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WSOP periodically runs this game on their mobile apps game. Roulette poker is a variant of Texas Hold 'Em in which you are restricted in how you can bet:

  • Pre-flop you can only CALL or FOLD
  • After the flop you can either shove (ALL-IN) or FOLD
  • Additionally, you are required to (and automatically) top-off or re-buy as needed, so you start each hand with at least the buy-in amount.

Based on the restricted betting options, my feel is that this game is closer to "solved" than basic NLH. It seems to play a bit more like limit poker, with the pre-flop bet being more like an ante, and only a single bet (or fold) after the flop. As such, playing a very tight game seems to yield success, but with extremely high variance, as players seem to be looser post flop and it isn't unusual for four players or more to be all-in after the flop. Because of this, it seems like opening up a bit more pre-flop and then playing tighter post-flop might be a good strategy.

For instance, a bit looser baseline strategy might be to call with J8s+, QJo+, 22+, and the shove on the flop only with top pair Queens or better and open-ended straight draws or better on an uncoordinated board, flush draws or better as long as the board isn't paired, sets as long as there aren't any straight or flush draws although lower sets maybe not even then if there are too many over cards. I will never bluff unless I start to notice everyone folding too easily to any bet.

It also seems like a decent strategy is to leave the table after one or two double-ups, because otherwise invariably one will suffer a bad beat and lose all the chips they have managed to get through tight play. I am also wondering if strategy needs to change in other ways than this as one manages amass a big stack. Obviously if there are other big stacks at the table versus not would affect this. Also, I'm wondering if this game really can be +EV as gambler's ruin seems to come into play at some point.

In the current variant running, the buy-in to BB ration is pretty low (10:1), although in general as this ratio increases I would expect looser pre-flop play.

However, I haven't found any literature that specifically talks about this variant of poker, and am looking for something more authoritative regarding the math behind how this variation plays out and whether or not my gut feel with regards to strategy is right or not.

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Not going to have an open ended straight draw on an uncoordinated board.

This is just an opinion. I have not run any simulations.

If it only cost 1 BB to see a flop you should be seeing more flops. Even 27o can flop the nuts. A nothing hand will make 2 pair 1 / 49. If the stacks are 50BB you can play every hand. It depends on the minimum buy in but it should be a very wide range.

Post flop is tricky. You have basically no fold equity.

If only 2 see the flop then play Ace plus. You need 14 outs to be 50% 50%. Draws don't play well heads up.

If 3 any mid pair or better (not counting pair on the board) or 9+ outs as you are getting 2:1. Behind 2 then can play any suite connector >= 56 and any Ax suited.

If more than 3 see the flop then any two pair or better (not counting pair on the board) or 8+ outs.

An out is not just improve. It is improve to the likely winner.

Discount your hand if the board is coordinated and you don't have any of the draws.

In a comment OP stated buyin is only 10 BB so that changes a lot

Ran numbers and is NOT even profitable to play suited connectors even if you get action from 4 other players. You are going to hit about 1/5 flops and play that flop is profitable but it does not pay for the $4 of the flops you missed.

A pair hits like 1/8 and trips are going to hold up most of the time
Play it as a pair if it is top pair T+ against 1 or 2

AK is clearly playable but after that is gets complex

Could run a simulation but is not that interesting to me
It is like short stack push fold chart but with one more dimension

If the buyin was 20 or 30 BB it would be much more interesting

  • There's probably a balance between how many flops you see and the buy-in to BB ratio... in this case it's pretty low (10) so you can't play too lose. – user1934 May 7 '17 at 19:07
  • @Michael 10 is small and critical. Put that in bold and in you question. – paparazzo May 7 '17 at 19:17
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In this game, it is also worth noting that if your bankroll exceeds the 10 BB buy-in then it auto refills...essentially you never have less than 10 BB. I imagine preflop and flop ranges vary quite a bit depending on how many callers there are and what position you are in. I've found that flush draws qualify on flop when you have strong middle pair or better against 2 callers. Open-ended straight flush draws qualify against 3-4 callers. Play trips or better on paired boards against 2-3 callers.

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