I want to create a lookup table for texas hold'em poker hands. Right now, I am using prime numbers to represent each card, and want to figure out what those cards represent as a total hand. This is because the order of the cards don't matter and the multiplication will provide us with a unique number. Now, I know about the hand evaluators, but they only evaluate the strength of the hand without draws, and do not separate the hands into as many categories as I need.
As an example take the following situation:
Hand: AdKd
Flop: Kc5d3d
(d = diamonds, c = clubs, h = hearts, s = spades)
Now, this would return from the lookup table a pair and also a flush draw.
Now this is more tricky:
Hand: AhAd
Flop: 5c5h3d
This would evaluate to overpair. So, basically, we cannot combine the hand and the flop into a single number, as we want to know exactly how the hand interacts with the flop.
I have already created a way of determining if a flush or a flush draw exists and whether a straight or a straight draw exists. So after that, the suits no longer matter, and we don't care about non-pair hands. Basically, given two numbers that represent the hand and the flop, we get back a hand category. For the last example, Aces are the prime number 41, so for the hand we get 41*41=1681 and for the board, we get 7*7*3=147. Ok now, we go to our lookup table and enter this lookup(147, 1681) and it should return OVERPAIR (or whatever constant we set it to), in constant time.
How do I implement first the lookup table? And the lookup function? (I'm already planning on using a perfect hashing algorithm for both the flop and the hand, but don't really know how to combine them.)
First, for encoding hands I find your approach very raw (not sure why you would use 41 for Ace, why not 37, and how do you differentiate different flavors of Aces). I would suggest the following.
For hand use a number between 1 and 52*51/2 to denote every combination. For flop use 52*51*50/(2*3) numbers and 52*51*50*49/(2*3*4) for flop+turn.
Each combination of these numbers will denote each unique situation. So store whatever annotation (straight, straight-flop etc) you want for each of these.
Related
I am looking for any direction on how to implement the process below, you should not need to understand much at all about poker.
Below is a grid of possible two-card combinations.
Pocket pairs in blue, suited cards in yellow and off-suited in red.
Essentially there is a slider under the matrix which selects a percentage of possible combinations of two cards which a player could be dealt. However, you can see that it moves in a sort of linear fashion, towards the "better" cards.
These selections are also able to be parsed from strings e.g AA-88,AKo-AJo,KQo,AKs-AJs,KQs,QJs,JTs is 8.6% of the matrix.
I've looked around but cannot find questions about the specific selection process. I am not looking for "how to create this grid" or , more like how would I go about the selection process based on the sliding percentage. I am primarily a JavaScript developer but snippets in any language are appreciated, if applicable.
My initial assumptions are that there is some sort of weighting involved i.e. (favoured towards pairs over suited and suited over non-suited) or could it just be predetermined and I'm overthinking this?
In my opinion there should be something along the lines of "grouping(s)" AND "a subsequent weighting" process. It should also be customisable for the user to provide an optimal experience (imo).
For example, if you look at the below:
https://en.wikipedia.org/wiki/Texas_hold_%27em_starting_hands#Sklansky_hand_groups
These are/were standard hand rankings created back in the 1970s/1980s however since then, hand selection has become much more complicated. These kind of groupings have changed a lot in 30 years so poker players will want a custom user experience here.
But lets take a basic preflop scenario.
Combinations:- pairs = 6, suited = 4, nonsuited = 12
1 (AA:6, KK:6, QQ:6, JJ:6, AKs:4) = 28combos
2 (AQs:4, TT:6, AK:16, AJs:4, KQs:4, 99:6) = 40
3 (ATs:4, AQ:16, KJs:4, 88:6, KTs:4, QJs:4) = 38
....
9 (87s:4, QT:12, Q8s:4, 44:6, A9:16, J8s:4, 76s:4, JT:16) = 66
Say for instance we only reraise the top 28/1326 of combinations (in theory there should be some deduction here but for simplicity let's ignore that). We are only 3betting or reraising a very very obvious and small percentage of hands, our holdings are obvious at around 2-4% of total hands. So a player may want to disguise their reraise or 3bet range with say 50% of the weakest hands from group 9. As a basic example.
Different decision trees and game theory can be used with "range building" so a simple ordered list may not be suitable for what you're trying to achieve. depends on your programs purpose.
That said, if you just looking to build an ordered list then you could just take X% of hands that players open with, say average is 27% and run a hand equity calculator simulation tweaking the below GitHub to get different hand rankings. https://github.com/andrewprock/pokerstove
Theres also some lists here at the bottom this page.
http://www.propokertools.com/help/simulator_docs
Be lucky!
I hope it's not too obvious a question: is there a random number generation algorithm that doesn't depend on previously returned values, so that I can get (for example) the 50th number in the sequence, without computing the previous 49?
The reason is that I am making roguelike that will be persistent (so that I can recreate the exact same level from the same seed), but to compute certain features of each level, I don't want to have to "compute" all previous features just to get the random number generator to the correct "state" of having been used, for example, 100 times so far. I would like to be able to query the 101st random number without determining previous values so that the program can create level features separately.
You can encrypt ordinary sequence number [1..N] with any cipher,
and by this way - generate unique pseudorandom value for each SeqNo.
If you use a linear congruential random number generator, it is trivial to compute the $n$-th element generated from a given seed. But it is probably easier just to stash away the state at the "interesting" points of the game.
OTOH, if you want to "restart" the game at a certain point, you'll presumably want to be able to recreate the dungeon's features, but (due to different player actions) the RNG usage will be different from then on. I.e., if started at the same point, if I shoot twice at a monster the RNG will be used more times than if I just run away; the next item generated will get different values. Perhaps what you really want is several independent random number streams, and saving the states as needed?
There are lots of roguelike games around, mostly open source. Some are limited/small (from "build a game in a day" sort of competitions), and might make a good starting point for you. Why start your own, and not hack on an existing one?
Here is the facts first.
In the game of bridge there are 4
players named North, South, East and
West.
All 52 cards are dealt with 13 cards
to each player.
There is a Honour counting systems.
Ace=4 points, King=3 points, Queen=2
points and Jack=1 point.
I'm creating a "Card dealer" with constraints where for example you might say that the hand dealt to north has to have exactly 5 spades and between 13 to 16 Honour counting points, the rest of the hands are random.
How do I accomplish this without affecting the "randomness" in the best way and also having effective code?
I'm coding in C# and .Net but some idea in Pseudo code would be nice!
Since somebody already mentioned my Deal 3.1, I'd like to point out some of the optimizations I made in that code.
First of all, to get the most flexibly constraints, I wanted to add a complete programming language to my dealer, so you could generate whole libraries of constraints with different types of evaluators and rules. I used Tcl for that language, because I was already learning it for work, and, in 1994 when Deal 0.0 was released, Tcl was the easiest language to embed inside a C application.
Second, I needed the constraint language to run fairly fast. The constraints are running deep inside the loop. Quite a lot of code in my dealer is little optimizations with lookup tables and the like.
One of the most surprising and simple optimizations was to not deal cards to a seat until a constraint is checked on that seat. For example, if you want north to match constraint A and south to match constraint B, and your constraint code is:
match constraint A to north
match constraint B to south
Then only when you get to the first line do you fill out the north hand. If it fails, you reject the complete deal. If it passes, next fill out the south hand and check its constraint. If it fails, throw out the entire deal. Otherwise, finish the deal and accept it.
I found this optimization when doing some profiling and noticing that most of the time was spent in the random number generator.
There is one fancy optimization, which can work in some instances, call "smart stacking."
deal::input smartstack south balanced hcp 20 21
This generates a "factory" for the south hand which takes some time to build but which can then very quickly fill out the one hand to match this criteria. Smart stacking can only be applied to one hand per deal at a time, because of conditional probability problems. [*]
Smart stacking takes a "shape class" - in this case, "balanced," a "holding evaluator", in this case, "hcp", and a range of values for the holding evaluator. A "holding evaluator" is any evaluator which is applied to each suit and then totaled, so hcp, controls, losers, and hcp_plus_shape, etc. are all holding evalators.
For smartstacking to be effective, the holding evaluator needs to take a fairly limited set of values. How does smart stacking work? That might be a bit more than I have time to post here, but it's basically a huge set of tables.
One last comment: If you really only want this program for bidding practice, and not for simulations, a lot of these optimizations are probably unnecessary. That's because the very nature of practicing makes it unworthy of the time to practice bids that are extremely rare. So if you have a condition which only comes up once in a billion deals, you really might not want to worry about it. :)
[Edit: Add smart stacking details.]
Okay, there are exactly 8192=2^13 possible holdings in a suit. Group them by length and honor count:
Holdings(length,points) = { set of holdings with this length and honor count }
So
Holdings(3,7) = {AK2, AK3,...,AKT,AQJ}
and let
h(length,points) = |Holdings(length,points)|
Now list all shapes that match your shape condition (spades=5):
5-8-0-0
5-7-1-0
5-7-0-1
...
5-0-0-8
Note that the collection of all possible hand shapes has size 560, so this list is not huge.
For each shape, list the ways you can get the total honor points you are looking for by listing the honor points per suit. For example,
Shape Points per suit
5-4-4-0 10-3-0-0
5-4-4-0 10-2-1-0
5-4-4-0 10-1-2-0
5-4-4-0 10-0-3-0
5-4-4-0 9-4-0-0
...
Using our sets Holdings(length,points), we can compute the number of ways to get each of these rows.
For example, for the row 5-4-4-0 10-3-0-0, you'd have:
h(5,10)*h(4,3)*h(4,0)*h(0,0)
So, pick one of these rows at random, with relative probability based on the count, and then, for each suit, choose a holding at random from the correct Holdings() set.
Obviously, the wider the range of hand shapes and points, the more rows you will need to pre-compute. A little more code, you can still do this with some cards pre-determined - if you know where the ace of spades or west's whole hand or whatever.
[*] In theory, you can solve these conditional probability issues for smart stacking with multiple hands, but the solution to the problem would make it effective only for extremely rare types of deals. That's because the number of rows in the factory's table is roughly the product of the number of rows for stacking one hand times the number of rows for stacking the other hand. Also, the h() table has to be keyed on the number of ways of dividing the n cards amongst hand 1, hand 2, and other hands, which changes the number of values from roughly 2^13 to 3^13 possible values, which is about two orders of magnitude bigger.
Since the numbers are quite small here, you could just take the heuristic approach: Randomly deal your cards, evaluate the constraints and just deal again if they are not met.
Depending on how fast your computer is, it might be enough to do this:
Repeat:
do a random deal
Until the board meets all the constraints
As with all performance questions, the thing to do is try it and see!
edit I tried it and saw:
done 1000000 hands in 12914 ms, 4424 ok
This is without giving any thought to optimisation - and it produces 342 hands per second meeting your criteria of "North has 5 spades and 13-16 honour points". I don't know the details of your application but it seems to me that this might be enough.
I would go for this flow, which I think does not affect the randomness (other than by pruning solutions that do not meet constraints):
List in your program all possible combinations of "valued" cards whose total Honour points count is between 13 and 16. Then pick randomly one of these combinations, removing the cards from a fresh deck.
Count how many spades you already have among the valued cards, and pick randomly among the remaining spades of the deck until you meet the count.
Now pick from the deck as much non-spades, non-valued cards as you need to complete the hand.
Finally pick the other hands among the remaining cards.
You can write a program that generates the combinations of my first point, or simply hardcode them while accounting for color symmetries to reduce the number of lines of code :)
Since you want to practise bidding, I guess you will likely be having various forms of constraints (and not just 1S opening, as I guess for this current problem) coming up in the future. Trying to come up with the optimal hand generation tailored to the constraints could be a huge time sink and not really worth the effort.
I would suggest you use rejection sampling: Generate a random deal (without any constraints) and test if it satisfies your constraints.
In order to make this feasible, I suggest you concentrate on making the random deal generation (without any constraints) as fast as you can.
To do this, map each hand to a 12byte integer (the total number of bridge hands fits in 12 bytes). Generating a random 12 byte integer can be done in just 3, 4 byte random number calls, of course since the number of hands is not exactly fitting in 12 bytes, you might have a bit of processing to do here, but I expect it won't be too much.
Richard Pavlicek has an excellent page (with algorithms) to map a deal to a number and back.
See here: http://www.rpbridge.net/7z68.htm
I would also suggest you look at the existing bridge hand dealing software (like Deal 3.1, which is freely available) too. Deal 3.1 also supports doing double dummy analysis. Perhaps you could make it work for you without having to roll one of your own.
Hope that helps.
I have this problem: I want to know how often a player holding a portfolio of poker hands beats another player holding a different portfolio of poker hands.
Each hand in a portfolio is given a weight (i.e. a likelihood). Each hand in a portfolio also knows it's own "strength". This effectively means all cards have been dealt. So please assume no more cards need to be dealt.
The reason this problem is annoying is because of duplicate card problems. For example, if I pick a random holding from each player's portfolio I must check that these holdings don't share a card -- obviously both plays can't be dealt the same card.
I want to do this quickly so that I can make many different RangeA vs RangeB comparisions per second. I have a solution, but I won't talk about it yet because I don't want to taint any responces.
-- For an Example --
Given a 5 card board of "Ah 3c 8c Td Jh":
HandRangeA = {{"As Ac", 2.5%}, {"As Ad", 2.5%}, {"Ac Kc", 5%}....}
HandRangeB = {{"As Ac", 7.5%}, {"As Ad", 7.5%}, {"Ac Kc", 5%}....}
(Each HandRange contains all possible holding that don't use a "board card")
Goal :: compute the probaility HandRangeA beats HandRangeB
I wrote some software that did this via monte carlo. That means I ran both hands to completion, 1000 times with random boards that could arrive given the situation, and counted wins and losses. It was surprisingly accurate.
Since I was doing it for texas holdem, I would do the same thing after the (1) deal, (2) flop, 3 (turn) so the player could see how their percentages changed given the board.
I really should have finished that software. But I stopped playing poker online....
I think Andrew Prock is considered the expert here; check out the discussion here, and links therein.
I think you want something like this:
probWin = 0
For Each HandA in RangeA
probA = getProbability(HandA)
For Each HandB in RangeB
probB = getConditionalProbability(HandB, HandA)
probWin += probA * probB * getProbabilityADefeatsB(HandA, HandB)
You need to consider conditional probability, because given HandA is As Ac, there is no longer a 7.5% chance that HandB is As Ac (in fact, there is a 0% chance of that). So you are taking the probability of A having a particular hand multiplied by the probability of B having a particular hand, given what A has, multiplied by the probability of A's hand beating B's hand. That should give you the probability of A having that hand against that particular hand of B's and winning. Iterating over all such pairs should give the desired result I think.
Since the approach is exhaustive, there is no need for any sort of Monte Carlo simulation. Of course this will be O(n^2) where n is the number of possible hands, but n here is relatively small.
EDIT:
I should note that since you are referring to the case where all cards have been dealt, the getProbabilityADefeatsB() function would return either 1 or 0. Also, getConditionalProbability() will either be exactly 0 (because the hands share a card) or simply what your regular weight was. It would be more complicated if the hands were less specific (if HandA is AA then HandB could be a different flavor of AA, but it is less likely).
As much as I like using GUIDs as the unique identifiers in my system, it is not very user-friendly for fields like an order number where a customer may have to repeat that to a customer service representative.
What's a good algorithm to use to generate order number so that it is:
Unique
Not sequential (purely for optics)
Numeric values only (so it can be easily read to a CSR over phone or keyed in)
< 10 digits
Can be generated in the middle tier without doing a round trip to the database.
UPDATE (12/05/2009)
After carefully reviewing each of the answers posted, we decided to randomize a 9-digit number in the middle tier to be saved in the DB. In the case of a collision, we'll regenerate a new number.
If the middle tier cannot check what "order numbers" already exists in the database, the best it can do will be the equivalent of generating a random number. However, if you generate a random number that's constrained to be less than 1 billion, you should start worrying about accidental collisions at around sqrt(1 billion), i.e., after a few tens of thousand entries generated this way, the risk of collisions is material. What if the order number is sequential but in a disguised way, i.e. the next multiple of some large prime number modulo 1 billion -- would that meet your requirements?
<Moan>OK sounds like a classic case of premature optimisation. You imagine a performance problem (Oh my god I have to access the - horror - database to get an order number! My that might be slow) and end up with a convoluted mess of psuedo random generators and a ton of duplicate handling code.</moan>
One simple practical answer is to run a sequence per customer. The real order number being a composite of customer number and order number. You can easily retrieve the last sequence used when retriving other stuff about your customer.
One simple option is to use the date and time, eg. 0912012359, and if two orders are received in the same minute, simply increment the second order by a minute (it doesn't matter if the time is out, it's just an order number).
If you don't want the date to be visible, then calculate it as the number of minutes since a fixed point in time, eg. when you started taking orders or some other arbitary date. Again, with the duplicate check/increment.
Your competitors will glean nothing from this, and it's easy to implement.
Maybe you could try generating some unique text using a markov chain - see here for an example implementation in Python. Maybe use sequential numbers (rather than random ones) to generate the chain, so that (hopefully) the each order number is unique.
Just a warning, though - see here for what can possibly happen if you aren't careful with your settings.
One solution would be to take the hash of some field of the order. This will not guarantee that it is unique from the order numbers of all of the other orders, but the likelihood of a collision is very low. I would imagine that without "doing a round trip to the database" it would be challenging to make sure that the order number is unique.
In case you are not familiar with hash functions, the wikipedia page is pretty good.
You could base64-encode a guid. This will meet all your criteria except the "numeric values only" requirement.
Really, though, the correct thing to do here is let the database generate the order number. That may mean creating an order template record that doesn't actually have an order number until the user saves it, or it might be adding the ability to create empty (but perhaps uncommitted) orders.
Use primitive polynomials as finite field generator.
Your 10 digit requirement is a huge limitation. Consider a two stage approach.
Use a GUID
Prefix the GUID with a 10 digit (or 5 or 4 digit) hash of the GUID.
You will have multiple hits on the hash value. But not that many. The customer service people will very easily be able to figure out which order is in question based on additional information from the customer.
The straightforward answer to most of your bullet points:
Make the first six digits a sequentially-increasing field, and append three digits of hash to the end. Or seven and two, or eight and one, depending on how many orders you envision having to support.
However, you'll still have to call a function on the back-end to reserve a new order number; otherwise, it's impossible to guarantee a non-collision, since there are so few digits.
We do TTT-CCCCCC-1A-N1.
T = Circuit type (D1E=DS1 EEL, D1U=DS1 UNE, etc.)
C = 6 Digit Customer ID
1 = The customer's first location
A = The first circuit (A=1, B=2, etc) at this location
N = Order type (N=New, X=Disconnect, etc)
1 = The first order of this kind for this circuit