Tuesday, July 23, 2013

Understanding Texas Hold'em

As a huge fan of the game of Texas Hold'em, I inevitably get into discussions with people who tell me that they just don't get it, or try telling me that the game is all about bluffing.  The reality is not as hard as people make it out to be, and what they're really talking about is hand reading.  Trying to figure out what your opponent is holding is not actually a mystical skill, but really a case of deductive reasoning and a little bit of math.  I'd like to discuss some of the basics of poker fundamentals for anyone who might be interested about the topic.
Card Combinations
The first thing to know is that there are 169 different two card combinations that a player can have as their hole cards:  13 pocket pairs, 78 unsuited card combos and 78 suited card combos.  This might seem low, but you keep in mind that the suits of the cards don't have any value over one another (Hearts have the same odds of appearing as Spades.)  After that, we need to roughly rank the 169 hands from top to bottom to be able to figure out what percentage of total hands they encompass.  I'm not going to list them out here, because exact math will rarely come into play during an actual game, instead you need to have a good feeling for general ranges.  I've listed out some ranges below along with the percentage of total possible hands that is included in the category, followed by the odds of being dealt one of those hands.  There are other combinations that can be calculated, but if you're looking for a place to start, the list below will do you well.

  • Pocket Pairs
    • AA or any specific pair (0.45%)(220 : 1)
    • AA, KK, QQ, JJ, or TT (2.26%)(43.2 : 1)

  • Suited Cards
    • Suited cards, 10 or better (3.02%)(32.2 : 1)
    • Suited connectors (3.92%)(24.5 : 1)

  • Connected Cards
    • Connected cards, 10 or better (4.83%)(19.7 : 1)
    • Connected cards, all (15.7%)(5.38 : 1)

  • Big Card Combos
    • Any 2 cards with rank at least queen (4.98%)(19.1 : 1)
    • Any 2 cards with rank at least jack (9.05%)(10.1 : 1)
    • Any 2 cards with rank at least 10 (14.3%)(5.98 : 1)
    • Any 2 cards with rank at least 9 (20.8%)(3.81 : 1)

So what this means is that you can choose a number of hands that you want to play, and match that up with the number of times that you'll be dealt those hands.  If you want to play tight, maybe you will play any 2 cards with a rank of Jack or better.  That means you'll be playing about 9% of the hands that you are dealt, or about 1 in every 10 hands.  The more hands you're playing, the more the average value of your hands drops.

Player Profiles
The next step is understanding the type of player that you're playing against.  Again, this isn't rocket science, it's really just deduction and math.  If the player is a maniac who is playing 90% of the hands that he is dealt, he isn't the luckiest guy in the world, he's playing a bunch of garbage hands!  If you only enter the pot with him when you are playing the top 9% of the hands that you're dealt that means that before the flop, your hand is going to be stronger than his hand 90% of the time.  The remaining 10% of the time you're not necessarily beat, but that portion of his range is the same as the cards that you are playing.

Subsequently, if a player is super tight and is only playing 5% of his hands and you're playing 10% of your hands, whenever you two are in the pot together, 50% of the time he will have a better hand than you do.

Bringing the two together
So the part that tends to lose people, is trying to answer the question: "How do you know that he doesn't have Aces?"  The true answer to that question is: "You don't."  What you do know, however, is that there is only a 0.45% chance of someone being dealt Aces, and you know what percentage of their total range includes Aces.  If someone is the tightest of the tight, and you know they only play pocket pairs of 10 or better, they are only going to play 2.26% of hands.  If you act before them in an unraised pot, you will get them to fold to a bet when you hold any two cards 97.74% of the time.  Then, whenever they call or raise your bet, you know that they are holding one of 5 possible hands, and you can play accordingly.

If you are playing against another player where their range is the top 15% of all hands, the odds of them having Aces when they play a hand against you is 3% (0.45/15).  Knowing these odds, and being able to characterize the people you are playing against are probably the two most important parts of the foundation for becoming a good player.  

Power of Position
There are generally 9 seats at a poker table, assuming the table is full, and the player who is first to act will rotate around the table with each hand.  This is very important, because acting later in the hand is far more powerful than acting first.  If you are last to act in a hand, you get to see what every person ahead of you does before you have to decide what you want to do.  Now this doesn't mean that everytime you act last you're going to win the hand, but it does mean that you should rarely be losing money when you're beat and you should be able to maximize what you gain when you're winning.  For example, if you have pocket 9's and you're first to act, you raise the hand, and two people behind you call.  The flop comes Q 10 4.  Now there are two over cards to your hand on the flop, since you're first to act, if you bet, it's easy for someone with either of those cards to call you and you have no idea what they have.  If you check, it's easy for someone with any two cards to bet their hand, and you have no idea what they have.  They could easily have a Q or 10 in their hand, or they could have a smaller pocket pair than yours, or even something like KJ.  Being able to see what another players interest in the pot is before you have to decide what to do is always going to be better then needing to act first.

Avoid being results oriented
If you've played poker before, I'm sure you've heard someone recant some horrible bad-beat story about how someone beat them in a pot when they had pocket Aces when their opponent only had pocket 7's.  So now, to make sure that no one calls them, they always overbet whenever they have a big hand to make sure they get all the "garbage" hands to fold.  This type of player is being results oriented, and he's losing a ton of money when he plays like this.  You want people to call with worse hands when you have Aces, you've got them beat!  You also want to try and get them to put even more money into the pot when they are beat, because this is how you make money!  Understand that about 15% of the time, they will win the pot with a smaller pocket pair, that's just the way the odds work.  But that means in the long run, you will be ahead whenever you bet with Aces and get called.  You have to think of poker over the long-term, not just an individual session.

For more information on probability in Texas Hold'em: http://en.wikipedia.org/wiki/Poker_probability_(Texas_hold_%27em)

Tuesday, July 16, 2013

Most Common Feedback for Board Game Designers

Designing board and card games is harder than it looks.  Just like everything else it life, it gets a lot easier after making a ton of mistakes and learning from them.  Here are some of the most common things you’ll hear from veterans in the industry that we can all easily avoid with a little bit of work.  This is not intended to be a list of rules that can never be broken, but instead a guideline of common occurences in designs that may not be an intentional choice.

Visit BoardGameGeek.com
If you are new to the industry, welcome!  There are some great resources that have been around for many years to assist in your journey.  Yes the site may be a little confusing and difficult to navigate at first, but consider the time spent a cost of entry to the hobby.  It’s worth it! 

No Roll and Move
Unless you have a time machine and are travelling back to the 1980’s to design games before anyone knew better, don’t use a single roll of the die to determine movement in your game.  It’s frustrating to the players and uninspiring design.

No Paper Money
This is simply a component that publishers and players alike just don’t like.  It wears out quickly and is harder to handle than the alternatives.  Don’t use it!

No Collectible Card Games
This is a distribution model that just is not feasible for any new game these days.  If you want to try and make a CCG, you’ll need that time machine again and go back to the 1990’s to get in on the fad when it was cool.  We can’t all be as lucky as Richard Garfield.  Many very large companies have tried and failed, these days a publisher would prefer a static expansion model instead.

Don’t use classic game parts
These are not attractive to publishers or to players.  If your game uses a chess board, or chess pieces, or a standard deck of cards, this is not a marketable game because people already own these items.  A game that combines chess and rummy is not a new game; it’s a variant of existing games.

A game is different from a simulation
The best games almost always use abstract representations to signify events.  It certainly takes more than 1 wood and 1 brick to build a road in real life, but it works just fine in Settlers of Catan.  Don’t bog your game down trying to simulate reality.

Do not create game effects that cause other players to lose their turns (literally or functionally)
This style of design is what I like to call a “negative play experience”.  This isn’t fun for the person that it happens to, it’s only mildly interesting for the person doing it, and the game is never better because it exists. 

Avoid linear dice rolls when possible
If you want to balance a random event to happen a certain percentage of the time, try using two or more dice to force the dice into a bell curved average instead of a linear one.  The sample size of dice in single play of a game is usually not enough to realize the true average of a linear roll.

Perception is just as important as reality
Just because a mechanism or event may be balanced on paper, or “fair” in the long run, doesn’t change the perception of the event when it takes place.  Just think about the old saying of “You only get one chance to make a first impression.”

Avoid player elimination
In general, you should avoid player elimination from your game.  If it is truly an essential or unavoidable part of your game, ensure that the time between a player being eliminated and the end of the game is not longer than 15 minutes.

Games need to be able to be taught
Hour long explanations are generally not something that anyone looks forward to when trying to learn a new game.  Think about what you can do to assist in teaching the game to new players by lowering the initial number of decisions or complexity, and ramping it up as the game continues.  Games should be interesting or fun to play the first time you play them.

Don’t have players make decisions that will impact the outcome of the game before they play
Trying to add variety to a game with a card draft is cool, but you need to have a way to play the game outside of using a draft as so people can learn it.  Even if it’s just playing with a random set for a few rounds before restarting the game with a draft, make sure this is an option for players, as well as the preferred way to teach your game.

If players start the game taking the same actions every game, start the game from there
If there are obvious first steps in the beginning of the game, build it into the setup.  You should always start the game from the position where players begin to make unique decisions from each other.  The exception to this advice is when it makes the game easier to learn.

Make decisions meaningful / Remove non-decisions
If I can always spend $1 to gain 1 point or I can spend $2 to gain 3 points, I will never spend $1 unless I am forced to.  This is a non-decision, and does not make the game more interesting if the player understands basic math.

Payouts should not always be linear
If you balanced your game in a spreadsheet, it is either going to be cleverly hidden, or transparently obvious.  Be aware about what side of the coin your game is falling into, and make sure that the balance is transparent to everyone who isn’t looking for it.  Keep in mind that a curved payout line is generally more interesting than a straight payout line.

Stealing from another player is twice as effective
Stealing 3 points from another player is better than gaining 5 points from the game.  The first gives a net gain of 6 points whereas the second is a net gain of 5.  Understanding this simple concept will prevent hours of wasted play time to fix simple imbalances.  The increase in your margin may be less with multiple players in the game, but the impact for the two players involved in the theft will be greater.

Edge cases will happen, if they ruin the experience, they need to be fixed
If there is a 1 in 100 chance that one player will get absolutely screwed, or one player will completely dominate the others, then it will happen sometimes.  If it happens sometimes, it’s going to happen to a player playing your game for the first time, and they will have a terrible experience.  You need to fix these issues.

If you need to make an exception to a rule, question the inclusion of the rule
If a player is always able to do something 98% of the time, but 2% of the time they are prevented by an arbitrary rule, this was likely an attempt to balance something.  Make sure that the situation that caused the 2% is really necessary for the game.  Try to avoid special case rules whenever possible.

Sometimes less is more
Games are not always about what you have included into the game, most often the game is about giving the feeling of an event in the simplest way possible.  The best games are the ones that express great complexity through simplicity.  Once you think your game is done, try taking something out.  Study which parts of the game people enjoy most, and which feel more like maintenance.

Graphic design is more important than people like to admit
Players need to be able to process the information in your game to be able to understand it and play it.  Anything you can do visually to assist with that goal is going to make everyone’s life much easier

Know your target audience
You should have an idea about what type of player your game is going to appeal to, and how long you expect your game to take.  This will help you in making decisions between various changes in your game.  If it is supposed to be a light family game, you probably don't want heavy math involved.   If it's supposed to be a tight economic engine game, you probably don't want heavy random swings based on dice.

Consider publication costs in your designs
Everything has a cost.  Games with 900 cards, 50 custom dice, or 400 wooden cubes are going to be expensive to produce.  When designing, think about ways to simplify your designs to remove components that don’t need to be there.

Be able to accept feedback
This should go without saying, but it’s easy to be offended by someone who is giving you feedback about your game.  Make sure that you separate yourself from the situation and look at the comments objectively.  They are trying to help, and they are talking about the game, not about you as a person.

This list was started and discussed on a trip back from Protospiel.org with James Mathe (@MinionGames) and Dustin Oakley (@CrassPip).  This list has been reposted with some additional commentary by James on his site:  http://www.jamesmathe.com/game-design-for-dummies/

Tuesday, July 9, 2013

Levels of Thinking

Have you ever made a decision in a game that wasn't necessarily the de-facto "best" decision to make at face value, but you thought it was the correct thing to do based upon how your opponent would respond?  Congratulations!  You've experienced a metagame.

Metagaming can be defined as any aspect of strategy that involves thinking about what your opponent is thinking.

I'm going to assume that you've played the game Rock-Paper-Scissors (RPS).  The "game" of RPS is almost entirely a metagame.  You are trying to figure out what your opponent will throw so that you can throw whatever will beat it.  This is the simplest form of a metagame, but it's a great way to introduce the concept of Levels of Thinking.

  • Level 0 Thinker

"I'm going to throw rock, nothing beats rock."

  • Level 1 Thinker

"I know my opponent is going to throw rock, so I'm going to throw paper."

  • Level 2 Thinker

"I know my opponent thinks I will throw rock, and so he's going to throw paper, so I'll surprise him and throw scissors."

Adding additional levels will continue to change what you throw based on about what you think your opponent thinks you think your opponent thinks you will throw.  Follow that?  Good.

This general thought process is used in nearly every game, and for most people, it doesn't go past the first or the second level of thinking, because anything beyond that requires that you have great judgement on the true level of thinking of your opponent.  In the case of RPS, the choice of a third level thinker is the same choice that a level zero thinker would choose, which illustrates how there are times where genius can look like ignorance and vice-versa.

In fact, if you judge your opponent as a 3rd level thinker who is going to throw rock, so you should throw paper, and he is really a 2nd level thinker who is going to throw scissors, you've obviously made the worst choice possible because scissors beats paper.  Since RPS only has three selections to choose from, the levels of thinking are overly simplified as they will circle themselves very quickly, but they illustrate well both the benefits of higher level thinking, as well as the pitfalls of poor judgement.

The poker variant of No-Limit Hold-em is probably one of the most major, yet recent, example where a new metagame has greatly changed and evolved in the last 10 years.  If you've watched any recent poker tournaments on TV, you've no doubt seen people re-raising a player with some very questionable hands.  This is due to the evolution of the poker metagame and the players understanding that the cards don't matter if you can get your opponent to fold.  It used to be that a re-raise meant that you had Kings or Aces in your hand.  Eventually, players started to use that line of thinking to their advantage, being able to represent those hands far more often than they were actually dealt them.  When their opponents realized this fact, they had to adjust their play accordingly, and push back with hands weaker than they used to.

In the end, all forms of competition will benefit from higher levels of thinking.  From video games to board games to sports to poker and even business, knowing what your opponent is going to do, or knowing what they think you are going to do is going to give you a huge advantage in your decision-making.