Three Card Poker question

Can someone please help me figure out the odds of just the Ante bet in 3 card poker. I know this isn't a bet you will find anywhere but I am aware that this bet alone fuels the house edge by compelling the Player to act first. If this was the only bet and all cards were face up it would be 50/50. This seems to be an almost psychological question as opposed to mathematical but I'll bet one you math geniuses has an answer.

Thanks

did you view WoO?
https://wizardofodds.com/games/three-card-poker/

Yes but my question isn't answered there as the game isn't played the way I describe. I am interested in a hypothetical situation where only the opening wager is considered in order to create a similar game. Thanks to anybody who can answer this.

If you're talking about a game like this...

1) Player places ante bet
2) Player and dealer each receive 3 cards
3) Player hand is compared to dealer hand
4) If player hand is better, ante wins even money
5) If dealer hand is better, ante loses
6) If player and dealer hands tie, ante pushes

...then there is neither a house edge nor a player edge.

I guess I am not being clear and that is why this question is difficult. Let's suppose you don't have to place the call bet but you will be flogged to death if you decide to continue and don't win. I am looking for what you give up by having to make a decision before the dealer reveals his/her hand.

The ante bet itself has an advantage. The play bet has a disadvantage.

I don't know what the numbers are, but they aren't 50/50.

if you didn't have to play the call bet, then it is exactly as what JB described.
In such case, you should never fold your hand, which also means you actually don't need to make any decision at all..

Quote: Liveforetravel

I guess I am not being clear and that is why this question is difficult. Let's suppose you don't have to place the call bet but you will be flogged to death if you decide to continue and don't win.

Are you asking what the return of the Ante bet is if the hand is always played out as if a Play bet had been made (but never is)? For example, you place the Ante bet, you are dealt unsuited 5-3-2, the dealer has unsuited J-10-8, and your ante bet wins even money because the dealer didn't qualify?

Quote: RS

The ante bet itself has an advantage. The play bet has a disadvantage.

I don't know what the numbers are, but they aren't 50/50.

You have this backwards. The Play bet has an advantage because it is made after you see your cards and is only made if your cards are favorable. The Ante is a negative expectation overall

Quote: Ncell

You have this backwards. The Play bet has an advantage because it is made after you see your cards and is only made if your cards are favorable. The Ante is a negative expectation overall

Hmmm.....I'm not sure about that. The disadvantage from the ante comes from the player folding his hand (ie: what JB said kinda in other words). I'd think the fact that the ante bet gets paid when the dealer does not qualify would give the ante a majority of its return.

But, I was thinking of holecarding, where most of the time you're making your play bet [which has 0% chance of winning] to keep your ante bet alive [that has a good/better chance of winning].

Quote: RS

Hmmm.....I'm not sure about that. The disadvantage from the ante comes from the player folding his hand (ie: what JB said kinda in other words). I'd think the fact that the ante bet gets paid when the dealer does not qualify would give the ante a majority of its return.

But, I was thinking of holecarding, where most of the time you're making your play bet [which has 0% chance of winning] to keep your ante bet alive [that has a good/better chance of winning].

With respect to Ante vs Play advantage, keep in mind that you have two ways to lose an ante (Folding or losing to a better hand) whereas you only have one way to lose a play bet (Losing to a better hand). And as I mentioned above, the Play bet is only made in situations where the player's cards warrant it. Granted, this could include hole carding. While you can win the Ante if the dealer doesn't qualify, this requires not only that you have a playable hand, but the dealer have a non-playable hand. Per the 3CP probabilities on WoO, this happens ~19.88% of the time, whereas the player folding happens ~32.64% of the time. That alone should convince you that the Ante is negative expectation. (This may be slightly skewed, as it's possible to play a straight and lose, still ending up with a net of -1 unit, same as folding)

With respect to hole carding, I disagree with your use of the phrase "most of the time" when you talk about protecting your Ante. In order to bet the Play solely for the purpose of keeping your Ante alive, two conditions must be met. First, you must have an otherwise non-playable hand, and second, the dealer must flash a 2-J. If you have a pair or better (~25.61% of the time) you are betting the Play based upon the strength of your hand. Likewise, if you have an Ace high (~17.38% of the time) and the dealer shows anything besides an Ace, you're again betting on the strength of your hand. Unless you're playing what would be a non-qualifying hand for the dealer, the only time your Play bet truly has a 0% chance of winning is if you're playing a Q-high hand and the flashed card is higher than your second highest card.

For example, if you hold Q95 and the dealer flashes a Jack, your Play bet has a 0% chance of winning, because the lowest qualifying hand the dealer could hold would be QJ2. But as long as the flashed card is less than a 9, there is a possibility that the dealer could qualify with less.

Quote: Ncell

Quote: RS

Hmmm.....I'm not sure about that. The disadvantage from the ante comes from the player folding his hand (ie: what JB said kinda in other words). I'd think the fact that the ante bet gets paid when the dealer does not qualify would give the ante a majority of its return.

But, I was thinking of holecarding, where most of the time you're making your play bet [which has 0% chance of winning] to keep your ante bet alive [that has a good/better chance of winning].

With respect to Ante vs Play advantage, keep in mind that you have two ways to lose an ante (Folding or losing to a better hand) whereas you only have one way to lose a play bet (Losing to a better hand). And as I mentioned above, the Play bet is only made in situations where the player's cards warrant it. Granted, this could include hole carding. While you can win the Ante if the dealer doesn't qualify, this requires not only that you have a playable hand, but the dealer have a non-playable hand. Per the 3CP probabilities on WoO, this happens ~19.88% of the time, whereas the player folding happens ~32.64% of the time. That alone should convince you that the Ante is negative expectation. (This may be slightly skewed, as it's possible to play a straight and lose, still ending up with a net of -1 unit, same as folding)

With respect to hole carding, I disagree with your use of the phrase "most of the time" when you talk about protecting your Ante. In order to bet the Play solely for the purpose of keeping your Ante alive, two conditions must be met. First, you must have an otherwise non-playable hand, and second, the dealer must flash a 2-J. If you have a pair or better (~25.61% of the time) you are betting the Play based upon the strength of your hand. Likewise, if you have an Ace high (~17.38% of the time) and the dealer shows anything besides an Ace, you're again betting on the strength of your hand. Unless you're playing what would be a non-qualifying hand for the dealer, the only time your Play bet truly has a 0% chance of winning is if you're playing a Q-high hand and the flashed card is higher than your second highest card.

For example, if you hold Q95 and the dealer flashes a Jack, your Play bet has a 0% chance of winning, because the lowest qualifying hand the dealer could hold would be QJ2. But as long as the flashed card is less than a 9, there is a possibility that the dealer could qualify with less.

The thing that skews your evaluation in this case, though, is that the player should NEVER fold. The OP condition is that there's no play bet to be made. So you'll lose your ante to a better hand, as you would in folding, but you'll pick up ALL the wins for a non-qualifying hand, whether your hand qualifies or not. That makes this a +EV situation IMO, at least compared to TCP as it's played now, and probably overall, because your worse hand will sometimes win anyway, and you won't lose any more hands than you would playing TCP. It's 3 card War with a PA because of the qualifier.

Quote: BBB

It's 3 card War with a PA because of the qualifier.

Thank you.



Just because Q64 is the cut off line doesn't mean any hand better than Q64 is a winning hand. Minimum winning hand is like K8x or something funky. Rest of the (worser) hands, you're betting on play to protect your ante. If you could bet on Play for $0 or Ante amount, you're in good hands. [If you find this game or are willing to offer it, let me know and I'll buy a plane ticket.]

A good chunk of the hands you play (in one card poker) are non-qualifiers and have a 0% (on play bet) chance of winning, not this "playing Q95 vs flashed J" nonsense.

Quote: RS

Thank you.
Just because Q64 is the cut off line doesn't mean any hand better than Q64 is a winning hand. Minimum winning hand is like K8x or something funky. Rest of the (worser) hands, you're betting on play to protect your ante. If you could bet on Play for $0 or Ante amount, you're in good hands. [If you find this game or are willing to offer it, let me know and I'll buy a plane ticket.]

A good chunk of the hands you play (in one card poker) are non-qualifiers and have a 0% (on play bet) chance of winning, not this "playing Q95 vs flashed J" nonsense.

Ah, I took that initial response as being back on the subject of the normal way to play the game, not the OP's condition. My mistake. In the simple showdown the OP described, the Ante would absolutely have a PA if the qualifying rule stands.

I'm still unsure how your point about holecarding relates though, as the holecarding "nonsense" I described is valid in the normal game. Minimum hand with +EV in the normal game is KQT. This doesn't mean that lesser qualifying hands are only being played to protect the ante, as it leaves plenty of Q-high and K-high hands which can win on their own.

Quote: Ncell

Quote: RS

Thank you.
Just because Q64 is the cut off line doesn't mean any hand better than Q64 is a winning hand. Minimum winning hand is like K8x or something funky. Rest of the (worser) hands, you're betting on play to protect your ante. If you could bet on Play for $0 or Ante amount, you're in good hands. [If you find this game or are willing to offer it, let me know and I'll buy a plane ticket.]

A good chunk of the hands you play (in one card poker) are non-qualifiers and have a 0% (on play bet) chance of winning, not this "playing Q95 vs flashed J" nonsense.

Ah, I took that initial response as being back on the subject of the normal way to play the game, not the OP's condition. My mistake. In the simple showdown the OP described, the Ante would absolutely have a PA if the qualifying rule stands.

I'm still unsure how your point about holecarding relates though, as the holecarding "nonsense" I described is valid in the normal game. Minimum hand with +EV in the normal game is KQT. This doesn't mean that lesser qualifying hands are only being played to protect the ante, as it leaves plenty of Q-high and K-high hands which can win on their own.

Any hand can win on its own. There's a difference between +EV and "can win".

But where is the +/- EV line drawn? That Q64 you're playing is to protect your ante, not because Q64 is +EV. Q64 is -EV....but folding the hand is even worse -EV. Oftentimes the play bet is -EV in normal TCP. In HC TCP, a big chunk of your play bets are at a strong disadvantage.

Quote: RS

Any hand can win on its own. There's a difference between +EV and "can win".

But where is the +/- EV line drawn? That Q64 you're playing is to protect your ante, not because Q64 is +EV. Q64 is -EV....but folding the hand is even worse -EV. Oftentimes the play bet is -EV in normal TCP. In HC TCP, a big chunk of your play bets are at a strong disadvantage.

You're correct that +EV is different than "can win". The +/-EV line is clear though, as I mentioned. KQT is +EV, KQ9 is -EV. Also, when I said win on their own, I mean against qualify hands, despite being -EV. I doubt that the play bet is -EV even half the time it is made in a normal game.