Some things to keep in mind, all these tips apply to both Standard and Premium editions of the game.
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EXPECT TO FAIL, this is a Poker game and thus you will lose hands and sometimes tournaments. You might barely make the top 10 of a tournament and run out of chips, this is unfortunate but it's all part of the game sadly. If you can accept this factor, you'll be better off for it.
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Although the game will tell you that you need to come top 3 or higher to win stars, this is false. I'm not sure how or why but as long as you come in the top 5 you will win the stars. THIS ONLY APPLIES TO CASINO TOURNAMENTS THAT GIVE CASH PRIZES TO THE TOP 5, IF YOU ARE IN A TOURNAMENT WITH 8 OR LESS PLAYERS YOU HAVE TO COME IN THE TOP 3, if you're playing to win a station or mode of transport, you HAVE to win the whole table. So if you're in a Casino Tournament and you get to the Top 5, you should Leave the Table and take your star (and winnings!).
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For some reason, when travelling you do not earn money from houses. I don't know why this happens but it's something to remember.
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When you go click on the calender to sleep until the next day, you'll be given a box showing your reputation and cash increase/decrease. You can skip this from popping up by clicking on anywhere that can be walked on before it pops up. This saves about a second at most, but over the course of a full run can likely save a couple of minutes since you need to sleep a lot to gain cash.
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Be prepared to make irrational moves. You are speedrunning this game, you don't have time to think. If you're Big Blind and your hand sucks, don't bother checking to see what comes up on the Flop, just Fold & Skip for another hand. This is obviously a really dumb move if you're playing poker normally, but we aren't playing poker normally.
That's about it I think. Your particular playstyle for this game depends on what you're comfortable with, ideally we'd play super aggressive and force our opponent's to go All-In every time we can guarantee us winning the hand, but sadly that's not realistic. What I do is I Fold & Skip any hand I'm not comfortable playing with, depending on how many chips I have.
That being said, for Heads-Up games (ie. 1v1), you should play aggressively. Raise a lot to drain the opponent's chips and keep betting to force them to fold, even if your hand sucks. If they keep calling/raising you, unless your hand is really good you should Fold and try again. Sometimes you will get stuck in a loop, but you should still play on.
I'll update this list as more things get discovered.