The oldest game on my iPad that still gets regular playtime is Strategery (http://strategerygame.com). First I'll review the game then give a few hints, tips, guide advice. There is a Lite version but the app is only a couple of dollars. That equates to micro-cents per hour of play time.
Strategery is a Risk-alike with a couple of rule changes that make all the difference. This is skilled game design; realising when the product is good, removing dross and adding polish rather than unnecessary bling. Risk has its own version of Rule 34 - if you can think of a theme then there is a Risk clone for it. The App store is clogged with "Risk-like" games that are essentially the same game with a few extra maps and varying amounts of annoying fluff. Strip away that shallow theme and that's just annoying time wasting stuff that gets old fast. No thanks.
Risk is an excellent game to play with humans because of the psychological aspects and diplomacy, but Risk can be improved for the casual gamer. Strategery can be played both psychologically with humans and as a casual game. The polished interface, the random maps, dynamic flow and speed make for a better casual experience. Strategery has a simple interface that just makes sense. There are subtle animations: these are tastefully done to enhance your situation awareness. I like the moment of tension when your dice roll is mediocre and you see the first opposing dice settling on sixes. Even this is done at exactly the right speed - fast.
Yes, maps are randomly generated and regions generally have more adjacent regions than Risk. There are choke points but you must deduce these for every new map. A standard region supports a maximum of seven army dots and mega-regions max out at ten dots. Resupply is at the end of turn (not the start) and the amount is based upon the largest contiguous clump of regions controlled. Each dot represents a six sided dice that is rolled to battle. All attacking armies less one are moved into a conquered regions so no time is wasted in awkward troop transfers.
Strategery's limited dots per region reduces the "build up and overrun" effect of Risk's choke points and thus encourages a more dynamic flow. The resupply rule rewards maintaining territorial integrity and incremental expansion over lightning raids. Having said that, late game, you will goad an attack that exposes a weakness for you to exploit.
There are two game modifiers that change the play style; The casualty modes "Winner Takes All" and "Attrition" and the resupply placement types "Manual", "Border" and "Random". That's six variations that play differently. There are other modifiers but they have less of an impact on the game. Smaller maps mean there is no late game stages so I typically only play Epic. You can also choose if the map starts with all regions claimed or not.
The casualty modes select whether or not the winner of a battle takes casualties. Winner Takes All makes for a brutally fast early game but the late game is a grind. Attrition makes for a slower early game but a much faster late game. The resupply placements are manual placement which is slow and I think actually focuses you away from grand strategy into small conflicts. The border strategy resupplies regions that border an enemy region and this mode is good for faster games but does leave you prone to overruns. Random resupply replacements do the most to emphasize territorial integrity and incremental expansion.
The general strategy in the early game is to limit your border regions by taking choke points and building a contiguous territory. This limits attack vectors and gives time to build strength. Try to conquer new regions while minimising the number of new borders. Enemy will generally attack the weakest regions so think twice before taking a low-dot region that borders a high-dot enemy; you might be better to let the seven-dot attack first then clear up the weakened survivor.
The mid-early game is about containing opponents. While you continue to expand, prioritise expansion towards your most threatening opponent while encouraging the other players to attack each other. Do not come between your enemies while they are killing each other. Keep your choke points and limit your borders but do make an opportunistic grab for a mega-region if that does not risk your territorial integrity. You should be building towards a dominant number of territories.
The mid-game is about finishing off weaker opponents and establishing territorial superiority. Continue to harass the largest opponent while finishing off weaker players if you can. Sometimes you can attack a well-entrenched (a few territories with high dot counts) player by waiting for an opponent to attack them first then striking in for a winning blow. A "buffer state" player will attack towards their easiest to win battles so ensure that is another opponent and not you.
The late game is all about resupply. By this time you have territorial superiority so you are getting more resupply per turn. Take advantage of this by increasing the number of regions with enemy borders. If you can make a run to a map edge and split the enemy territory then you strike a huge blow to their resupply. The simple math is that if you inflict more casualties than the enemy can replace then you will win. If your dot count is increasing while the opponent's dot count is decreasing then you are winning.
Late in attrition games you will be attacking with every possible region (even a two-dot into a ten-dot) because you know that your two-dot region will be fully resupplied and you will inflict casualties that will not be replaced. Late in Winner Takes All games you will generally be attacking seven-dot versus seven-dot so conquer regions where you increase your number of seven-dot attack vectors onto further single enemy regions. In the late-late Winner Takes All games you will conquer regions where the enemy has more attack vectors onto your regions - because they will not be able to resupply fully.
My favourite game is Winner Takes All casualties with Random resupply but this can make for long games. In this game type you want a strong hinterland. These are regions that experience long-periods of peace so they eventually fill up and that focuses your resupply forward. When your border is overrun then you can "blow" one of your hinterland regions to retake lost territory. As you push into the opponent's hinterland expect them to "blow" their seven dots and overrun you in counter-attack. This is fine provided they are unable to fully resupply the hinterland. This ebb and flow is what makes Winner Take All / Random resupply an exciting game.
For shorter games try attrition with border resupply. That's enough writing - I'm off to play.