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Rolled Up – Being dealt three of a kind on third street in any one of several types of Seven Card Stud games.
In most seven card stud games, players are dealt a three card starting hand before the first round of betting. This is commonly
referred to as third street, and usually consists of two cards delivered face down followed by one card delivered face up. If all
three cards have the same ranking (if they were all Jacks, for instance), the player would have three of a kind on the first 3 cards
dealt to him. This condition, having three of a kind on the first three cards, is called being “rolled up.”
This term is mostly used in stud games which employ a three card starting hand. This includes 7-Card Stud Hi/Lo and
Razz. However, since Razz is a
lowball game, being rolled up is a bad thing; it
makes your hand practically worthless. By contrast, in High Only and Hi/Lo games, it is extremely valuable to be rolled up. It is a
premium starting hand in both games, but it is especially valuable in the High Only game. In this game, being rolled up is far and
away the best starting hand, and will win a good percentage of hands without improving. If you are rolled up in 7-Card Stud High, you
will be in the lead unless someone else is rolled up with a higher rank.
In Seven Card Stud Hi/Lo a rolled up hand also has a lot of value, although not nearly as much as in the High Only game. This is
because the high hand must often split the pot with the low hand in Hi/Lo Stud. This significantly mitigates the value of a high only
hand. Two way hands like low straight flush
draws and hands with aces will often perform as well if not better then being rolled up, depending upon the situation.
The odds against being rolled up are 1/ 425, which is commonly written as 424 to 1 against. For those who are unfamiliar with how to
calculate this, I will go over it here. Keep in mind that this method of calculation is useful for other types poker calculations as
well.
First, let me state the obvious by saying that you will be dealt three cards at the start of the hand. In order to be rolled up all
three cards must match in rank. In order to determine how likely this is we need to consider all the ways it is possible to be rolled
up, as well as all the ways it is not possible. A probability is essentially a comparison between an event happening and that same event
not happening. Since it is a comparison it can be evaluated using fractions. We will build the equation, but first, consider the following:
The first card you are dealt will have no bearing on whether or not you are rolled up. No matter the rank of the first card, so long
as the second card matches it, you will have a chance to be rolled up We also know that there are 52 cards in the deck with 4 cards
of each rank.
We know we will be dealt a first card. Of this we are 100% sure so we will give it a probability of 1, which is equivalent to 100%.
For our second card, we now have the possibility of receiving the remaining 51 cards in the deck, of which only 3 will match our rank
and allow us to continue our quest to be rolled up. We are now ready to set up the first part of the equation. We take the probability
of receiving a first card (1) and multiply it by the probability of us receiving a second matching card (3 out of 51, or 3/51).
So the first part of our equation is: 1 x (3/51)
So we know that 3 out of 51 times our first two cards will match, but to be rolled up all three of our cards must match. We now have
to add our third card to the equation. At this point we have seen two cards, leaving us with 50 possibilities for our third card.
Assuming that our first two cards matched, only two of the 50 cards will result in us being rolled up (2/50). So if we consider the
possibility that our first two cards will match 1 x (3/51) and consider further when our third card also matches (2/50), we are left
with an equation of:
1 x (3/51) x (2/50) = 6/2550, which reduces to 1/425. This means that for every 425 starting hand you are dealt, on average, 1 will be
rolled up. Written as odds (a ratio) this is 424:1.
Usage: Was Rolled-Up, Rolled up Aces
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