Casino poker game- beatable?

[Dice Man]

World Series Of Poker Texas Hold Em Bonus casino table game- is it beatable?

Technically this should go in the casino forum, but it seems to me that forum is mostly full of donks who think betting on 0 in roulette is +EV, so I thought better of posting it there.

First- the rules.

Every player at the table pays a stake, let’s say £1. They are then dealt 2 hole cards which they may look at, and so is the dealer. As in blackjack, the dealer doesn’t look at their hand until the player’s action is over.

After looking at your cards you can decide to see a flop by wagering another £2. If you decide to fold you give up your ante.

The flop is dealt. You may then choose to check or bet £1. The turn is dealt. You may then choose to check or bet £1. Then there is a showdown. If the dealer has a better hand playing the same board then he takes your stake and ante. If you have a better hand then he doubles each of your stakes, but NOT your ante. Your ante is returned to you however. BUT, if you have the better hand and your hand is also a qualifying hand (straight, flush, higher…) you have your ante doubled as well. If your hand is equally as good as the dealer’s, you “split the pot”, which entails just taking back what you have staked, including your ante.

The game seems beatable on the principle that when you have a good hand you can bet and maximize your wins, and when you have a bad hand you can check and minimize your losses.

There is also a side bet game as well. You can bet up to £3 (note this is actually up to £3, not 3x your ante) on what is essentially a prop bet at the same time you play your ante. You get paid of in the following ways, regardless of how your hand fared against the dealer.

Players Hand-------------------Paytable
AA (and dealer also has AA)-----1000 to 1
AA------------------------------30 to 1
AKs-----------------------------25 to 1
AQs, AJs------------------------20 to 1
AKo-----------------------------15 to 1
KK, QQ, JJ----------------------10 to 1
AQo, AJo------------------------5 to 1
TT-22---------------------------3 to 1

If you win, your initial bet is also returned.

The Optimal Strategy

The optimal strategy is clearly the one where 1) pre-flop you play only the hands you have odds to call with (considering your ante is already in there), 2) on the flop and the turn, you bet if your expected best 5-card hand is better than the expected best 5 card hand made by 2 random cards, and check if it is not.

Questions

1) Is the bonus side bet worth playing?
2) Can playing the optimal strategy beat the house?
3) What is the optimal strategy? How do we play it?
4) Can we add EV to the optimal strategy by other means?


1) Is the bonus side bet worth playing?

No. This isn’t completely obvious because you can only play the bonus side bet if you play the main game, so the casino could make the bonus side bet +EV if the main game is –EV enough to make the whole game –EV. However, the bonus side bet is –EV. Here are some calculations to prove it.

EV = 1001/276250 + 31/221 + 52/663 + 84/663 + 96/663 + 33/221 + 108/663 + 36/221

(These probabilities correspond to each of the 8 winning combinations, starting from AA in the dealer’s and player’s hand.)

EV = 1001/276250 + (93+52+84+96+99+108+108 ) / 663

EV = 1001/276250 + 640/663

EV = (663663 + 176800000) / 18315370

EV = 177463663 / 18315370

EV = 0.9689329945

Hence for every £1 we bet on the bonus side bet, we can only expect about 97p back.


2)Can playing the optimal strategy beat the house?

This is a bit difficult to work out. I suspect one would need to do masses of calculations and simulations to find out. My guess is that there’s a very real chance the optimal strategy beats the house, simply because I doubt they would expect anybody to be able to work out how to play perfectly in every situation. If you sat there with a laptop with software on it, where you could input your exact hole cards and the cards on the board I think this might beat the house. But if you just used an elementary blackjack-counting-cards +1,-1 system I don’t think this would beat the house.


3) What is the optimal strategy? How do we play it?

Since I am a donk I don’t know. I can put forward my hypothesis though. The whole way we are betting against the average hand.
Therefore pre-flop, Q7o and above are beating the dealer. There are maybe some hands we should fold pre-flop. If we have a weak hand like 76o, then we are being asked to wager £2 to win £5 back. That means we need be only 40% against the average hand pre-flop to play. Further remember that we have some implied odds too. If we flop/turn cards that make us more likely to beat the dealer we can bet and maximize our wins. Also remember that if we make a straight or higher we get our ante doubled as well. I’m not sure how to factor all this into our theory, but I’m guessing that this means we can play all hands that have at least 35% against the average hand, possibly even less EV than that. In my opinion I think we probably only fold the bottom 5-10% of all hands for that reason.
Post-flop: we should bet if we hit a pair or higher, or have a pocket pair, since they say that heads up, there is only a 1/3 chance your opponent has connected with the board. But suppose we had Q7o pre-flop and failed to improve on the flop, suppose it is 24K or something. Queen-high is probably now losing to the average hand, since several possible hands that the dealer could have, have moved from the “we beat” category to the “beats us” category. My guess is that any ace-high or better is above average on the flop, and K/Q highs where we have flush/straight draws.
Post-turn: My instinct is that ace-high is no longer above average if we have again failed to improve. A pocket-underpair is probably also below average so I check it. I bet any pair or higher here, or possibly any under-pair/ ace high with flush/straight possibilities.

4) Can we add EV to the optimal strategy by other means?


-If we are playing on a table with other players, they can help us make borderline decisions based on what they do. If they bet on the flop then this indicates they have connected with it. It might be +EV for us to bet with Q high. If more than the expected number of players are checking the flop, it might be +EV for us to check A-high.
-Seeing the hole cards of other players. Now: this game is supposed to be played with the hole cards face down. They don’t seem to discourage people who hold their hands up so that their neighbours can see, but I think they would stop all players from sharing their cards with the whole table. I can only think of two reasons why they would do this: 1) to make the game resemble texas holdem poker more convincingly. If people have to keep their cards secret more perhaps they think they are playing something that is more like poker. As poker is popular, one can expect a game that resembles it to be more popular, and hence to make more profit. 2) If the players shared their cards they might be able to beat the house as a team, particularly on full tables. This raises the potential for a team of players to either sit next to each other and covertly share, or sit around the table and communicate their cards to each other in some other manner, and for them to beat the house. I noticed that the dealer did not penalize or warn anybody who casually stated what they had during the hand, saying things like “I have JJ and have hit my bonus!” or, “Damn that 4th heart has probably beaten my flopped set”.

Conclusion: maybe beatable, fun to play.

[KD1]

Was playing this on Thursday, got chatting to a few guys who stated that the casino has a 30% edge. Not sure how accurate that is. But I certainly didnt win anything and wont be playing again!

[jjh]

Diceman, the length of that post and the time it must have taken is worrying

[waltypies]

I played it today Dice and i cant see how you could possibly lose in the long term in this game.

[Raiser]

having never played this game and not bothering readin dices post... i would guess that the odds and payouts would be like roulette?? i.e. if its 100-1 to hit a s8 then they would pay (i.e.) 90-1?! If that makes no sense then ignore this post - iam half asleep! lol

[Prowler]

if its beatable it wont ever be in a casino

[Dice Man]

Originally Posted by waltypies

I played it today Dice and i cant see how you could possibly lose in the long term in this game.

Yeah this is THE INTUITION, that you, I and Matt share. However, we have to take into account that somebody somewhere makes a living designing games like this, and they don't get paid unless they can demonstrate 1) that it has a house edge, and 2) that donks like us will have THE INTUITION that it is beatable.

When I first saw this game I didn't think poker skill would have much to do with it, but I think most people don't realise that their ace high is probably the best hand post-flop, plus they wouldn't take into account the further evidence of how the other people are playing, and factoring in the cards they are showing/talking about too. This might be one of those games where the casino will make money on it because most people don't play it very well, even though it's possible to beat it. As I write that last statement I am very aware that I sound like one of the clearly-deluded roulette/fruit machine players that think they have the edge while everybody else loses.

Therefore at the moment my conclusion is that the game isn't beatable, and I'm just curious as to why my intuition is false. So I might play some more of this game in the future.

[Prowler]

the problem with this is theres not enough preflop action or money in the pot for the casino to justify playing 1 hand against 5 others, another mandatory bet might edge the action into +ev for the house

[Dice Man]

Originally Posted by Prowler

the problem with this is theres not enough preflop action or money in the pot for the casino to justify playing 1 hand against 5 others, another mandatory bet might edge the action into +ev for the house

So you're saying that it currently sounds +EV for the player?

Some new theory:

Every hand we have a 50% chance of winning. It's not like blackjack where the house wins if they get the same value as you. Let's say that when we think our hand is probably the best (and we keep betting), we actually win 60% of the time, and when we think we're probably behind (and check) we win 40% of the time (ignore the times when we bet/check or check/bet).

So let's just consider 4 examples, each of which has a 0.25 chance of occurring each hand:

We think we're ahead, we bet and win. We win 4 (ignore the doubled antes for good hands)
We think we're behind, check and win. We win 2
We think we're ahead, we bet and lose. We lose 5
We think we're behind, check and lose. We lose 3

Surely our EV then is (0.25 x 0.6 x 4) + (0.25 x 0.4 x 2) + (0.25 x 0.4 x -5) + (0.25 x 0.6 x -3)

EV = 0.6 + 0.2 - 0.5 - 0.45

EV = -0.15

Then if we add the other scenarios, bet/check/win, bet/check/lose, check/bet/win and check/bet/lose, surely these cancel each other out don't they? Leaving us with an EV of -0.15? The doubled ante when you hit a winning straight/higher can't be worth much can it? Probably about 0.03. The returned ante only comes into play when we think we're ahead and we are. So of the times we think we're ahead, we are, how often do we also have a straight/higher? I'd guess 0.2 is very generous. So if we change the previous calculation so our prize of thinking we're ahead, and winning, is 4.2, our total EV is still -0.12.

So to those who think this game is beatable, how do you explain the above? Is my figure of 60/40 wrong? Can we be more sure of winning with good hands than just 60%? I can't see as how we can, since we surely have to bet hands like A high post-flop which don't have 60% chance of being ahead, as much as we will bet the nuts which are close to 100%. I am currently persuaded the game isn't beatable, and in fact has a significant house edge, that maybe the optimal strategy could get down to -0.05 or so.

In conclusion I think that the maximising wins/ minimising losses principle doesn't counteract the power of the ante.

[tfeilding]

I spent 5 mins this evening writing down all the payouts to start a thread about it - I havent read the original post, but I will tomorrow and will comment more fully then, but from my experience it seems that it can be beaten as long as you avoid the bonus box.