What are the odds of being dealt all 7 cards in the same suit?
The odds of pulling 7 spades in 7 cards the number of ways to pull 7 spades (from among the 13 spades) divided by the number of ways to pull 7 cards (from among the 52 cards).
13c7 = 1716
52c7 = 133784560
1716 / 133784560 = 0.0000128 = 0.00128 %
For general suit (not just spades), multiply ...
It's just one of many forms of a class of games called Contract Rummy. (The various rounds' goals are called contracts).
The major variation here seems to be:
The discard (or rather lack of discard): I guess by your description (since one cannot make three sets with only seven cards) that players just draw a card each turn and are not required (or ...
Some slightly watered down math (that still gives the right answer).
You have a 100% chance of your first card being a "good" card.
There are then 51 cards left, of which 12 will be a card that matches suit, so you have a 12/51 chance that the second card will be "good".
11/50 chance that the third card will be "good".
So, you have 1x(12/51)x(11/50)x(...
L. Scott Johnson is mostly correct except for 2 things:
You specified it wasn't a straight flush (there are 7 8-card straight flushes per suit he should have removed.)
You asked about the 7 card flush, which you were dealt before the draw, not the 8 card flush you drew into.
This gives us:
13C7 as the nCr we care about, giving us 1716 possible flushes of ...
You describe a variant of a Rummy game. With the following special rules:
2's act as jokers.
Special pick-up-from-discard pile rule: can pick up any number of cards from discard or a single face-down card from the deck.
Target goal of points, similar but not the same as in Pagat:Kalooki
starting hand of 9 cards
Paget:Rummy have a long list of Rummy games, ...
That set is acceptable only in Indian Rummy's three deck variant. (I'll call Indian Rummy by its name Paplu here for some better clarity.)
Two-deck Paplu and regular Rummy only has sets (same card value, different suites) and runs (same suit, sequential card values) and that move isn't legal in this format.
Three-deck Paplu allows the set type you describe, ...
The way rummy figures in doesn't seem very clear from your description. It sounds similar to Pounce; in that game you have a personal tableau, common piles of cards that you're building on, and a bunch of cards you hold--although it's a stack, not a hand.
If you remember the objective of your game, that would be helpful.