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  2. The problem asked me to find the highest possible hand for a given set of cards, so I tried to keep things simple by writing a checkhand function that checks each hand starting from straight flush down to high card. As soon as a condition for a hand was satisfied, I returned a number that corresponded to the strength of the hand (1 for high.
  3. (9) Write a method to check for 3 of a kind. (10) Write a method for 4 of a kind. (11) Write a method to check for a straight. This is tricky, as the ranks must go in order (5,6,7,8,9), but the ranks of Jack, Queen, King, and Ace don't follow a simple order. (12) Write a method to SCORE a hand. The scoring for poker goes like this: 0 - no pairs.

10.4 Use the methods developed in Exercise 10.3 to write a program that deals two five-card poker hands, evaluates each hand, and determines which is the better hand. 10.5 Modify the program developed in Exercise 10.4 so that it can simulate the dealer.

I've never actually seen the full description in one place on the net, so I thought I'd do a public service.
First, if you're playing a game with extra cards, like Hold'em or 7 stud, you first use recursion thusly: Iterate through the set of cards, removing one at a time and recurse. From the recursion results, save the best hand and return it.
Once you get down to 5 cards, you first take a histogram of the card ranks. That is, for each rank in the hand, count how often it appears. Sort the histogram by the count backwards (high values first).
If the histogram counts are 4 and 1, then the hand is quads.
If the histogram counts are 3 and a 2, then the hand is a boat.
If the histogram counts are 3, 1 and 1, then the hand is a set.
If the histogram counts are 2, 2 and 1, then the hand is two pair.
If the histogram has 4 ranks in it, then the hand is one pair.
Next, check to see if the hand is a flush. You do this by iterating through the cards to see if the suit of a card is the same as its neighbor. If not, then the hand is not a flush. Don't return a result yet, just note whether or not it's a flush.
Next, check for straights. Do this by sorting the list of cards. Then subtract the rank of the bottom card from the top card. If you get 4, it's a straight. At this point, you must also check either for the wheel or for broadway, depending on whether your sort puts the ace at the top or bottom. I would expect most folks to put the ace at the top of the sort, since it is usually a high card. So to check for the wheel, check to see if the top card is an ace and the 2nd to top card is a 5. If so, then it is the wheel.
If the hand is a straight and a flush, it's a straight-flush. Otherwise if it's one or the other, you can return that.
If we haven't matched the hand by now, it's High Card.

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Once you know what the hand is, it is fairly straightforward to compare two hands of the same type. For straights, you simply compare the top card. For flushes, you iterate down through a reverse sort of the ranks until you find a higher card or run out. For the histogram-based hands, you start at the beginning of the reverse-sorted count list and compare the ranks (two pair is tricky - you must always evaluate the higher of the two pairs for each hand first - the histogram won't help, then the lower pair, then the kicker).
Checking for a low (for high/low or Razz) is a little easier. Sort the hand by rank. Iterate through the list. If any card is bigger than an 8 or is the same rank as it's neighbor, it's not a low hand.

In poker there are only five different betting actions to remember, depending on whether or not anyone has already made a bet on this round. Let's start with your options when someone has already placed a bet (known as opening the betting).

If you do not like your hand you can fold, relinquishing your cards and taking no further part in the hand. Any money that you have already contributed to the pot is lost. Once you have folded your hand it is placed in a pile of other discarded hands (known as the muck) by the dealer. Having touched the muck, your hand is now dead. It cannot be retrieved even if you were to realise that your hand had been discarded by accident.

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However, let's assume that you do want to continue in the hand after someone else has bet. In that case you may either call or raise. A call involves matching the amount already bet in order to see the next card (or to see the showdown, if the last card dealt was the river card). However, if you particularly like your hand you may also raise, forcing the original bettor to match your raise if he wants to continue in the hand.

Of course, whenever you raise, the original bettor has the option to reraise, putting the onus back on you to match his bet to stay in the hand. Most cardrooms have a limit on the number of bets and raises allowed. Usually only a bet and three raises (or four raises) are allowed on each round of betting. However, when there are only two players left in the hand some cardrooms allow unlimited bets and raises.

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When there has not yet been any betting on this round, you have the option of either betting or checking. If you like your hand (or choose to bluff) and decide to bet out, you simply place your bet in front of you towards the centre of the table. The other players must now at least match your bet if they want to remain in the hand.

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If you instead decide to check, you are deferring your betting rights for the time being. Another player may now bet, in which case you may fold your hand, call the bet or raise (the action of first checking and then raising when an opponent bets is known as a check-raise). If no-one bets on that round then the next card is dealt and again the first player has a choice whether to bet or check.