Motivation

Have you ever played Texas Hold 'em and wondered, "Why do my cards always suck? I often only have one pair, and sometimes it's already on the table and we're left comparing kickers." Indeed, the distribution of hands in Texas Hold 'em is quite skewed towards the bottom:

Texas Hold 'em Hand Distribution

Keep in mind that these are the best five-card hands out of seven randomly chosen cards. Indeed, most hands do suck; only 15% of the time is there something better than two pair.

Introducing: Red Seven Poker

The game of Red Seven Poker is played with a 49-card deck with seven suits (the seven colors of the rainbow) and seven numbers (1 through 7). The deck comes as a part of another game, Red Seven by Carl Chudyk and Chris Cieslik, which is available from Asmadi Games on Amazon.

The structure of Red Seven Poker is the same as regular Texas Hold 'em. Each player has two secret cards to themselves and there are (eventually) five cards available to everyone. At the end of all of the betting, if more than one player is left, the player left with the best five-card hand out of the seven cards available to them wins the pot. (For full Texas Hold 'em betting rules, follow the link above.)

Ranking Hands

Here is the short reference version of the hand rankings Red Seven Poker.

  1. Royal Flush
  2. Straight Flush
  3. Flush / Five of a Kind
  4. Double Straight
  5. Full House Straight
  6. Four of a Kind
  7. Double Two Pair
  8. Double Three of a Kind
  9. Rainbow Straight
  10. Rainbow
  11. Straight
  12. Full House
  13. Three of a Kind
  14. Two Pair

Notice that there are many more possible hands than in regular poker, which adds variety. As we'll see later, many of those hands are also more common.

General Rules and Tiebreakers

Hand Explanations and Examples

  1. Royal Flush. A flush is five cards of the same color or number. For the flush to be considered royal, it must be the highest five cards of the set: Either 7/6/5/4/3 or R/O/Y/G/B. Here are two examples of royal flushes:
    Royal Flush 1Royal Flush 2
    The highest possible hand in the game is therefore the 7's royal flush.
  2. Straight Flush. A flush is five cards of the same color or number. A straight is five cards with consecutive values, either numbers (3-7, 2-6 or 1-5) or colors (R-B, O-I, or Y-V). A straight flush is a straight in color and a flush in number or the other way around. Here are two examples:
    Straight Flush 1Straight Flush 2
    As with regular poker, all royal flushes are also straight flushes, but royal flushes are considered higher than all straight flushes.
  3. Flush. A flush is five cards of the same color or number. Here are two examples:
    Flush 1Flush 2
    Of course, all straight flushes are also flushes, but those all rank higher.
  4. Double Straight. A straight is five cards with consecutive values, either numbers (3-7, 2-6 or 1-5) or colors (R-B, O-I, or Y-V). A double straight is five cards which form a straight in both colors and numbers. Notably, order of the cards in the two straights does not need to be the same; it just needs to be the same five cards. Here is one example, depicted as a straight in two different ways:
    Double Straight, By ColorDouble Straight, By Number
  5. Full House Straight. A full house consists of three cards of one color and two cards of a second color, or alternatively three cards of one number and two cards of another number. A straight is five cards with consecutive values, either numbers (3-7, 2-6 or 1-5) or colors (R-B, O-I, or Y-V). A full house straight is therefore a set of five cards which form a straight by colors and a full house by numbers or a straight by numbers and a full house by colors. Here is one example of the latter:
    Full House Straight, By Color (Full House)Full House Straight, By Number (Straight)
  6. Four of a Kind. Because of the deck's symmetry, we will say that a kind can refer to either a color or a number. So four of a kind can refer to either four cards of the same number or four cards of the same color:
    Four of a Kind 1Four of a Kind 2
  7. Double Two Pair. This hand is one of the new additions. Two pair refers to four cards, two of which are one color and two of which are another color, or two of which are one number and two of which are another number. Just like Double Straight, double two pair refers to four cards which form two pair in both senses: The four cards are all one of two colors and one of two numbers. Like Four of a Kind, the fifth card can be anything. Here is one example, depicted both ways:
    Double Two Pair, By NumberDouble Two Pair, By Color
  8. Double Three of a Kind. This hand is another new addition. Three of a kind refers to three cards that are the same color or the same number. Double three of a kind refers to five cards, three of which are the same color and three of which are the same number. Of course, those threes of a kind must share one card in common, the anchor. Here is one example, seen both ways:
    Double Three of a Kind, By ColorDouble Three of a Kind, By Number
  9. Rainbow Straight. A rainbow is five cards, no pair of whom share a color or number. A straight is five cards with consecutive values, either numbers (3-7, 2-6 or 1-5) or colors (R-B, O-I, or Y-V). So a rainbow straight is simply both a rainbow and a straight. Here are two examples:
    Rainbow Straight 1Rainbow Straight 2
    All double straights are rainbow straights as well, but rank higher.
  10. Rainbow. A rainbow is five cards, no pair of whom share a color or number. Here is an example:
    Rainbow
  11. Straight. A straight is five cards with consecutive values, either numbers (3-7, 2-6 or 1-5) or colors (R-B, O-I, or Y-V). Here are two examples:
    Straight 1Straight 2
  12. Full House. A full house consists of three cards of one color and two cards of a second color, or alternatively three cards of one number and two cards of another number. Here are two examples:
    Full House 1Full House 2
  13. Three of a Kind. Three of a kind refers to three cards that are the same color or the same number. Here are two examples:
    Three of a Kind 1Three of a Kind 2
  14. Two Pair. Two pair refers to four cards, two of which are one color and two of which are another color, or two of which are one number and two of which are another number. Here are two examples:
    Two Pair 1Two Pair 2

Frequencies

So Red Seven Poker introduces more possible hands, but that doesn't help if they're all super rare. What is the frequency of getting each hand?

Red Seven Poker 7-Card Hand Frequencies

As you can see, there is a lot more variety than in original poker. A full 86% of hands are better than two pair, which is now the lowest-ranked hand. The median hand is a straight, and there is plenty of competition higher. Anecdotally, I've been burned by betting high on Double Two Pair only to be beaten by a Four of a Kind or a Double Straight.
We can make this judgment a bit more rigorous by calculating the entropy of these two distributions. Indeed, original poker hands have an entropy of 2.2 bits, while Red Seven Poker has entropy of 3.2 bits. That might not seem like much, but that one additional bit of entropy corresponds to roughly doubling the number of potential hand ranks you could get.

Frequently Asked Questions