Many players at play money tables play most hands they get dealt. They often call big raises with bad hands. Because of this, it's easy to succeed in most play money games. I'm going to teach you a different approach. There might be some approaches that are more profitable, but this approach will probably make you a winning player (if you're not already winning).
There are certain hands that you should be willing to go all-in with pre-flop. I'm going to divide them into two categories.
Pushing hands: These hands are so good that you would happily put all your chips into the pot pre-flop. There are three hands that definitely qualify as pushing-hands: AA, KK and QQ. I'm pretty sure that I've never folded any of these hands preflop at a play money table. There are some situations where you can fold QQ or even KK preflop, but they're extremely rare at play money tables. Don't even consider it (at play money) unless you're a very good poker player and knows your opponent very well.
I'm going to give you two "safe" ways to play these hands:
1) Go directly all-in no matter what. You will probably get called by someone anyway. It's pretty common that you get multiple callers. If that's not common at your table, you should probably change to another table.
2) Raise when the action gets to you. Be sure to get at least 10 % of your stack into the pot preflop. You should normally get the rest in on the flop unless an overcard flops. The only time you should ever consider to call is with AA when you will get at least half of your remaining chips into the pot by calling and you want more players to get involved in the pot. It's often better to go all-in in that situation, so be sure that you want the extra players in the pot before you smooth call with AA.
Here are two other ways to play "pushing hands", that I don't recommend if you want to win much play money (build a bankroll) as easily as possible. These plays might be better if your goal is to practice for real money games though.
3) Raise a small amount when the action gets to you. If nobody else has raised, raise approximately 5-10 times the big blind. If someone else has raised, reraise to about 3-5 times the amount you have to pay to call. This is a little different from how I'd play these hands in a real money game, but I just came up with those numbers to make things easy.
4) This option should only be used if you're almost certain that someone else will raise if you just call. The method is to smooth call. You expect someone else to raise, so you can reraise a pretty big amount when the action gets back to you. This is a risky play, because someone might get a cheap flop with a bad hand and beat you (if noone raises behind you).
I normally prefer method 2 because I like to get a little flop play, but I think method 1 is also a great way to win play money with pushing hands. Methods 3 and 4 are best suited for advanced players that know what they're doing.
I normally treat JJ and AK as Pushing hands too. If you want to get all-in preflop relatively often, you can use TT, 99, 88, AQ, AJ, AT and KQ as pushing hands. I normally prefer seeing flops with these hands, but it's probably profitable to go all-in preflop with them as well. AJ, AT and KQ might be too weak if some tight opponents (opponents that play much less than half of the hands they get dealt) are getting involved in the hand, though. If I have to put in more than 30 % of my stack to call, I usually push instead of calling with TT, 99, 88 and AQ. I normally fold AJ, AT and KQ to big raises, but at certain tables it might be better to go all-in with those hands too.
Summary: You should want to get all-in preflop with pushing hands, but you might decide to not push directly. I advice that you use one of the two methods I mentioned (pushing or raising a big amount) unless you're a very good player and has a good reason not to do so.
Main pushing hands: AA, KK, QQ, JJ, AK
Optional/situational pushing hands: TT, 99, 88, AQ, AJ, AT, KQ
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