Since fumbbl is a natural habitat for addicted gamers I guess that some of you are interested in Poker too. As writing down what I learnt about this fascinating game helps me to keep it all in my head I decided do a multipart guide. I´ll restrict myself to Texas Holdem since it´s the only Poker variant I´m really familiar with.

Before I start with rules and strategies I want to introduce you to some basic gambling concepts. Some of those concepts are useful for other games too and may even be applied to Bloodbowl.

"Isn´t Poker a game of pure luck?", some of you may ask. In the long run, it isn´t. If you play only one or ten hands, anything can happen - if you get dealt awesome hands you can win against anyone. You have to see this long-term. In the long run, everyone expects to receive the same distribution of good and bad hands. Being lucky doesn´t make you a long-term winner, playing better than your opponents does. Eventually, the bad players will lose and the good players will win. (anyone see a connection to Bloodbowl there?) Poker is not like playing Roulette - that´s the reason why there are no Roulette tournaments, for example. (Roulette is such a boring game that I wonder why anyone even bothers playing it).
When you play Poker, you have to make several decisions for each hand. In Holdem, there are 4 betting rounds, and for each of those rounds you have the options of folding, checking/calling and raising. When your opponents make wrong decisions you can exploit them to your advantage.

Expectation:

Expectation is the amount of money that you will win or lose on average by making a wager. Say you and a friend agree to bet on the outcome of a coin flip. If the coin lands on heads, he will pay you 1€. If it lands on tails, you will pay him him 1€. Your expectation for this bet is zero. You expect to win 1€ half the time and lose 1€ the other half. On average, this bet is break-even.
To calculate expectation mathematically, you must take an average of all the possible results, weighted by the likelihood of each one. In this case, we have two results: +1€ and -1€. Each result has a likelihood of 1/2. Thus, your expectation (often abreviated as EV for "expected value") is 0.

0 = (1/2)*(1) + (1/2)*(-1)

Now let´s say your friend decides to pay you 2€ for heads, but you still pay only 1€ for tails. Now your EV is 0,50€.

0.5 = (1/2)+(2) + (1/2)*(-1)

On any given flip, you will either win 2€ or lose 1€. But on average, you expect to win 50 cents per coin flip. Since money doesn´t come from nowhere, your friends EV is -0,50€.

Making gambling decisions

To win money gambling over the long term, you need to choose options with a positive expectation and avoid those with a negative expectation. This is why you can´t win money long-term playing Roulette, for example, because the expectation is always negative, no matter on what you bet.

Making Poker Decisions

Likewise, to win at Poker you must make as many plays with a positive expectation as possible, while avoiding those with a negative one. As I explained above, you have three choices each time you act during a Poker hand: fold, check/call, or raise. Each of these plays has an expectation. To win long-term, you "simply" have to chose the option with the highest expectation. Now that is easier said than done, as the most important informations to make that decision are not available to you: your opponents hands and the cards that are still to be dealt. I´ll get back to this later...
As I mentioned, quantifying your expectation for calling and raising is often difficult, but for folding it´s easy: It is always zero. When you fold, you are guaranteed to win or lose nothing more. If either calling or raising has a positive expectation, you should not fold. Note that this means that you do not have to be very sure you´ll win, you just need a positive expectation.
A very simple example: Say you get dealt an Ace and a King (a very good starting hand) and play against 5 opponents. You estimate that if you bet and play you will win the hand one out of four times. Therefore, risking one bet to win five (since you have to five opponents who must call too if they want to play), and you win one of four times, so your immediate EV is 0,5 bets.

0.5 = (3/4)*(-1) + (1/4)*(5)

Even though you don´t know yet if you´ll win the hand (actually you only win 25% of the time), your play has a positive expectation. As a sidenote, in this case not only should you play but raise, because the more money is in the pot, the more you will win on average in this situation.

To maximize your long-term winnings, you must consistently choose the plays that maximise your expectation.

to be continued...