All poker variants share the same system of hand rankings. But how are they decided?
Quite simply it’s down to the likelyhood of the hand occuring, with rarer hands worth more. We can calculate the probability of being dealt a hand by looking at the number of ways five cards can make that hand.
There are 311,875,200 ways (permutations) of being dealt five cards from a 52 card deck. However since a poker hand has the same value whatever order the cards are arranged in we are interested in the number of unique ways (combinations). To find this we divide by the number of ways a five card hand can be arranged, which is 5! = 5*4*3*2*1 = 120.
Thus the number of distinct hand combinations is 311,875,200 / 120 = 2,598,960.
Since a royal flush is just a particular (the best) straight flush we start by enumerating the straight flushes.
A straight flush is a hand of five cards in sequence, all of the same suit. When comparing straight flushes, the hand with the highest card wins. Suits have no relative value and are all ranked equally. Obviously there are 4 royal flushes, and 36 other possible straight flushes. So the probability of being dealt a straight flush is 40 / 2,598,960 ≈ 0.0015%.
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Winning Low Limit Hold’em
Lee Jones
A great beginner’s book on hold’em. The emphasis is on solid fundamental play to beat loose, low limit games. It is an easy read and is particularly successful in pointing out the big mistakes which can cost a new player dearly. A perfect choice for newcomers to hold’em.
Content
The first section “Hold’em : The Game” serves as an introduction and gives an overview of the fundamentals of the game. Jones covers topics such as calculating pot odds and reading the board. The focus is very much on bricks and mortar poker, so some adjustment to online stakes is required. I would suggest that the games he is discussing would be roughly analogous to $0.5/$1 tables online. The section ends with a quiz on the material it has covered.
The majority of the book is within the second section “Play of the Hand from Deal to Showdown”. The author details the basics of winning play from preflop to showdown. The advice will be no surprise to veterans (although they may feel it is not aggressive enough), advocating an ABC game of tight hand selection and betting for value. I particularly like the preflop treatment - it’s a good introduction to starting hand selection, which is probably the single most important thing for beginners to learn. There are preflop and post-flop quizzes, which I feel are both valuable.
The third section “Miscellaneous Topics” contains a number of short essays. Some are more useful than others but I think the discussions of bluffing, bankroll, player types and discipline will be interesting to the new player. For more advanced players the essay on implicit collusion will probably be the biggest draw.
Presentation
The book is well presented with an easy writing style. Complicated concepts are well described, again making it ideal for newer players.
Perhaps not a presentation problem but unfortunately the book’s discussions of online play (or lack thereof) have not dated well.
Conclusion
A good buy for beginners. However if you already play and win at small stakes then the book has less to offer you. For instance Small Stakes Hold’em is much better suited to the intermediate player.
Poker is a name given to any number of card games sharing some key characteristics.
The players bet on the value of their hand which is the best 5 card combination they can make from those available to them. Some games only allow players to use cards dealt to them while others allow a combination of those held by players individually and those shared amongst all the players (board or community cards).
Gameplay is usually similar with the dealership rotating amongst the players, some or all players being subject to forced betting (e.g. ante or blinds) each hand and a round of betting on each street (i.e. each time cards are changed/revealed). Betting follows the usual protocols with each player being required to fold or match the current level of betting (calling) before optionally increasing the bet (raising). A betting round ends when either all players have contributed equally to the pot or there is only one player remaining. Note that players are not normally able to “bet out” other players due to lack of funds. A player with all his money in the pot is all in and may continue without contributing more. However if he wins he does not take any money contributed after his all in has been matched by the other players - the remainder goes to the player with the second best hand.
What is shared amongst all poker variants are the established hand rankings:
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So you’ve tried coding your first bot along the lines of our previous post. If you’ve gone to those lengths then you’ve probably also watched it do some stupid things. So where can we improve upon our basic design?
Preflop
Probably the biggest single area for improvement is the preflop play. If you get preflop right then it can really help the rest of the bot’s game. Every good poker player knows that if you play correctly preflop you cut down on mistakes in later streets.
It’s quite hard to get a dynamic preflop system working. One of the reasons is that preflop win percentages tend to be all bunched up. Against nine opponents even pocket aces only have a 30.8% chance of winning (if all opponents go to showdown). The other reason is the lack of information, particularly if we are not in late position. These two factors make a dynamic preflop very sensitive. Often it will perform well in late position when we have a good idea of how many players will hit the flop and what the pot size is, but poorly in early position.
A popular solution is to implement a static preflop strategy before switching to a dynamic strategy postflop. Personally I would advocate Sklansky groups but I’ve also had some success with Lee Jones’ preflop strategy. Basically any of the established preflop systems will work fine.
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A betting system is a method of bet sizing depending on predetermined factors. The most common betting systems use a progression where you bet more or less depending on whether you have just won or lost. There are also betting systems where you look for an event which is statistically “due” (e.g. you’re playing roulette and the last 4 numbers have been red so you bet black). Obviously the latter are examples of the gambler’s fallacy.
The problem with all betting systems is that bet sizing does not affect the house edge. It can increase your chance of winning in the short term, but that will always be balanced out by a large loss later (as in the martingale system). The longer you play, the closer your loss will be to the house edge.
The reason that bet sizing cannot affect the house edge is simple - expected value is linear. This means that:
expected value (A+B) = expected value (A) + expected value (B)
In other words it doesn’t matter what the individual amounts you wager are, overall your loss will equal the total you wager multiplied by the house edge. There cannot be a clever way of sizing bets which would change this - otherwise expectation would not be linear.
Thus we find (although we already knew) that the equation for your loss at a gambling table is:
loss = (total amount wagered) * (house edge)
No betting system can alter that.
