In a number of games I play there are a play deck and a discard deck (for example Ticket to Ride and Pandemic). The discard deck, by the way the games are constructed, becomes organised as cards are discarded in groups. However, the play deck needs to be as close to random as possible for the games to work well. I would like to know if there is an optimal way to shuffle a deck to overcome the self organisation of the discard decks in these circumstances. I can riffle shuffle well but have read some research that it would take 7 full riffle shuffles to effectivley remove the affects of an organised deck. Are there any other methods of cuttings of the deck or shuffle types that create a random deck in a more efficient manner?
The article on Shuffling at the Wikipedia discusses the famous paper by Persi Diaconis and Dave Bayer which shows that a 52 card deck of cards doesn't become random until the fifth shuffle, and requires seven shuffles to become "truly" random.
Your question "Are there any other methods of cuttings of the deck or shuffle types that create a more random deck?" isn't really asking the right question. Even just cutting the deck will randomize the deck just as well as any other method, given enough cuts. No other method will make it any "more random". The real question is "how many cuts are required to fully randomize a deck of X cards?" or "How many riffle shuffles are required?".
Pokerology.com has videos and tutorials for six different methods of shuffling cards. I think that for smaller decks like Ticket To Ride, simply splaying them out on the playing surface face down and messing them about, followed by a few riffle and overhand shuffles should be enough to randomize the deck.
With Ticket to ride, 3-5 riffle shuffles should be sufficient to randomize the deck sufficiently for play. As long as the runs of matched cards aren't 5-6 cards long, it's not a big issue.
I'll note that japanese style block shuffling is inadequate for TTR until about the 9th or time through the deck, which I discovered due to using sleeved cards in Nordic.
However, for sleeved cards, riffling is a nearly surefire way to strip the sleeves, so sliding a block sideways into the deck works well. Holding the deck loosely, pull a block, the place it looselysideways against the side of the deck, and gently push - it should interpenetrate. This is actually about as efective as riffling if done with half the deck at a time, but it's easier to stack a deck this way, so have someone else cut the deck.
I've found that mixing shuffling techniques, especially in a random order, will result in a fairly nice card distribution and randomization.
Generally speaking, I shuffle using a combination of overhand and Hindu shuffle. I start with the pack in my left hand, pluck out the middle half with my right, and then proceed to drop blocks of cards alternatively onto the top and then bottom of the pack, using a quick flick of fingers or thumb to swap between cards dropping onto the top or bottom of the pack. Two or three rounds of this do a pretty good job of randomising for most games. For highly ordered discard piles however, this can leave small clusters of related cards, even after quite a few rounds.
If I really want to ensure that I break up sequences though, I use a Pile shuffle with the slight variation that I deal each card onto a random pile rather than visiting each pile in turn. One round of this is usually enough to break up the sequences, then I usually finish off with a quick round or two of hand shuffling, as I describe above.
If I have the time, I'll do a pair of pile shuffles, picking two different prime numbers for the number of piles in each round. This can can substantially amplify the randomisation, even if you use a sequential pile shuffle, since correlations between number of piles and sequence length will be broken by lack of correlation between the number of piles in each round.
I'll let people I trust riffle shuffle game cards, but it is far to easy to damage cards with this technique if you aren't good at it. I certainly don't trust myself not to damage my cards.
Finally, when playing at a table, with plenty of space, it's very tempting to just do a big wash, but I've never been happy with the results of a this technique. It is far too easy for related cards and even quite large blocks to end up staying together.
For Ticket to Ride, as cards are turned in I distribute them across up to six stacks, trying to not place cards on top of like cards (orange does not go on top of orange). Sometimes a card gets tucked to the bottom of a stack. When it comes time to shuffle, the stacks get shuffled together pair by pair (stack 1 with 2, then 3 with 4, etc.), ultimately combining things. It seems to make things more random than otherwise.
(For Pandemic, there's often very few cards, so things can go bad very fast and it may just seem like it's not random.)
I guess my point (and others') is, doing some kinf of pre-shuffling the cards during play as cards are discarded can help with randomization.
ghoppe already posted the link to wikipedia and aramis told you about shuffling sleeved cards.
I personally employ a strategy of about 2 riffle and 1 strip shuffle repeated 2-3 times depending on how heavily the deck is ordered. Riffle is good to mix cards, and strip to reorder the top and bottom part of the deck. If you have a smooth and large enough surface also don't underestimate a wash shuffle - it's an especially convenient way to shuffle large and heavily ordered decks.