Ultimate Texas Holdem Trips

I've been to casinos where trips is paid regardless if the player wins the hand. I've also been to casinos where trips is ONLY paid if the player wins the hand.

How much bigger is the house edge for trips on Ultimate Texas Holdem if trips is ONLY paid on hands where the player wins?

Trips Payout Scale:
50
40
30
8
7
4
3

Does a Push between player and dealer result in a Trips bet Push or loses the Trips bet?

Quote: WoT

I've been to casinos where trips is paid regardless if the player wins the hand. I've also been to casinos where trips is ONLY paid if the player wins the hand.

How much bigger is the house edge for trips on Ultimate Texas Holdem if trips is ONLY paid on hands where the player wins?

Trips Payout Scale:
50
40
30
8
7
4
3

Fwiw. Trips is designed to be an independent event. The distributor (Scientific Gaming Inc) does not want casinos to offer the game in a fashion that requires the player to bet the play if they don't want to. Last I heard, when SCI hears of those procedures, they go to the casino and insist the game is offered in accordance with the lease. So you might consider informing them of any casino that's currently doing this.

It's come up before. If I recall correctly, it adds less than 1% to the game HE, because it doesn't come up that often. Maybe someone has an actual number?

It would take a result on the board like trips or quads, perhaps a flush with a deuce on the board in limited cases (like somehow you know nobody else on your full table has the board flush suit in hand). Otherwise you'd be playing for the push and win, and be in anyway.

OK, I read your post again. I think I misunderstood what you asked, because what I described is a pet peeve of mine.

There are states/jurisdictions where the player MUST win the Trips bet to get paid. The paytable for those are usually better than the one you posted because of that. I think you probably quoted one where you don't have to win to get paid.

The places I've seen that beat the dealer rule are in Florida (non-NA card rooms - the Seminoles pay it properly ), some parts of CA, and several Indian casinos. I just refuse to play in their casinos.

In this casino a push between the player and dealer will result in a trips bet push as well.

Quote: WoT

In this casino a push between the player and dealer will result in a trips bet push as well.

If nobody else gets to this, I’ll be on it later tonight or tomorrow for you. It’s pretty easy, just time consuming.

Quote: beachbumbabs

Fwiw. Trips is designed to be an independent event. The distributor (Scientific Gaming Inc) does not want casinos to offer the game in a fashion that requires the player to bet the play if they don't want to. Last I heard, when SCI hears of those procedures, they go to the casino and insist the game is offered in accordance with the lease. So you might consider informing them of any casino that's currently doing this.

It's come up before. If I recall correctly, it adds less than 1% to the game HE, because it doesn't come up that often. Maybe someone has an actual number?

It would take a result on the board like trips or quads, perhaps a flush with a deuce on the board in limited cases (like somehow you know nobody else on your full table has the board flush suit in hand). Otherwise you'd be playing for the push and win, and be in anyway.

OK, I read your post again. I think I misunderstood what you asked, because what I described is a pet peeve of mine.

There are states/jurisdictions where the player MUST win the Trips bet to get paid. The paytable for those are usually better than the one you posted because of that. I think you probably quoted one where you don't have to win to get paid.

The places I've seen that beat the dealer rule are in Florida (non-NA card rooms - the Seminoles pay it properly ), some parts of CA, and several Indian casinos. I just refuse to play in their casinos.

You are right. I posted the wrong the trips payout scale. The correct trips payout scale for this casino is:

50
40
30
10
8
6
3

You have to beat the dealer to win the trips bet. A push with the dealer result in a trips bet push.

If I calculated it correctly, this results in +0.139601% return for the trips bet which makes it appear attractive at first glance but that doesn't take into account that you don't get paid on trips bet unless you beat the dealer.

Edit: Thanks for your time and replies.

Quote: Mission146

If nobody else gets to this, I’ll be on it later tonight or tomorrow for you. It’s pretty easy, just time consuming.

Thanks, I appreciate your time and replies. I've included the correct trips payout scale in an earlier post. I posted the wrong payout scale in the original post.

Quote: WoT

You are right. I posted the wrong the trips payout scale. The correct trips payout scale for this casino is:

50
40
30
10
8
6
3

You have to beat the dealer to win the trips bet. A push with the dealer result in a trips bet push.

If I calculated it correctly, this results in +0.139601% return for the trips bet which makes it appear attractive at first glance but that doesn't take into account that you don't get paid on trips bet unless you beat the dealer.

Edit: Thanks for your time and replies.

Yeah, if you're coming up with .14%, there's something wrong there. It's more like 9-10%, where the regular Trips paytables are 5-7%

Quote: beachbumbabs

Yeah, if you're coming up with .14%, there's something wrong there. It's more like 9-10%, where the regular Trips paytables are 5-7%

My mistake again. I meant 14%.

Quote: WoT

You are right. I posted the wrong the trips payout scale. The correct trips payout scale for this casino is:

50
40
30
10
8
6
3

You have to beat the dealer to win the trips bet. A push with the dealer result in a trips bet push.

If I calculated it correctly, this results in +0.139601% return for the trips bet which makes it appear attractive at first glance but that doesn't take into account that you don't get paid on trips bet unless you beat the dealer.

Edit: Thanks for your time and replies.

Okay, so the first thing that we want to do is calculate the overall return for the paytable listed above as if losing the main bet did not lose the Trips bet. We can get our probabilities from the WoO UTH page:

https://wizardofodds.com/games/ultimate-texas-hold-em/

(50 * 0.000032) + (40 * 0.000279) + (30 * 0.001681) + (10 * 0.025961) + (8 * 0.030255) + (6 * 0.046194) + (3 * 0.048299) - (.8473) = 0.139601

This results in an expected profit of .139601 units, which is a 13.9601% player advantage.

Now, we have an even easier job than I thought thanks to the Bad Beat side bet in Liechtenstein, which is listed on the WoO UTH page:

https://wizardofodds.com/games/ultimate-texas-hold-em/

This bet pays varying amounts if either player or dealer lose with a 3OaK, or better. All we need to do to get the overall percentage we need to subtract from above is to subtract half of the bad beat probability from each hand from the overall probability. (Player and Dealer each do it half the time) The table for this also conveniently includes the Push rate for us!

Straight Flush: 0.000004/2 = .000002
4OaK: 0.000169/2 = .0000845
Full House: 0.003033/2 = .0015165
Flush: 0.006987/2 = 0.0034935
Straight: 0.006569/2 = .0032845
3OaK = 0.023028/2 = .011514

Okay, so each of these individual probabilities need to be subtracted from the wins on the formula above. The cumulative probability also must be added to the loss rate, so let's go ahead and get that:

.000002 + .0000845 + .0015165 + .0034935 + .0032845 + .011514 = 0.019895

Now, we have to adjust the formula above:


(50 * 0.000032) + (40 * (0.000279-.000002)) + (30 * (0.001681-.0000845)) + (10 * (0.025961-.0015165)) + (8 * (0.030255-.0034935)) + (6 * (0.046194-.0032845)) + (3 * (0.048299-.011514)) - (.8473 +.019895) = 0.019729

Okay, that returns an expected return of 1.9729 cents per dollar bet, but this does not include pushes.

We're going to have to get a little creative to approximate a Push rate here. The first thing that we know is that the following hands can only be pushed with all five on the board:

Royal*
Straight Flush*
4OaK
Full House
Flush*
Straight
3OaK

Therefore, the probability of pushing those hands is instantly the same as the five card probabilities for each hand:

0.00000154+.0000139+.001965= 0.00198044

Thus, we subtract those from the win rates for each respective hand:

(50 * (0.000032-.00000154)) + (40 * (0.000279-.000002-.0000139)) + (30 * (0.001681-.0000845)) + (10 * (0.025961-.0015165)) + (8 * (0.030255-.0034935-.001965)) + (6 * (0.046194-.0032845)) + (3 * (0.048299-.011514)) - (.8473 +.019895) = 0.003376

That knocks us down to an expected win of .003376 or a player advantage of 0.3376%.

This does not account for pushing with a 4OaK, Full House, Straight or 3OaK.

What we do know is that a Full House on the board would either have to push, or would be a win for either the player or the dealer. The wins for the dealer FH beating the player FH have already been accounted for. A hand such as AA999 with either the player (or dealer) having an Ace, but not the other, would be a win for the dealer or player. If both dealer and player had an Ace, then this hand would again be a push. Player or dealer winning with both having FH have already been accounted for.

For the purposes of approximation, let's just assume that any FH on the board is a push.

(50 * (0.000032-.00000154)) + (40 * (0.000279-.000002-.0000139)) + (30 * (0.001681-.0000845)) + (10 * (0.025961-.0015165-.001441)) + (8 * (0.030255-.0034935-.001965)) + (6 * (0.046194-.0032845)) + (3 * (0.048299-.011514)) - (.8473 +.019895) = -0.011034

By itself, that brings us to an expected loss of 1.1034 cents (very approximated) for each dollar bet. This represents, at a minimum, a 1.1034% house edge.

That leaves us with Push 3OaK's, Straights and 4OaK's, and all of that is, unfortunately, above my pay grade. I also can't see any easy way to find those figures.

For what it's worth, the majority of board straights will push and the probability of a board straight is .003925. Any Ace high board straight will push, so that probability is:

(20/52 * 16/51 * 12/50 * 8/49 * 4/48) - 0.00000154 = 0.00039246375 (The .00000154 subtracts royals)

Next, the probability of any other dealt straight is: .003925 - .00039246375 = 0.00353253625

The probability that neither dealer or player will have the next card to continue other straights is:

(43/47 * 42/46 * 41/45 * 40/44) = 0.69189583158

So (0.00353253625*.69189583158) + .00039246375 = 0.00283661085

Is the probability of an Ace high straight, or a straight in which both dealer and player cannot continue the straight.

(50 * (0.000032-.00000154)) + (40 * (0.000279-.000002-.0000139)) + (30 * (0.001681-.0000845)) + (10 * (0.025961-.0015165-.001441)) + (8 * (0.030255-.0034935-.001965)) + (6 * (0.046194-.0032845-0.00283661085)) + (3 * (0.048299-.011514)) - (.8473 +.019895) = -0.0280536651

That brings us to a House Edge of 2.80536651% which doesn't include:

A.) The fact that some three-to-a-straight and four-to-a-straights on the board will push with both having straights.
B.) The fact that some five card straights on the board will be continued by both player and dealer and will push.
C.) The fact that a few 4OaKs will push. All of which will be on the board.
D.) The fact that some 3OaKs will push.
E.) Assumes that any FH on the board will push, which isn't true, but is somewhat offset by the fact that we are not including Two Pairs on the board which both dealer and player turn into a Full House of the same rank.

All 4OaK must be on the board and roughly 1/13 would include an Ace kicker or be Aces with a King kicker.

.000240 * 1/13 = 0.00001846153

All other 4 Oaks are .000240-.00001846153= 0.00022153847

(50 * (0.000032-.00000154)) + (40 * (0.000279-.000002-.0000139)) + (30 * (0.001681-.0000845-.00001846153)) + (10 * (0.025961-.0015165-.001441)) + (8 * (0.030255-.0034935-.001965)) + (6 * (0.046194-.0032845-0.00283661085)) + (3 * (0.048299-.011514)) - (.8473 +.019895) = -0.028607511

Also, many 4OaKs will not have an Ace kicker, but neither player or dealer will be able to outkick the kicker.

King Kicker, No Ace 0.00022153847 * (43/47 * 42/46 * 41/45 * 40/44) = 0.00015328154
Queen Kicker, NO AK 0.00022153847 * (39/47 * 38/46 * 37/45 * 36/44) = 0.00010215995
Jack Kicker, No QKA 0.00022153847 * (35/47 * 34/46 * 33/45 * 32/44) = 0.0000650338
10 Kicker, No J-A 0.00022153847 * (31/47 * 30/46 * 29/45 * 25/44) = 0.00003489387
9 Kicker, No 10-A 0.00022153847 * (27/47 * 26/46 * 25/45 * 24/44) = 0.00002179799
8 Kicker, No 9-A 0.00022153847 * (23/47 * 22/46 * 21/45 * 20/44) = 0.00001099836
7 Kicker, No 8-A 0.00022153847 * (19/47 * 18/46 * 17/45 * 16/44) = 0.00000481419
6 Kicker, No 7-A 0.00022153847 * (15/47 * 14/46 * 13/45 * 12/44) = 0.00000169539
5 Kicker, No 6-A 0.00022153847 * (11/47 * 10/46 * 9/45 * 8/44) = 0.00000040987691
4 Kicker, No 5-A 0.00022153847 * (7/47 * 6/46 * 5/45 * 4/44) = 0.0000000434717935
3 Kicker, All Deuces 0.00022153847 * (4/47 * 3/46 * 2/45 * 1/44) = 0.00000000124205124

That means an additional:

0.00000000124205124+0.0000000434717935+0.00000040987691+0.00000169539+0.00000481419+0.00001099836+0.00002179799+0.00003489387+0.0000650338+0.00010215995+0.00015328154 = 0.00039512968 of the 4OaK will tie by those means.

(50 * (0.000032-.00000154)) + (40 * (0.000279-.000002-.0000139)) + (30 * (0.001681-.0000845-.00001846153-.00039512968)) + (10 * (0.025961-.0015165-.001441)) + (8 * (0.030255-.0034935-.001965)) + (6 * (0.046194-.0032845-0.00283661085)) + (3 * (0.048299-.011514)) - (.8473 +.019895) = -0.0404614014

That brings us to a 4.04614014% House Edge not including:

A.) The fact that some three-to-a-straight and four-to-a-straights on the board will push with both having straights.
B.) The fact that some five card straights on the board will be continued by both player and dealer and will push.
C.) The fact that a few 4OaKs will push that we have not listed by way of dealer and player having the same kicker card in each of their hands.
D.) The fact that some 3OaKs will push.
E.) Assumes that any FH on the board will push, which isn't true, but is somewhat offset by the fact that we are not including Two Pairs on the board which both dealer and player turn into a Full House of the same rank.

In any case, we have conclusively determined that this is not a player advantage despite the paytable that appears liberal. A surprising number of these hands will either push or will be beaten by the dealer. In sum, (1-(0.919536+0.040674))/2 = .019895, or nearly 2% of all hands, will have the player with 3OaK or better getting beaten by the dealer.

I'm going to guess that, if we factor in the missing hands, the house edge is probably going to come out in the neighborhood of 5%. Why any casino would want to offer this weird side bet is beyond me. Part of what players seem to like about the Trips bet is that they profit (or at least get some money back) when they have a strong hand that is beaten by the dealer. They also get paid for pushes.

Getting into anything that requires actual simulation or programming is beyond my abilities, sorry about that. Honestly, I thought I saw something on Heads-Up Texas Hold 'Em somewhere that discussed the overall probabilities of pushing each given hand rank on the final hand (that would have made this much easier) but I was either mistaken or just can't seem to find it again.

At a guess, I'd say a house edge between 5-7%.

The above post was edited, should be fine now. Copied a formula wrong.

Quote: Mission146

The above post was edited, should be fine now. Copied a formula wrong.

Nice thinking-out-loud. I would have to question one assumption you've made, though, If I followed your post correctly. There are 8 cards outstanding on a flush. I think it's fair to estimate very little impact of a SF on the board, and none from a RF (both are going to push nearly every time), but it happens nearly every time I've seen a board flush that someone has a better flush (you really retain that memory when it's the dealer!), so I disagree with discounting that factor.

Quote: beachbumbabs

Nice thinking-out-loud. I would have to question one assumption you've made, though, If I followed your post correctly. There are 8 cards outstanding on a flush. I think it's fair to estimate very little impact of a SF on the board, and none from a RF (both are going to push nearly every time), but it happens nearly every time I've seen a board flush that someone has a better flush (you really retain that memory when it's the dealer!), so I disagree with discounting that factor.

A flush getting beaten by a flush or better was included in the first part under the Bad Beats. After that, I just had to figure out the push rate. The dealer and player can only push a five card flush on the board.

I think I might see what you mean, though, not all five card flushes on the board are a push. Most of them are, of those eight outstanding cards, only 4-4.5 on average has any chance to change anything.

Board Flush
A High-0
K-High-1
Q-2
J-3
10-4
9-5
8-6
7-7
6-8

So, four on average.

4/47 = 1 in 11.75

Okay, so let me take the formula and subtract out .08510638297 from the five card flushes in the final formula...

(50 * (0.000032-.00000154)) + (40 * (0.000279-.000002-.0000139)) + (30 * (0.001681-.0000845-.00001846153-.00039512968)) + (10 * (0.025961-.0015165-.001441)) + (8 * (0.030255-.0034935-(.08510638297*.001965)))+ (6 * (0.046194-.0032845-0.00283661085)) + (3 * (0.048299-.011514)) - (.8473 +.019895) = -0.02607927374

Okay, so 2.61% house edge plus all the other stuff after that correction. I’d still say between 4-5% all told, good catch, though. Thanks! I’ll fix my previous post a little later.

Quote: Mission146

Okay, so the first thing that we want to do is calculate the overall return for the paytable listed above as if losing the main bet did not lose the Trips bet. We can get our probabilities from the WoO UTH page:

/games/ultimate-texas-hold-em/

(50 * 0.000032) + (40 * 0.000279) + (30 * 0.001681) + (10 * 0.025961) + (8 * 0.030255) + (6 * 0.046194) + (3 * 0.048299) - (.8473) = 0.139601

This results in an expected profit of .139601 units, which is a 13.9601% player advantage.

Now, we have an even easier job than I thought thanks to the Bad Beat side bet in Liechtenstein, which is listed on the WoO UTH page:

/games/ultimate-texas-hold-em/

This bet pays varying amounts if either player or dealer lose with a 3OaK, or better. All we need to do to get the overall percentage we need to subtract from above is to subtract half of the bad beat probability from each hand from the overall probability. (Player and Dealer each do it half the time) The table for this also conveniently includes the Push rate for us!

Straight Flush: 0.000004/2 = .000002
4OaK: 0.000169/2 = .0000845
Full House: 0.003033/2 = .0015165
Flush: 0.006987/2 = 0.0034935
Straight: 0.006569/2 = .0032845
3OaK = 0.023028/2 = .011514

Okay, so each of these individual probabilities need to be subtracted from the wins on the formula above. The cumulative probability also must be added to the loss rate, so let's go ahead and get that:

.000002 + .0000845 + .0015165 + .0034935 + .0032845 + .011514 = 0.019895

Now, we have to adjust the formula above:


(50 * 0.000032) + (40 * (0.000279-.000002)) + (30 * (0.001681-.0000845)) + (10 * (0.025961-.0015165)) + (8 * (0.030255-.0034935)) + (6 * (0.046194-.0032845)) + (3 * (0.048299-.011514)) - (.8473 +.019895) = 0.019729

Okay, that returns an expected return of 1.9729 cents per dollar bet, but this does not include pushes.

We're going to have to get a little creative to approximate a Push rate here. The first thing that we know is that the following hands can only be pushed with all five on the board:

Royal*
Straight Flush*
4OaK
Full House
Flush*
Straight
3OaK

Therefore, the probability of pushing those hands is instantly the same as the five card probabilities for each hand:

0.00000154+.0000139+.001965= 0.00198044

Thus, we subtract those from the win rates for each respective hand:

(50 * (0.000032-.00000154)) + (40 * (0.000279-.000002-.0000139)) + (30 * (0.001681-.0000845)) + (10 * (0.025961-.0015165)) + (8 * (0.030255-.0034935-.001965)) + (6 * (0.046194-.0032845)) + (3 * (0.048299-.011514)) - (.8473 +.019895) = 0.003376

That knocks us down to an expected win of .003376 or a player advantage of 0.3376%.

This does not account for pushing with a 4OaK, Full House, Straight or 3OaK.

What we do know is that a Full House on the board would either have to push, or would be a win for either the player or the dealer. The wins for the dealer FH beating the player FH have already been accounted for. A hand such as AA999 with either the player (or dealer) having an Ace, but not the other, would be a win for the dealer or player. If both dealer and player had an Ace, then this hand would again be a push. Player or dealer winning with both having FH have already been accounted for.

For the purposes of approximation, let's just assume that any FH on the board is a push.

(50 * (0.000032-.00000154)) + (40 * (0.000279-.000002-.0000139)) + (30 * (0.001681-.0000845)) + (10 * (0.025961-.0015165-.001441)) + (8 * (0.030255-.0034935-.001965)) + (6 * (0.046194-.0032845)) + (3 * (0.048299-.011514)) - (.8473 +.019895) = -0.011034

By itself, that brings us to an expected loss of 1.1034 cents (very approximated) for each dollar bet. This represents, at a minimum, a 1.1034% house edge.

That leaves us with Push 3OaK's, Straights and 4OaK's, and all of that is, unfortunately, above my pay grade. I also can't see any easy way to find those figures.

For what it's worth, the majority of board straights will push and the probability of a board straight is .003925. Any Ace high board straight will push, so that probability is:

(20/52 * 16/51 * 12/50 * 8/49 * 4/48) - 0.00000154 = 0.00039246375 (The .00000154 subtracts royals)

Next, the probability of any other dealt straight is: .003925 - .00039246375 = 0.00353253625

The probability that neither dealer or player will have the next card to continue other straights is:

(43/47 * 42/46 * 41/45 * 40/44) = 0.69189583158

So (0.00353253625*.69189583158) + .00039246375 = 0.00283661085

Is the probability of an Ace high straight, or a straight in which both dealer and player cannot continue the straight.

(50 * (0.000032-.00000154)) + (40 * (0.000279-.000002-.0000139)) + (30 * (0.001681-.0000845)) + (10 * (0.025961-.0015165-.001441)) + (8 * (0.030255-.0034935-.001965)) + (6 * (0.046194-.0032845-0.00283661085)) + (3 * (0.048299-.011514)) - (.8473 +.019895) = -0.0280536651

That brings us to a House Edge of 2.80536651% which doesn't include:

A.) The fact that some three-to-a-straight and four-to-a-straights on the board will push with both having straights.
B.) The fact that some five card straights on the board will be continued by both player and dealer and will push.
C.) The fact that a few 4OaKs will push. All of which will be on the board.
D.) The fact that some 3OaKs will push.
E.) Assumes that any FH on the board will push, which isn't true, but is somewhat offset by the fact that we are not including Two Pairs on the board which both dealer and player turn into a Full House of the same rank.

All 4OaK must be on the board and roughly 1/13 would include an Ace kicker or be Aces with a King kicker.

.000240 * 1/13 = 0.00001846153

All other 4 Oaks are .000240-.00001846153= 0.00022153847

(50 * (0.000032-.00000154)) + (40 * (0.000279-.000002-.0000139)) + (30 * (0.001681-.0000845-.00001846153)) + (10 * (0.025961-.0015165-.001441)) + (8 * (0.030255-.0034935-.001965)) + (6 * (0.046194-.0032845-0.00283661085)) + (3 * (0.048299-.011514)) - (.8473 +.019895) = -0.028607511

Also, many 4OaKs will not have an Ace kicker, but neither player or dealer will be able to outkick the kicker.

King Kicker, No Ace 0.00022153847 * (43/47 * 42/46 * 41/45 * 40/44) = 0.00015328154
Queen Kicker, NO AK 0.00022153847 * (39/47 * 38/46 * 37/45 * 36/44) = 0.00010215995
Jack Kicker, No QKA 0.00022153847 * (35/47 * 34/46 * 33/45 * 32/44) = 0.0000650338
10 Kicker, No J-A 0.00022153847 * (31/47 * 30/46 * 29/45 * 25/44) = 0.00003489387
9 Kicker, No 10-A 0.00022153847 * (27/47 * 26/46 * 25/45 * 24/44) = 0.00002179799
8 Kicker, No 9-A 0.00022153847 * (23/47 * 22/46 * 21/45 * 20/44) = 0.00001099836
7 Kicker, No 8-A 0.00022153847 * (19/47 * 18/46 * 17/45 * 16/44) = 0.00000481419
6 Kicker, No 7-A 0.00022153847 * (15/47 * 14/46 * 13/45 * 12/44) = 0.00000169539
5 Kicker, No 6-A 0.00022153847 * (11/47 * 10/46 * 9/45 * 8/44) = 0.00000040987691
4 Kicker, No 5-A 0.00022153847 * (7/47 * 6/46 * 5/45 * 4/44) = 0.0000000434717935
3 Kicker, All Deuces 0.00022153847 * (4/47 * 3/46 * 2/45 * 1/44) = 0.00000000124205124

That means an additional:

0.00000000124205124+0.0000000434717935+0.00000040987691+0.00000169539+0.00000481419+0.00001099836+0.00002179799+0.00003489387+0.0000650338+0.00010215995+0.00015328154 = 0.00039512968 of the 4OaK will tie by those means.

(50 * (0.000032-.00000154)) + (40 * (0.000279-.000002-.0000139)) + (30 * (0.001681-.0000845-.00001846153-.00039512968)) + (10 * (0.025961-.0015165-.001441)) + (8 * (0.030255-.0034935-.001965)) + (6 * (0.046194-.0032845-0.00283661085)) + (3 * (0.048299-.011514)) - (.8473 +.019895) = -0.0404614014

That brings us to a 4.04614014% House Edge not including:

A.) The fact that some three-to-a-straight and four-to-a-straights on the board will push with both having straights.
B.) The fact that some five card straights on the board will be continued by both player and dealer and will push.
C.) The fact that a few 4OaKs will push that we have not listed by way of dealer and player having the same kicker card in each of their hands.
D.) The fact that some 3OaKs will push.
E.) Assumes that any FH on the board will push, which isn't true, but is somewhat offset by the fact that we are not including Two Pairs on the board which both dealer and player turn into a Full House of the same rank.

In any case, we have conclusively determined that this is not a player advantage despite the paytable that appears liberal. A surprising number of these hands will either push or will be beaten by the dealer. In sum, (1-(0.919536+0.040674))/2 = .019895, or nearly 2% of all hands, will have the player with 3OaK or better getting beaten by the dealer.

I'm going to guess that, if we factor in the missing hands, the house edge is probably going to come out in the neighborhood of 5%. Why any casino would want to offer this weird side bet is beyond me. Part of what players seem to like about the Trips bet is that they profit (or at least get some money back) when they have a strong hand that is beaten by the dealer. They also get paid for pushes.

Getting into anything that requires actual simulation or programming is beyond my abilities, sorry about that. Honestly, I thought I saw something on Heads-Up Texas Hold 'Em somewhere that discussed the overall probabilities of pushing each given hand rank on the final hand (that would have made this much easier) but I was either mistaken or just can't seem to find it again.

At a guess, I'd say a house edge between 5-7%.

Impressive post. Thanks for your work!

Quote: Mission146

A flush getting beaten by a flush or better was included in the first part under the Bad Beats. After that, I just had to figure out the push rate. The dealer and player can only push a five card flush on the board.

I think I might see what you mean, though, not all five card flushes on the board are a push. Most of them are, of those eight outstanding cards, only 4-4.5 on average has any chance to change anything.

Board Flush
A High-0
K-High-1
Q-2
J-3
10-4
9-5
8-6
7-7
6-8

So, four on average.

4/47 = 1 in 11.75

Okay, so let me take the formula and subtract out .08510638297 from the five card flushes in the final formula...

(50 * (0.000032-.00000154)) + (40 * (0.000279-.000002-.0000139)) + (30 * (0.001681-.0000845-.00001846153-.00039512968)) + (10 * (0.025961-.0015165-.001441)) + (8 * (0.030255-.0034935-(.08510638297*.001965)))+ (6 * (0.046194-.0032845-0.00283661085)) + (3 * (0.048299-.011514)) - (.8473 +.019895) = -0.02607927374

Okay, so 2.61% house edge plus all the other stuff after that correction. I’d still say between 4-5% all told, good catch, though. Thanks! I’ll fix my previous post a little later.

Sorry Mission, but I think you have made a conceptual error.

Lets say the board is an A-High flush: AT872 of hearts. Literally any of the 8 outstanding hearts will be greater than the 2-hearts and allow the player or dealer to have a higher flush.

Never heard of the trips bet ever to push or lose. I thought every casino was the same, it’s treated as an independent bet. You could have a royal on the board and the trips bet pays. You can fold your hand but still qualify for the bonus. Now the blind bet is different, you must beat the dealer.

I’ve come across a casino that does not use the shuffle machine but hand shuffles instead, and has one of the players cuts the card, which I like.

Quote: Vegasrider

Never heard of the trips bet ever to push or lose. I thought every casino was the same, it’s treated as an independent bet. You could have a royal on the board and the trips bet pays. You can fold your hand but still qualify for the bonus. Now the blind bet is different, you must beat the dealer.

That's the way I've seen it as well--the player that folds after the river is still involved in the trips bet.

But then, I've only seen it played in a couple of casinos in Vegas and three in Oklahoma, so I'm hardly an expert.

JClay

Quote: JoeClayton

That's the way I've seen it as well--the player that folds after the river is still involved in the trips bet.

But then, I've only seen it played in a couple of casinos in Vegas and three in Oklahoma, so I'm hardly an expert.

JClay

It's that way in jurisdictions where the house can't bank the game. Florida card rooms is one example. California card rooms is another.

There's another player who represents a syndicate, and they bank your bet. The house just deals it and takes a rake.

Quote: beachbumbabs

It's that way in jurisdictions where the house can't bank the game. Florida card rooms is one example. California card rooms is another.

There's another player who represents a syndicate, and they bank your bet. The house just deals it and takes a rake.

This casino is one of the Florida card rooms.

Quote: beachbumbabs

It's that way in jurisdictions where the house can't bank the game. Florida card rooms is one example.

Because of the way Florida defines poker, winners only collect when they WIN against another player, which is what routinely occurs in a standard poker game. However, the implementation of this rule has some strange effects for the so-called carnival games.

In Florida, carnival game bonus bets -- regardless of what the standard rules say -- only pay if the player wins against another player, which in this case is the House (via its player-banker). Consequently, the UTH Trips bet only pays if the player remains in the hand and beats the Dealer.

Same for 3-Card Poker, where the Pair Plus bet only pays if the player beats the Dealer. Also, the Ante Bonus (usually paid if Player hand is a straight or better) is completely absent from the game. To compensate, the various pay tables are "adjusted." For example, at a card room near me, the Pair Plus on its TCP paid 2-to-1 for any pair (among other changes).

That is true for Florida card rooms but not at the 5 major casinos. The trips wager is a separate wager and paid irregardless of the poker hand.

Quote: beachbumbabs

It's that way in jurisdictions where the house can't bank the game. Florida card rooms is one example. California card rooms is another.

There's another player who represents a syndicate, and they bank your bet. The house just deals it and takes a rake.

What is the rake for UTH? I've only played against the house, but there's a non-Indian California card casino somewhat near to me that I hear has it and I'd like to check it out.

Quote: Commish

That is true for Florida card rooms but not at the 5 major casinos. The trips wager is a separate wager and paid irregardless of the poker hand.

Right. There's a difference, actually many, between card rooms and casinos here.

Quote: Gialmere

What is the rake for UTH? I've only played against the house, but there's a non-Indian California card casino somewhat near to me that I hear has it and I'd like to check it out.

In the FL card rooms, the rake is paid by the syndicate player only. It's collected every hand before the hand is dealt, and is a percentage of how much is wagered for that hand. There is no rake for the regular players (other than the HE of the game).

Not sure if the CA card rooms are the same way.

Quote: Joeman

In the FL card rooms, the rake is paid by the syndicate player only. It's collected every hand before the hand is dealt, and is a percentage of how much is wagered for that hand. There is no rake for the regular players (other than the HE of the game).

Not sure if the CA card rooms are the same way.

Clever. Heh. It's amazing how good we humans are at making rules and than figuring out how to get around them.

Quote: LuckyPhow

Because of the way Florida defines poker, winners only collect when they WIN against another player, which is what routinely occurs in a standard poker game. However, the implementation of this rule has some strange effects for the so-called carnival games.

In Florida, carnival game bonus bets -- regardless of what the standard rules say -- only pay if the player wins against another player, which in this case is the House (via its player-banker). Consequently, the UTH Trips bet only pays if the player remains in the hand and beats the Dealer.

Same for 3-Card Poker, where the Pair Plus bet only pays if the player beats the Dealer. Also, the Ante Bonus (usually paid if Player hand is a straight or better) is completely absent from the game. To compensate, the various pay tables are "adjusted." For example, at a card room near me, the Pair Plus on its TCP paid 2-to-1 for any pair (among other changes).

Before this thread vanishes over the horizon, what happens to these card room side bets (Trips, Pair Plus etc.) if the player and dealer push? The player still doesn't "win". Do the bets win, lose or draw?

In the case of Florida card rooms, they push.

This topic came up on my live stream yesterday.

As I understand it, in Florida on the Trips bet the player player must also win. If he ties with a paying hand, the Trips bet is a push. Is this correct? I just asked if this is the policy in California and was told "no."

Here is my analysis of the standard 50-40-30-8-7-4-3 pay table under the Florida rule.

Player	Pays	Combinations	Probability	Return
Royal flush	50	85,615,200	0.000031	0.001539
Straight flush	40	734,237,144	0.000264	0.010559
Four of a kind	30	4,240,864,800	0.001525	0.045742
Full house	8	62,810,500,464	0.022582	0.180660
Flush	7	71,523,195,288	0.025715	0.180005
Straight	4	103,685,076,072	0.037278	0.149113
Three of a kind	3	97,664,829,948	0.035114	0.105341
Trips or better and push	0	28,636,706,336	0.010296	0.000000
Two pair or less	-1	2,356,664,171,400	0.847300	-0.847300
Trips or better and lose	-1	55,335,805,748	0.019895	-0.019895
Total		2,781,381,002,400	1.000000	-0.194235

In other words, a house edge of 19.42% (ouch!). Compare this to the 3.50% house edge if winning is not required.

Any comments or disagreements?

That is not true at the Florida casinos. It is true at the casinos in Florida at the racetracks.

Quote: Commish

That is not true at the Florida casinos. It is true at the casinos in Florida at the racetracks.

Thank you. Has anyone else done the math on it?

I had the raw numbers for it already here.

Quote: Wizard

This topic came up on my live stream yesterday.

As I understand it, in Florida on the Trips bet the player player must also win. If he ties with a paying hand, the Trips bet is a push. Is this correct? I just asked if this is the policy in California and was told "no."


In other words, a house edge of 19.42% (ouch!). Compare this to the 3.50% house edge if winning is not required.

Any comments or disagreements?

I have played at 2 of the Seminole casinos and they paid trips on losing hands just like normal.

I didn't see UTH at any of the "Racinos" all the ones I visited has Heads-up-holdem from Galaxy instead. Not sure how they handled the Trips Plus or whatever it's called in that game.

I don't know much about the scene in Florida, but in California the card clubs around LA and SF are a horse of a different color compared to the tribal casinos.

Quote: Wizard

I had the raw numbers for it already here.

Were those raw numbers generated by a looping code that went through every combination of cards for player and his opponent? Or by combination theory?

Quote: gordonm888

Were those raw numbers generated by a looping code that went through every combination of cards for player and his opponent? Or by combination theory?

Looping.

Quote: Wizard

I don't know much about the scene in Florida, but in California the card clubs around LA and SF are a horse of a different color compared to the tribal casinos.

In FL, the Seminole Hard Rock casinos are pretty much regular casinos except they don't have live craps (they do have bubble craps). Carny games there are basically played by Vegas rules.

On the other hand, parimutuel outlets - dogs, horses and jai-alai - have been allowed to have poker rooms for about 20 years, but are only allowed to spread poker games. Over that time the games have evolved from strictly limit games with a $10 max pot to now where they are essentially the same as other poker rooms.

About 5 years ago, they branched out to spreading Carney games. However, by FL law, the house cannot be a participant in the games.

There is a 'designated player' at each table, usually an employee of a syndicate not affiliated with the card room, who banks the game as if he were the house. He pays a rake to the house, and will pay winning bets, and collects losing ones, including side bets.

Each player at the table is essentially playing heads up against the designated player, and only the best hand wins the 'pot.' Thus, you can't lose the hand and win the side bet. It's the way they work around the state's poker laws, which were originally written to only permit traditional poker.

To compensate for this, the pay tables for side bets are tweaked to make the house edge more palatable for the player. For UTH Trips, I believe it is 50-40-30-10-8-6-3, with increased payouts for full house, flush, and straight.

Also, you won't find any games like MS Stud at the card rooms, since there is no opponent, no hand to compete against. There aren't any such restrictions at the Hard Rocks.

Quote: Joeman

To compensate for this, the pay tables for side bets are tweaked to make the house edge more palatable for the player. For UTH Trips, I believe it is 50-40-30-10-8-6-3, with increased payouts for full house, flush, and straight.

Thank you. I don't believe anybody mentioned this pay table yet in this thread. Here is my analysis of it.

Player	Pays	Combinations	Probability	Return
Royal flush	50	85,615,200	0.000031	0.001539
Straight flush	40	734,237,144	0.000264	0.010559
Four of a kind	30	4,240,864,800	0.001525	0.045742
Full house	10	62,810,500,464	0.022582	0.225825
Flush	8	71,523,195,288	0.025715	0.205720
Straight	6	103,685,076,072	0.037278	0.223670
Three of a kind	3	97,664,829,948	0.035114	0.105341
Trips or better and push	0	28,636,706,336	0.010296	0.000000
Two pair or less	-1	2,356,664,171,400	0.847300	-0.847300
Trips or better and lose	-1	55,335,805,748	0.019895	-0.019895
Total		2,781,381,002,400	1.000000	-0.048799

I almost forgot that Florida follows an
alternate pay table for the Pairplus in Three Card Poker.

Here is my new page on the Florida Variant of Trips Bet. I welcome all comments.

Derby Lane in Tampa, at least as of 2018, uses a 100-50-40-10-8-4-3 Trips paytable.

Last I checked, the other two Tampa rooms use the casino standard 50-40-30-8-7-4-3 Trips paytable with a nasty ~20% house edge given the FL parimutuel card room rules.