The first is a natural way, and the second is with a triple and a wild card. There are two ways to make four of a kind. For an ace high straight flush (a royal flush), the wild card can be any of the five cards: A,K,Q,J,T and there are four suits, so there are 20 ways this can happen.įor an non-royal straight flush there are nine possible high ending cards, and the wild card can be any one of the four higher cards, and there are four suits, so with a middle wild card there are: 9 × 4 × 4 = 144.Ĥ0 + 20 + 144 = 204 Straight flush hands. Let's deal with the latter special case first. In this case, the wild card can be any of the cards, even the lowest one. The exception to this is when the straight is Ace high. A wild card can be used to fill any possible position of a straight flush, except the lowest card of the straight (because if there were four cards in a row the player would select the wild card to be at the top end of the straight remember, we're assuming the player makes the highest possible hand). When a wild card is added, things are a little more complicated. There are ten possible straight flush hands per suit, and four suits, so 40 possible natural straight flushes. A straight flush can be have an Ace as the top card, or a King, or Queen … down to the five. Once the top card of a straight flush is defined, the rest of the cards follow on automatically. The first is the natural way (no wild card involved). There are three different ways to make a straight flush when there is, potentially, a wild card. There is only one way to make five of a kind for each of the thirteen values in the deck.ġ3 five of a kind hands. The wild card must be present, and the other four cards need to be quads. There are only 13 sets of cards in the entire deck that can result in five of a kind. Let's repeat the exercise from last week of going through all hand rankings and finding out number distinct sets of cards that make each of these groups when there is one wild card in the deck. The addition of a wild card adds an additional card to the set 53C 5 = 2,869,685. There are 52 cards in a standard deck and so 52C 5 possible sets of cards, resulting in a total of 2,598.960 possible combinations. The way these figures were derived are explained in last weeks article. To the left is a table showing the frequency of all possible five card poker hands. Let's refresh ourselves on the basic odds. (It’s impossible to have a high card hand with a wild card, as this wild card will automatically pair with the highest natural card). Similarly, the lowest possible hand including a wild card is a pair. ![]() ![]() ![]() (And if a hand was two natural pairs and a wild card, it would automatically be a full house). If you have a wild card, you would be better off making three of a kind from the natural pair. ![]() What this means is that, if the player is dealt a wild card, s(he) uses it in a position that results in the highest possible ranking hand.Ī consequence of this is that you will never see the hand two pairs including a wild card. It also means that five of kind is possible.īecause the wild card can be used to represent any card, we’re going to make the assumption that the player uses the wild card to maximum advantage. This can cause some interesting effects (as we'll see later). This week, I’m going to look at how these odds change if we add a wild card into the mix.Ī wild card, sometimes called a joker, can be used to represent a card of any value and suit. If you missed the article you can read it here. Last week I wrote about the odds and probabilities of every five card poker hand.
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