Bridge by NeuralPlay is a decent Android App to try.
I've only just come across this app which I believe is actually in its fourth year now. I've always used Bridge Baron when I want to play bridge on my 'phone without an internet connection but I know a number of people seem to have trouble with it not running too well on their 'phone or tablet. Bridge by NeuralPlay offers a similar set of features and it's free whereas Bridge Baron cost me £12 many years ago. If you take to Bridge by NeuralPlay then it's probably worth paying about £4.50 to remove the ads though.
You can play Acol, Standard American Yellow Card, (SAYC), SAYC 2/1, or precision club. Various conventions can be chosen within these basic systems but it doesn't play Benji Acol. You can play 3 weak twos, however. I like to play 5 card majors but with weak NT and it manages this, together with Stayman, Jacoby transfers, negative doubles, fourth suit forcing, Jacoby 2NT, Michaels cuebids, unusual 2NT, Roman Key Card Blackwood 1403, and Cappelletti or Landy over 1NT. As your partner, the play algorithm gives attitude signals on your lead and count signals on opponents' leads but its play takes no notice of your signals yet.
You can play rubber bridge, Chicago, duplicate teams, matchpoint practice and play practice. I generally play dupicate teams where your score on a hand (you and three computer players) is compared with the score achieved by the computer playing all four hands and the differenc in score is converted to IMPS. Matchpoint practice isn't really matchpoints since there is no comparison of your score on a hand with other results on the same hand. It is effectively aggregate scoring for NS vs EW which still favours making game or slam contracts. It would be better if it offered teams scored by point a board as the strategy needed here is similar to matchpoints. It can be worth risking going down in your contract in order to make overtricks, since you score a point if you only beat your opponents by the smallest of margins.
The standard of play depends upon how much processor time you can devote to analysing the best play at any point. On my phone I can set the highest level of play (6) without haviing to wait more than a few seconds for the computer to play but on my old Chromebook, anything more than level 3 can result in the computer taking ten seconds or more to decide what card to play in the early stages of the game. Even at level 6 it's not up to the standard of Jack (my Windows bridge game) but that costs more like £70! If I put my mind to it, I can usually beat it over an 8 game teams match but it's up to local club standard.
The bidding is rule based and not dependent upon processor power. It's not too bad at the first few bids in an auction but it doesn't go for exploratory bidding to determine how well hands fit together. Here is an example where the computer is bidding all 4 hands. Starting with South, the bidding went:
pass - 1S - 2C - 2H - pass - 3NT
which duly went two off. Jack, however, bids 3D instead of 3NT, gets 3H from partner, and bids the making 4H game. Playing teams there really isn't any need to rush to bidding 3NT., especially with a singleton ace of clubs.
The authors recognise the program's shortcomings and freely admit that it isn't good at bidding slams. They are working on improving it.
The program has a number of extra features. I particularly like the way that you can get 'hints' about what to bid or play at any point in the program. A beginner can choose to see a hint before every bid or play. An improving player may choose to see a hint only if the program disagrees with their choice or hints may be displayed only when asked for. You can define the types of hand that you want to play. Choices include one no trump opening hands, two club hands, game or better deals etc.. You can also choose to have the best hand at the table! Hands can be reviewed and replayed from any point. They can be saved and shared with friends. Recent deals can be retrieved. There are more features than most people will need.
So, for a free program it's pretty good. It's a learning aid for beginnes and improvers but not likely to challenge the better player. I don't have an iPhone so can't review any iPhone bridge apps. I would be happy to publish something written by someone else though if there are any offers?
As I write this blog the 16th World Bridge Series is running in Wroclaw, Poland. The Open Teams and Women's Teams events are in progress and the top matches are being shown on VuGraph on BBO, some of which will probably have live text or audio commentaries. Keep a lookout for team Spector in the Open teams (currently lying 14th). Gavin Wolpert, a player I have been following recently, is playing in this team. Gavin is an engaging player who produces free bridge videos on YouTube which I find extremely interesting. I particularly like his commentaries on his practice matches which he plays before big events. It's amazing how quickly he can analyse a hand. Try this video. He plays essentially two over one, a five card major system but there is a lot to learn about how he visualises opponents hands and plans his play of the hand.