strategy question about new casino game

[JoshuaMayes]

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While I was in AC last week, I was playing a new table game they had called texas holdem bonus. The way it worked was this:
1. you put in ante and got your hole cards.
2. at this point you could fold(give up your ante) or place a bet twice the ante in the turn bet circle(you would now have three bets on the table).
3. flop was then dealt and you had an option to place a bet equal to the ante in the river bet circle.
4.dealer then flips his cards and if you have him beat he pays all your bets. if not he takes them.


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There must be more to the game than this.

[AaronBrown]

The "bonus" bet is a bonus for the casino, not you. You will lose 16.4% of each bet on average, by my calculation.
You will win 9.5% of the time and get paid an average of 7.8 to 1.

Small pair (2 to 10) 9 ranks times 6 suit combinations per rank gives you 54/1,326 = 4.1% chance. At 3-1 you multiply that by 4 to get 16.3% for the expected value of the payoff. If we add all the expected values, it tells us how much we get back per $1 bet.

Face card pair, three ranks, 6 suit combinations gives 18/1,326 or 1.4%, multiply by 11 to get 14.9%.

Aces, 1 rank, 6 suit combinations give 6/1,326 = 0.5%, times 31 gives 14.0%.

AQ or AJ unsuited, 2 rank combinations, 12 suit combinations gives 24/1,326 = 1.8%, times 6 give 10.9%.

AK unsuited, 1 rank combination, 12 suit combinations gives 12/1,326 = 0.9%, times 11 gives 10.0%.

AQ or AJ suited, 2 rank combinations, 4 suits gives 8/1,326 = 0.6%, times 16 give 9.7%.

AK suited, 1 rank combination, 4 suits gives 4/1,326 = 0.9%, times 26 gives 7.8%.

Add up the probabilities of winning and you get 9.5%. Add up the expected returns (which includes your bet plus what the house pays) and you get 83.6%. So you lose 16.4% of any bet.

[AaronBrown]

I haven't worked out the exact odds, but I can make some rough recommendations.

Clearly you make the flop bet if and only if you have better than a 50% chance of winning. Since you see the flop at this point, it's not hard to calculate how many hands beat you. For example, you hold J 9 and the flop is rainbow K 7 4. Any hand with A, K, Q, 7 or 4 beats you, along with any pair or J 10. That's 894 of the 1,326 hands, or 67%. So you wouldn't add to your bet.

If we ignore the option to increase the bet after the flop, you would make the pre-flop bet as long as you had one chance in three of winning the hand. If you fold you get nothing. If you bet you lose two chips if you lose and gain four chips if you win (your ante, plus three chips from the dealer). So you need to win one time for every two losses to make betting equally good as folding. You might bet with slightly less than one chance in three due to the option of increasing the bet after the flop; but I don't think this matters much.

I think we can ignore straights and flushes, they're too rare in a five card hand to matter much. If you have a pair, you're clearly a favorite, so you bet.

If you don't have a pair, there's about one chance in three that you'll pair on the flop. There is about a 36% chance that your opponent either has a pocket pair or has paired with the flop.

Now we have four situations to consider assuming you do not have a pocket pair. Both you and your opponent pair (not counting pairs within the flop, 12%), you pair and your opponent doesn't (21%), your opponent pairs and you don't (25%) and neither of you pair (43%). In the first case and last case, you'll win depending on whether your pocket cards are higher than your opponent's (if you both pair, it matters who has the higher pair, if neither pair, then whoever has the high card counts, with the second card only mattering in ties). Your chance of winning is 21% plus 12% times the chance that a card picked at random from your hand outranks one from your opponent's plus 43% times the chance that your hole cards together outrank your opponent's. That must be 33% or better for you to bet.

It turns out that happens as long as your cards add up to 12 or more in blackjack (make the Ace 11). So I think that's pretty close to the optimal strategy. You should probably play suited or connecting cards down to a total of 11, and suited connectors down to 10. The option to add to the bet if you pair on the flop might also arguing for betting slightly lower totals.

[LoosenUp]

oops it is one of Sklansky's games. I was just kidding about don't play it. Please don't kick me off this site!

[KKbluff]

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click here for the full rundown

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My mistake, I thought you were refering to the Sklansky game which is similiar, but not the same. Sorry [img]/images/graemlins/blush.gif[/img]

[AaronBrown]

Actually, it has only superficial similarities to Sklansky's game. I don't say that to make fun of the people who linked to Sklanky's game, they gave us useful information and at quick read the games sound the same. But Sklansky's game has a tiny house edge, about the smallest you will get in a casino without card counting in blackjack, and really teaches basic poker skills. This game is a lame rip-off (even the name) with a large house edge and no useful training for poker.

[JoshuaMayes]

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oops it is one of Sklansky's games. I was just kidding about don't play it. Please don't kick me off this site!


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It is not one of Sklansky's games. It is Texas Holdem Bonus Poker by Mikohn. Sklansky's game is called something like World Poker Tour All-In Texas Holdem.

[JoshuaMayes]

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Actually, it has only superficial similarities to Sklansky's game. I don't say that to make fun of the people who linked to Sklanky's game, they gave us useful information and at quick read the games sound the same. But Sklansky's game has a tiny house edge, about the smallest you will get in a casino without card counting in blackjack, and really teaches basic poker skills. This game is a lame rip-off (even the name) with a large house edge and no useful training for poker.

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I see that the bonus game has a large house edge, but if the main game is as OP described it then a skilled player would have a huge edge on the casino. It would be like playing heads-up poker with the ultimate calling station. You both ante, and then your opponent never folds or raises but calls every bet you make. You would have a huge edge just by betting above average hands all the way to the river and folding below average hands. You get 4 bets worth of action on your above average (heads-up) hands and give 1 bet worth of action with below average (heads-up) hands. The game OP described is way too good to be true, without even taking into account optimizing play on the later betting round by considering the board cards or playing below average hands to account for the antes. I cannot believe that any casino would be foolish enough to offer this game.

[dabluebery]

I played this game for about 15 minutes at the Borgata over the weekend. If I remember correctly, any of the post-flop bets can only be equal to the amount of the ante. (You might know this, but you indicated that there was an option to increase the amount of the bet) Not so.

The basic strategy at the table, without any math, was to see every flop and then go from there. I was playing at a $5 min table, and made about 25 bucks and got the hell out of there. I win.

I hit two overcards and a flush draw on the flop in my "big" hand, and put in my turn and river bets immediately, then flushed.

There were people making crazy folds, like K3 preflop, which can EASILY be a hi card hand. I didn't know too much, and figured that the casino edge was HUGE, (I could SEE the money disappearing) but I figured probably correctly that folding a king preflop and just giving away your ante is a bad idea.

[JoshuaMayes]

Is the game really structured as OP described?