opponent wont steal it from you. If youíre trying to decide whether or not to buy the penultimate province, decide whether you need just one or both to win. If itís both, well you have to hope the other guy canít snag the other first.

Specific Examples

It would take too much pixel ink to go over every instance of luck in the game. Iím giving what I feel are the most important. Itís not comprehensive so please feel free to add anything you want in the comments.

First Turn Advantage:
There is a lot of debate about exactly how much first turn advantage is worth, and it varies from board to board, but it is quite significant. For reference, my winning percentage in games where I go first is 8.9 percentage points higher than in games where I go second.

The opening split: There is a 27.8% chance that both players do not get the same opening split. (And this is even more exaggerated when Noble Brigand and Nomad Camp are in play). Most boards favor either a 4/3 or a 5/2 opening to some extent. In fact, some strategies are only possible with one split or the other (Mint/Foolís Gold comes to mind). This means that in more than a quarter of games, one player is given an advantage simply by how good they are at stacking the deck.

Missing the reshuffle (openings): The opening buys are often structured by what you want on turns 3 and 4. but sometimes you never even see those cards until turn 5. The odds are fairly low (26.7% for one missing, 1.7% that both missing) but the results can be devastating.

Missing the reshuffle (general):
In the general case, you want to play your good cards as often as possible. Barring several unique cases, the most you will see a card is once per shuffle. But if a card falls to the bottom of the pile, you miss one play of it. Especially early and with good cards, these misses can have a large snowballing effect.

Terminal Collisions: Terminal collision odds can be found here. In an optimal terminal/deck size ratio, you still expect a few collisions, especially early. If you donít get them, you got lucky. If you get more than expected, you got the opposite. Congrats.

Turns 3 and 4: Iíd recommend reading the forum posts on openings. Part 1 and Part 2. If you open silver/silver, the odds of drawing a $6 hand on turns 3 or 4 is 42.4%. Hitting Gold (or Goons!) is somewhat lucky, but can be hugely beneficial. Additionally, if thereís a $5 you really want, you have a 91.2% chance of getting it. So to open silver/silver and not get your Witch is quite unlucky (and often game over). Opening things which donít guarantee $2 (Fishing Village, Spice Merchant, Salvager, Loan, etc. ) decreases your chances by varying amounts. So keep that in mind during the first two turns.

The Potion Cards: A special case of the above. When opening potion/silver your chances of missing 2P, 3P or 4P are 18.3%, 34.5%, and 66.3%, respectively. And particularly in the case of Familiar, it could very well be game over if you miss. So donít do it.

Swingy Cards: Some cards are simply higher variance than others, but canít often be overlooked due to their strength. Familiar, Swindler, Tournament, Embassy, Mountebank - Iím looking at you. My Mountebank hits 5 for 5 and you get 1 for 4? Tough cookies. Deal with it.

Overpaying: Generally, you donít want to pay more than you have to for something. This doesn't mean you should never overspend. Indeed itís often the correct play. But for instance when thereís a critical $5 card, youíd much rather your opening split be 5/5 instead of 6/4. This is also true when youíre paying $7 for Duchies and Golds (usually when youíd rather have a province).

The Midgame: By far the hardest part of the game to judge luck is in the midgame. So much so that I donít really have any general tips for you. Well maybe this: If youíre building an engine, pay attention to your deck composition at any given turn. What are the odds of drawing all the key engine components you need on any given turn?

End Game: And finally, we come to the end of things. The most obvious and frustrating possibility of luck is failure to draw enough to buy a province. But before you go crying bad luck from drawing a couple of $7ís in a row, consider you may in fact have beaten the odds to get even that much. Check your final deck composition. If your average $/card is much less than 1.6, donít be expecting too many provinces. Also, if you find you have to spend $13 for a province, youíve also likely been unlucky.

Conclusions

Bad luck sucks.
« Last Edit: February 27, 2012, 11:35:26 pm by jonts26 »
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ecq

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Re: A Primer on Luck
« Reply #1 on: February 27, 2012, 11:12:51 pm »
+1

Nice article!  It's a great topic to address.

Quote
Terminal Collisions: Terminal collision odds can be found here.

Is this missing a link?

Quote
The Potion Cards: A special case of the above. When opening potion/silver your chances of missing 2P, 3P or 4P are 18.3%, 34.5%, and 66.3%, respectively. And particularly in the case of Familiar, it could very well be game over if you miss. So donít do it.

I'm pretty sure that in the case of Familiar, the odds of missing 3P are more like 90%.  Maybe I need to reread section 2.

*edit Okay, I meant the second part there as a joke, but thinking about it, the odds of getting 2P or having the Potion miss the shuffle (or, I shudder to think, both) are closer to 50%, right?  This compounding effect is probably worth mentioning.  While the odds of a specific unlucky thing happening may be low, the odds of something unlucky happening are pretty good.
« Last Edit: February 27, 2012, 11:19:14 pm by ecq »
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WanderingWinder

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Re: A Primer on Luck
« Reply #2 on: February 27, 2012, 11:17:24 pm »
+1

I'd add a bit about how last-shuffle-of-the-deck luck can be totally massive. Probably there's a province hand or two in there, but whether it's on the first hand or the fifth can make a big difference. I guess that's a bigger deal in BM than in engines.

jonts26

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Re: A Primer on Luck
« Reply #3 on: February 27, 2012, 11:37:16 pm »
0

Nice article!  It's a great topic to address.

Quote
Terminal Collisions: Terminal collision odds can be found here.

Is this missing a link?

Quote
The Potion Cards: A special case of the above. When opening potion/silver your chances of missing 2P, 3P or 4P are 18.3%, 34.5%, and 66.3%, respectively. And particularly in the case of Familiar, it could very well be game over if you miss. So donít do it.

I'm pretty sure that in the case of Familiar, the odds of missing 3P are more like 90%.  Maybe I need to reread section 2.

*edit Okay, I meant the second part there as a joke, but thinking about it, the odds of getting 2P or having the Potion miss the shuffle (or, I shudder to think, both) are closer to 50%, right?  This compounding effect is probably worth mentioning.  While the odds of a specific unlucky thing happening may be low, the odds of something unlucky happening are pretty good.

Link added. And the odds I gave for potion cards includes the odds of missing the reshuffle. So there's still about a 2/3 chance of hitting your familiar on turns 3/4. If you think it's worse than that, see the section on cognitive biases.
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yuma

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Re: A Primer on Luck
« Reply #4 on: February 27, 2012, 11:44:29 pm »
0

Since there are quite a few links in the article--well done by the way--a link to WanderingWinder's method of calculating deck $ density might also be appropriate. I looked for it a few days ago and couldn't find it. Does anyone know where it is?
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DG

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Re: A Primer on Luck
« Reply #5 on: February 28, 2012, 12:03:15 am »
0

There is pretty much only one random factor in dominion: the sequence of cards in the decks. It might seem obvious once it is said but I'm sure that players often lose sight of that and get confused by looking at small sections of that sequence (such as a hand).

I'll add a few other luck scenarios
  Bottom of the draw pile - Some decks can't trash their poor cards yet contain some actions can negate many of these poor cards or make use of them. Golem, chancellor, tactician, warehouse, or hunting party are examples. If those actions are at the bottom of the draw pile then you can have absolutely unnecessary wasted hands with the poor cards before you draw down to the good stuff.
  Hidden estates - Cards like salvagers, islands, or barons often want to be drawn with estates on turn 3 or 4. If they're not then not only does your action card perform badly but the estates will give you low spending on another early hand as well.
  Mismatch - One hand you draw three villages. Next hand you draw three torturers. In those three of four hands before you shuffle again the game could easily be lost while your deck goes nowhere.
« Last Edit: February 28, 2012, 08:56:53 am by DG »
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ecq

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Re: A Primer on Luck
« Reply #6 on: February 28, 2012, 12:12:53 am »
0

Link added. And the odds I gave for potion cards includes the odds of missing the reshuffle. So there's still about a 2/3 chance of hitting your familiar on turns 3/4. If you think it's worse than that, see the section on cognitive biases.

Good to know, but I guess my point was that while the odds of some individual unlucky thing happening may be low, odds are pretty good that something unlucky will happen, given enough chances.  For Familiar, maybe you opened 5/2 or Familiar/Potion missed the second shuffle, or your opponent emptied the curse pile while your Familiars sat at the bottom of the draw pile.  Looking at odds for one bad luck event doesn't tell the whole story.
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jonts26

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Re: A Primer on Luck
« Reply #7 on: February 28, 2012, 12:17:02 am »
0

Link added. And the odds I gave for potion cards includes the odds of missing the reshuffle. So there's still about a 2/3 chance of hitting your familiar on turns 3/4. If you think it's worse than that, see the section on cognitive biases.

Good to know, but I guess my point was that while the odds of some individual unlucky thing happening may be low, odds are pretty good that something unlucky will happen, given enough chances.  For Familiar, maybe you opened 5/2 or Familiar/Potion missed the second shuffle, or your opponent emptied the curse pile while your Familiars sat at the bottom of the draw pile.  Looking at odds for one bad luck event doesn't tell the whole story.

Oh no not at all. To have nothing unlucky happen would be indeed quite lucky. With neutral luck you expect some good and some bad. The thing is though, early bad luck tends to be a bigger factor. Missing your familiar on 3/4 is going to be worse than missing a second familiar on the next shuffle. But like I said, that list is just a sample. Real games are much more complicated.
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timchen

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Re: A Primer on Luck
« Reply #8 on: February 28, 2012, 12:22:36 am »
0

Is the 34.5% of missing the familiar enough for one to ignore it, say in a smithy+BM board?
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jonts26

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Re: A Primer on Luck
« Reply #9 on: February 28, 2012, 12:57:01 am »
0

Is the 34.5% of missing the familiar enough for one to ignore it, say in a smithy+BM board?

Against smithy/big money? No, you should still go Familiar. If you miss, it should be a somewhat close game. If you hit, you have it easy. But it is ignorable more often than I think people realize.

EDIT: Someone better at optimizing the simulator can probably actually check this but my instinct tells me that any particularly fast BM like masq, wharf, courtyard, or any BM or engine which can effectively deal with junk like masq again, jack, vault, oracle should be reason enough to skip familiars.
« Last Edit: February 28, 2012, 01:10:22 am by jonts26 »
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blueblimp

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Re: A Primer on Luck
« Reply #10 on: February 28, 2012, 01:51:04 am »
0

Is the 34.5% of missing the familiar enough for one to ignore it, say in a smithy+BM board?

For what it's worth, in the simulator, the included Smithy bot narrowly beats out the included Familiar bot. Results:
  Win: 51.5% +/- 0.4%
  Loss: 45.7% +/- 0.4%
  Tie: 2.8% +/- 0.1%
If the Familiar bot is modified to buy a single Smithy after getting a Potion, it's still somewhat close:
  Win: 43.7% +/- 0.4%
  Loss: 53.2% +/- 0.4%
  Tie: 3.0% +/- 0.1%
I had no idea Familiar was so ignorable.
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jonts26

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Re: A Primer on Luck
« Reply #11 on: February 28, 2012, 01:52:51 am »
0

I think the built in Familiar bot is pretty bad actually. It keeps buying familiars even after the curses run out. In actuality, it should do a bit better in a real game situation.

But yes, I often see people automatically rush familiar all the time when it's a bad play.
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DStu

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Re: A Primer on Luck
« Reply #12 on: February 28, 2012, 02:03:09 am »
0

Since there are quite a few links in the article--well done by the way--a link to WanderingWinder's method of calculating deck $ density might also be appropriate. I looked for it a few days ago and couldn't find it. Does anyone know where it is?

Don't know where it is on the forums, but at least there is a version on the blog. Probably with link to the forum article...
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HB

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Re: A Primer on Luck
« Reply #13 on: February 28, 2012, 07:07:36 am »
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you linked that youarenotsosmart blog and I lost hours of my life.
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Davio

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Re: A Primer on Luck
« Reply #14 on: February 28, 2012, 07:26:51 am »
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I think the built in Familiar bot is pretty bad actually. It keeps buying familiars even after the curses run out. In actuality, it should do a bit better in a real game situation.

But yes, I often see people automatically rush familiar all the time when it's a bad play.
Even with 2 Familiars (which seems optimal), Smithy seems to have a slight lead. When I examine some sample games, the Smithy player is sitting there handsomely with his 10 Curses and 6 Provinces, smiling broadly at the Familiar player.
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Kuildeous

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Re: A Primer on Luck
« Reply #15 on: February 28, 2012, 08:41:40 am »
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you linked that youarenotsosmart blog and I lost hours of my life.

Think of it more as having invested hours in your life.

It is a fun read, though.
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chogg

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Re: A Primer on Luck
« Reply #16 on: February 28, 2012, 09:46:51 am »
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+1 for emphasizing human cognitive biases.
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WanderingWinder

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Re: A Primer on Luck
« Reply #17 on: February 28, 2012, 09:59:37 am »
0

Strong BM can beat weakly-supported familiar, sure. Probably need a little better than just smithy though. But I expect something like wharf to do it without much problem.

A_S00

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Re: A Primer on Luck
« Reply #18 on: February 29, 2012, 01:19:05 am »
0

Even with 2 Familiars (which seems optimal), Smithy seems to have a slight lead. When I examine some sample games, the Smithy player is sitting there handsomely with his 10 Curses and 6 Provinces, smiling broadly at the Familiar player.
Rather than a fixed number of Familiars, I'd say that ceasing to buy Familiars when there are around 4 Curses left in supply seems to work best (though I can't find much of any difference between stopping at 4 Curses and 6 Curses).  This bot beats HME's optimized Smithy bot 49-46, for instance:
Code: [Select]
<player name="Familiar"
 author="Geronimoo"
 description="Familiar is often one of the defining cards on a board.">
 <type name="TwoPlayer"/>
 <type name="BigMoney"/>
 <type name="Bot"/>
 <type name="UserCreated"/>
 <type name="Attacking"/>
 <type name="SingleCard"/>
 <type name="Province"/>
   <buy name="Province"/>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="4.0"/>
      </condition>
   </buy>
   <buy name="Estate">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="4.0"/>
      </condition>
   </buy>
   <buy name="Gold"/>
   <buy name="Familiar">
      <condition>
         <left type="countCardsInSupply" attribute="Curse"/>
         <operator type="greaterThan" />
         <right type="constant" attribute="4.0"/>
      </condition>
   </buy>
   <buy name="Potion">
      <condition>
         <left type="countCardsInDeck" attribute="Potion"/>
         <operator type="smallerThan" />
         <right type="constant" attribute="1.0"/>
      </condition>
   </buy>
   <buy name="Silver"/>
</player>
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Ozle

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Re: A Primer on Luck
« Reply #19 on: February 29, 2012, 07:24:37 am »
0

Can we change the word luck to probability?
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Re: A Primer on Luck
« Reply #20 on: February 29, 2012, 08:51:18 am »
+1

Can we change the word luck to probability?
Given how much of the article is about things like cognitive biases to see ourselves as unlucky and what to do specifically in those cases where, through no fault of our own, we end up on the crappy end of the distribution, I think it's more appropriate to call this a primer on luck than on probability.  A primer on probability would, to my mind, be an appropriate name for just the bit toward the end about opening probabilities.
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Davio

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Re: A Primer on Luck
« Reply #21 on: February 29, 2012, 11:06:28 am »
+4

I think it's important in any board game to try and stay objective. The cards have no memory, they can't help if your genius strategy fails because you can't shuffle good enough. Every turn you start with a fresh game state and you have to optimize your path to victory from there on. Sometimes the correct decision will be to abandon your original game plan and go for that hail mary pass.

Our sense of pride gets in the way sometimes. Instead of trying something waaay out there when we're behind, we sometimes just try to get as many VPs as possible to make it more bearable. I won't recommend switching strategies to beginning players, but experienced ones should know when it's time to switch gears. In the end it doesn't matter  if you lose 40-39 or 40-0, a loss is a loss (barring some tournament rules).

It's good to have a backup plan. Sure you'd love to get that Familiar on turn 2, but what if you fail? Are you just going to ragequit or is there something else that you can try? Alternative VP cards for instance or Embargoing a crucial pile. You must consider these options even before buying your first card. A lot of the times when there are attack cards and I see my hand of cards I think to myself: "I will discard these cards if he attacks me and buy this and if not, I will do that." Not only does this speed the game up, it also prepares you mentally for the attack. You shouldn't go "Aaaaaargh, why did he have to play his Militia at this point @#&*$?" Just take it in stride and go with your backup plan for that turn.

Don't be scared by your opponent playing an attack card or buying a Province. If he can do so, he will do so anyway and your anger won't change it. Play your own game, go with the flow and go for broke sometimes when there's no other way.
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WanderingWinder

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Re: A Primer on Luck
« Reply #22 on: February 29, 2012, 11:12:54 am »
0

I think it's important in any board game to try and stay objective. The cards have no memory, they can't help if your genius strategy fails because you can't shuffle good enough. Every turn you start with a fresh game state and you have to optimize your path to victory from there on. Sometimes the correct decision will be to abandon your original game plan and go for that hail mary pass.

Our sense of pride gets in the way sometimes. Instead of trying something waaay out there when we're behind, we sometimes just try to get as many VPs as possible to make it more bearable. I won't recommend switching strategies to beginning players, but experienced ones should know when it's time to switch gears. In the end it doesn't matter  if you lose 40-39 or 40-0, a loss is a loss (barring some tournament rules).

It's good to have a backup plan. Sure you'd love to get that Familiar on turn 2, but what if you fail? Are you just going to ragequit or is there something else that you can try? Alternative VP cards for instance or Embargoing a crucial pile. You must consider these options even before buying your first card. A lot of the times when there are attack cards and I see my hand of cards I think to myself: "I will discard these cards if he attacks me and buy this and if not, I will do that." Not only does this speed the game up, it also prepares you mentally for the attack. You shouldn't go "Aaaaaargh, why did he have to play his Militia at this point @#&*$?" Just take it in stride and go with your backup plan for that turn.

Don't be scared by your opponent playing an attack card or buying a Province. If he can do so, he will do so anyway and your anger won't change it. Play your own game, go with the flow and go for broke sometimes when there's no other way.
I'd be much more scared if I bought a familiar turn 2 than if I didn't (though hey, I guess it's possible).

Davio

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Re: A Primer on Luck
« Reply #23 on: February 29, 2012, 11:48:35 am »
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Point taken. A bit of overkill to quote the entire post to point out one typo though. :)
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WanderingWinder

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Re: A Primer on Luck
« Reply #24 on: February 29, 2012, 11:49:46 am »
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Point taken. A bit of overkill to quote the entire post to point out one typo though. :)
Oh that's me just being lazy.
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