Texas Hold'em Shootout casino game. How can the house have an advantage?

The Game Room
1

There’s a game called “Texas Hold’em Shootout” I’ve seen recently at several online casinos. Like most games at first glance it seems to favour the player, but unlike any others after giving it a cold hard stare I still can’t work out the house advantage.

It works like this:

You have 2 opponents in a hand of Texas Hold’em, a red guy and a blue guy. The order of play is you-red-blue.

You place a bet of 1 unit and each player is dealt 2 hole cards

The red guy can see the blue guy’s hand (but not yours, or into the deck). If he has the better hand he will raise 1 unit. If he has a worse hand he will fold or call. If he has an equal hand he will raise, fold or call. (Calling is a useless manoeuvre for him, as he will always fold in the second round if he calls.)

The blue guy will fold if the red guy raised, and will raise if he folded/called.

In the second round therefore you are always left with a raise of one unit to you. Your options are to fold, call for 1 unit, raise 1 unit (spending another 2), or raise 7 units, “all in” (spending another 8). If you fold you lose only your stake. If you go all in then you don’t bet any more this hand. If you call or raise then the flop is dealt, and you have another opportunity to raise 1 unit or you can check. Same with the turn, (raise the stakes an additional unit if you wish). Then the river is dealt. Highest hand wins, draws are split. The remaining opponent will always match your bets and will never raise.

So how can it be a dealers edge game? If I simplify it to the players disadvantage we can get

  1. Player bets 1 unit
  2. If player has a hand with a 50% chance of winning a 3 hand game he goes all-in, else he calls and checks. He never raises or folds

Even under these conditions he can increase his bet from 2 units to 9 units at will. He’ll only win 33% of hands, but most of the hands he’ll win are worth 4.5 times most of the ones he’ll lose. Each side has got equal opportunity to snag a lucky river card so that should work out evenly. Adding in the other betting options, and the occasional call by the red guy it seems like a clear player edge game, which it can’t be, otherwise it wouldn’t exist.

The casinos that host it are reputable and claim random card drawing. I’d be very surprised if that wasn’t true. So where is the casino edge?

2

Can Red or Blue fold when you raise or go all in?

Basically you are playing 1 hand versus the better of 2 hands. That’s a pretty heavy house edge right there. If the House never goes all-in and never folds to your all-in bet then you can probably offset that house edge by timely large bets, but you have to be reall good at knowing the percentages to make that work.

Overall I think you are underestimating how massive an advantage playing the better of 2 hands versus your one is, especially if they both stay in to see the flop.

3

Neither computer player will raise or fold except as described in round 1.

It’s impossible for both players to see the flop. The one that didn’t raise will fold. (In the case of the red guy originally calling rather than folding, that just means free money.)

4

I did some Googling and found this description. I presume its the same rule set you are playing with.

First, it’s important to note that the player cannot go all-in once the flop is played and you can only increase your bet 1 unit at a time on the flop and the turn, but not the river. This means that even if you flop a nut straight the most you can bet is 4 units assuming that you aren’t all in on the deal.

I don’t know how to do the math, but I think it’s pretty safe to bet that the disadvantage of playing one hand versus the best of two hands pre-flop offsets the slight advantage you have in the ability to go “all-in” pre-flop on the occasional high pair.

5

I see another potential downside - the player always has to post a blind. (“Place an initial Blind bet and click the DEAL button to start.” - from Omniscient’s link). In conventional games, most of the time you get to see your cards first before deciding to match someone else’s blind.

6

I wonder if you could use that knowlege to work out an optimum strategy. Like “play As and Ks, fold 8s and 9s, but play 2s, 3s and 4s” because if you do hit a low pair on the flop it has almost certainly missed the hand you’re up against.

I still think there’s probably a house advantage overall.

7

Also note that the 2 house hands only wager half of what you are wagering for the opening blind. You put in 1 unit and they put in a combined 1 unit, so you are essentially always the big blind playing against 2 small blinds.

The fact is that you have a big disadvantage on every hand, playing against the better of two hands who are betting half what you are, which in the long run will offset any advantage you have by controlling the post flop betting since “all-in” hands are in the vast minority of total hands.

8

By my calculations, there are 2.44 billion ways to deal out the first six cards to the human and the computer players. It’s fairly easy to compute the odds of winning for each player for each combination, and then recalculate if the weaker computer player folds. Even if the exact math is elusive, a brute-force calculation can show if the player is at a long-term disadvantage.

In fact, it’s such a easy thing to write, I’d be amazed if the on-line casinos didn’t run through all 2.44 billion a few thousand times just to be sure. That’d probably a few weeks on a quad-core, tops. Add to that the player has to effectively “ante” each hand, and just let the money roll in. Sucker game.