Ultimate Texas Hold 'Em Question

Does anybody understand the section where the Wizard writes:

"For each rank on the board there are three more that can beat you. For example, if the dealer has the jack of hearts, diamonds, or spades he will pair up and beat you. So, 5×3=15 cards will give the dealer a hidden pair. Also, all four queens and aces will beat you. So, 15+8=23 cards will beat you. If the dealer has one of the three remaining tens, then you'll lose lose. That brings us to 26. You need to have less than 21 outs to stay in, so fold."

On this page:

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

If someone could explain it in a simple, easy-to-understand method that would be great.

I assume you understand why another jack will beat you in the example. He is going on to say all 5 community cards shown could be paired. You don't have a pair, see? each of the 5 cards has three others since it is one deck. Any Queen, any Ace will beat pairless you, and there are 8 of those.

This is become simpler for me over time. Realize the example where there are no pairs in the community cards, and you don't have a pair*, the 5 cards then represent 15 outs and you don't have far to go. A king in your hand is 'good' and you bet it as that means besides the 5 only the 4 aces beat you [that gets it to 19]. I have come to count down from the King; I see a King on the board, or a pair on the board, then the Queen is good counting it down.

I think you are a little inexperienced in Poker generally, so that gives you a learning curve, I know. But any time you have a 10 or better, you have to think of it as a possible kicker, as the kickers are hugely important in this game. I think that is because if you fold you lose all bets, thus those times a kicker saves your butt it has great value.

You just have to be slow to fold period. Look for the chances you will tie because of those times the community cards probably have the best kicker along with, say, 2 pair. If the best hand is the 5 community cards, everybody has the same hand.

*if you had a pair you would have already bet, or that means you should bet end of problem

I don't know. It's all still confusing.

If you don't have a pair or better by using one or more of your hole cards...then you have to count up all the single cards where the dealer could possibly beat you. If it's 21 or more, then you should fold.

For example, lets say you have 97 on a 2 5 8 J K board

For each card on the board, there are 3 cards the dealer could have to beat you because any pair beats you... 3 2's, 3 5's, 3 8's, 3 J's, and 3 K's for 15 cards...

The dealer can also beat you with a Ten, Queen or Ace...and for each of those 4 cards exist...so that's 12 more cards...

This gives 27 single cards the dealer could have to beat you; therefore, you should fold in this example.

I can now see quickly if you had a queen, it'd be good [in the example given]

understand, it's the odds of the queen being best kicker ... doesn't win every time

why? the 5 cards are 15 outs. Ace is 4 more to 19. You do not have a King, but you counted the King already as part of the 15 outs. Thus the Queen is 'good'

the Jack would not be good since it is lower rank than queen, and that it is in the community is thus irrelevant.

That's why I count this way: King is good, I see a community King, now the queen is good. This really gets much simpler and perfection is not necessary. Believe me, this goes from complicated to easy [using a simple strat.] pretty quick

Here's a short list; perhaps this will help, then you can refine it as you play more.

If anything in your hand pairs the board, or you have a pocket pair, or an ace, or a king, you bet (now or before now, mostly before now).

Else

If you have a queen and haven't already bet it, look at the board. If there is any pair on the board, any ace, or any king, (or better) bet. Otherwise, fold.

Else

If you have a jack, and there are 2 pair or 3OAK on the board, bet. If there are at least 2 aces, kings, queens (could be paired, could be 1 each), bet. If there is a pair AND an ace, queen, or king on the board, bet. Otherwise fold.

Else

If you have a 10 or a 9, and there are 2 pair or 3OAK on the board and your 9 or 10 improves the board, bet. Otherwise, fold.

EXCEPTIONS:

If the board is very strong, like a made straight or flush, or 2 pair with an ace or face kicker, or 3OAK with high kickers, bet anything. (You're playing for a push).

If the board has 4 to a flush or 4 to an outside straight, I would fold Q kickers and below.

Others are welcome to refine this/correct it as necessary, but I'm going for a very simple list here.

I understand what he meant when talking about single cards, but are pairs of dealer hole cards taken into account?

For example, in the example on the Wizard's page, if the dealer's hole cards are a pair, then the dealer wins, but these aren't counted towards the "21 outs." Should each particular pair of hole cards, where either one isn't an out by itself, be counted as an out?

As for the original question, it's simple - which cards would cause the dealer to win if they were one of his hole cards?

Your hand is K-J-10-8-6
Jack of Spades, Hearts, or Diamonds gives the dealer a pair of jacks, and the dealer wins
6 of Spades, Hearts, or Clubs gives the dealer a pair of 6s, and the dealer wins
King of Hearts, Clubs, or Diamonds gives the dealer a pair of kings, and the dealer wins
5 of Spades, Hearts, or Diamonds gives the dealer a pair of 5s, and the dealer wins
8 of Spades, Hearts, or Clubs gives the dealer a pair of 8s, and the dealer wins
Any of the four Aces gives the dealer ace high, which beats your king high
Any of the four Queens gives the dealer KQ high, which beats your K-10 high

I'm not quite sure why the dealer having the 10 of Spades, Clubs, or Diamonds is counted as a loss, since if the dealer's other hole card is a 2-4, then both of you have K-J-10-8-6.
Even if you ignore the 10s, that's 3 + 3 + 3 + 3 + 3 + 4 + 4 = 23 "outs," which is more than 20, so you fold.

I understand the less than 21 outs rule to be the player's 'last resort' decision. The assumption is you have checked up to the river and if nothing plays on the river (you have a busted hand) and you have 21+ outs - FOLD, otherwise with 20 or less outs - BET. The Wiz explanation should be simple enough to follow. Why make this more difficult than necessary?

Quote: ThatDonGuy

I understand what he meant when talking about single cards, but are pairs of dealer hole cards taken into account?

For simplicity sake, no. Pocket pairs won't be there that often.

Quote: CharmedQuark

I understand the less than 21 outs rule to be the player's 'last resort' decision. The assumption is you have checked up to the river and if nothing plays on the river (you have a busted hand) and you have 21+ outs - FOLD, otherwise with 20 or less outs - BET. The Wiz explanation should be simple enough to follow. Why make this more difficult than necessary?

Yes, that's a given, that you don't already have a hand that should cause you to bet then or before.

look upthread and you will see the Wizard respond to the question about other possible outs. Basically, don't try to make this harder than it is, is what he says.

this game is simpler than what it first seems. The more sophisticated strategies especially make it seem daunting. One that is probably pretty good uses so much poker jargon that it is unusable to me. The Wizard page recommends buying a strategy card from Grosjean, and if I find myself playing more I might buy it.

but the Wizard's simple strategy is good to go for me for the most part. It seems a little complicated when you get to the 1X decision, but trust me you get an instinct for it pretty quickly. You could play half drunk and do OK, better than you'd do going with the strategies the other players use anyway LOL ... the impairment to recognizing certain situations is enough for me not to drink ... I'm just saying.

I think I can tell Hot Blond is not quite comfortable with poker generally, judging by other threads. This makes it all seem complicated for sure.

Yeah I'm not used to playing poker. I've played 3-card poker a lot of times but that's a super easy game to play.

Anyway, I braved up and sat at an Ultimate Texas Hold 'Em table by myself last night and gave it a shot. I had sat at a table the night before with a forum member but had him tell me what to do on each hand, but now I was on my own. I was a bit nervous but told the dealer and she said she would help me. Basically I did really well! Wrote out the basic strategy on paper and had it on the table with me. When it came down to the 1x bet I just used the easy "Jacks or better" suggestion that was made to me by a couple people already and it seemed to work out. I was also able to show my hand to the dealer so they could tell me whether to bet or fold. I sat for 60 minutes and won $605! I must admit, although the Wizard won't like this, I did bet on Trips just about every hand. One hand I forgot to bet it (she took it away in a loss from a previous bet and I forgot to replace it) and I ended up getting a full house! Damn! I would have made an extra $80!! I basically startedy bets at $10 per spot then upped it to $20 when I saw that I kept winning. Later on I told one dealer how much I won and he said it's hard to win money on that game, but I told another one and he said that the other dealer was wrong, that it's easy to win money on that game. Either way I won money on it both nights and am taking a liking to the game!

Still wish I could figure out the 21 outs rule! Maybe if I had someone sit down and explain it to me with cards. And as mentioned I'm not really familiar with poker so that's a weakness in this situation.

Whem you mean jacks or better suggestion, i hope you mean a jack high or better in your hand, not a pair of jacks. Any pair made from your hand is a 1x call. Jack high or better in your hand for a 1x call is a good approximation though.

Quote: HotBlonde

... I was a bit nervous but told the dealer and she said she would help me. Basically I did really well! ...

It's great that you won but you have to be careful about taking the dealer's advice at this game. Most of them have no idea and give horrible advice. Especially on the first decision, I have had dealers scold me for raising 4x with hands such as KQs or TT. At the D a dealer told me to raise 4x with AA or KK, 3x with QQ or AKs, and otherwise only raise if I want to gamble. This is TERRIBLE advice because whenever the player has a raising hand on the Wizard's strategy chart, there is a player advantage on that hand. They will also always tell you to play the Trips bet because "that's where you make your money." In actuality, they are just hoping for a nice tip if you hit one of the bigger payouts, because that's where they make THEIR money.

It is good to know the 21 outs rule, but that is a more marginal play. If you err once in a while by putting in the 1x raise in a close situation, it isn't that costly. It's much more costly to miss the 4x raises when you have the best of it.

Quote: HotBlonde

Still wish I could figure out the 21 outs rule! Maybe if I had someone sit down and explain it to me with cards.

I thought I did, except for the "sitting down" part.

You know 7 of the 52 cards in play - your two hole cards, and the five up cards. Each of the remaining 45 cards has to be checked, one at a time, and it is an "out" if you would always lose if the dealer has it in his hand.

Going back to the Wizard's example, with you having hole cards of 2d-10h and the five up cards being Jc-6d-Ks-5c-8d, your hand is Ks-Jc-10d-8d-6c, or just K-J-10-8-6 since there's no flush involved.

Maybe I can "talk you through this" if you have a deck of cards handy. It helps to have them sorted in order.
First, remove the two cards that are in your hand, and the five "up" cards. Set the five up cards separately from your two cards.

I'll do this "the long way" for now; when you are playing, you won't be able to go through all 45 of the cards one at a time.
Start with the four Aces still in the deck. If the dealer has one of them, the worst he can do is have an Ace-high hand, which beats your King-high hand, so all four of the Aces are "outs". Put the Aces in a pile which I'll call the "outs" pile.
Now go to the three 2s (there are only three since the 2 of diamonds is one of your hole cards). The best hand the dealer has is K-J-8, but you have K-J-10, which is a better hand, so the 2s are not outs; set those aside. (Never mind that if the dealer has a pair of 2s, the pair would beat your King-high; we're not taking this into account.)
Now go to the four 3s; a 3 also gives the dealer K-J-8, but again, your K-J-10 beats it.
The same goes for the four 4s.
However, with each of the three 5s, the dealer has a pair of 5s, which beats your King-high, so the 5s are all outs; put them in the outs pile.
The same goes for the three 6s; each one gives the dealer a pair of 6s, which beats your King-high, so the three 6s are all outs.
Now go to the four 7s; the dealer has K-J-8, but that loses to your K-J-10, so set the 7s aside.
No go to the three 8s; each one gives the dealer a pair of 8s, which beats your King-high, so the three 8s are all outs; put them in the outs pile.
Now go to the four 9s; the dealer has K-J-9, but that loses to your K-J-10, so set the 9s aside.
Here's the one I'm not entirely sure about: go to the three 10s. The dealer's hand is K-J-10-8-6, but your hand is also K-J-10-8-6, so it's a push. I am assuming that these are not considered outs, so set them aside.
Now go to the three Jacks; each one gives the dealer a pair of jacks, which beats your King-high, so the three Jacks are all outs; put them in the outs pile.
Now go to the four Queens; each one gives the dealer K-Q high, which beats your K-J high, so the three Queens are all outs; put them in the outs pile.
Finally, go to the three Kings; each one gives the dealer a pair of Kings, which beats your King-high, so the three Kings are all outs; put them in the outs pile.
Count the number of cards in the outs pile: four Aces, three 5s, three 6s, three 8s, three Jacks, four Queens, and three Kings is 23 cards. This is 21 or higher, so you fold. If there were 20 or fewer, you would make the final Play bet.

To make things easier, notice that the only time you need to bother with suits when counting outs is when four of the five up cards are the same suit. This is the only way that one card can make a flush.

Thanks for taking the time to write all that out! This makes it easier to understand. I'm just trying to think of how, as an inexperienced player, I can calculate all this in my head at the table quickly before I miss my opportunity to bet.

Quote: ThatDonGuy

Now go to the four Queens; each one gives the dealer K-Q high, which beats your K-J high, so the three Queens are all outs; put them in the outs pile.

I think you meant to say the four queens are all outs.

When the Wizard posted "If the dealer has one of the three remaining tens, then you'll lose" why is that?

Quote: ThatDonGuy

I understand what he meant when talking about single cards, but are pairs of dealer hole cards taken into account?

No. The strategy is complicated enough as it is, as we can see from this thread.

Quote: HotBlonde

When the Wizard posted "If the dealer has one of the three remaining tens, then you'll lose" why is that?

Because the dealer will likely out-kick you. However, I can see how that is a bad example. Let me try to find a better one.

Here is my new example.



There are 5*3=15 cards that will pair up the dealer. Then there are 2*4=8 jacks and queens that will outkick the player. So we can see 23 single cards that will beat the dealer. 23>=21, so we fold.

We don't count the other three nines, because those don't beat the player, but result in a push.

We also don't count combinations, like two spades, or a pocket pair. Just single cards.

EV of raising = -2.136364
EV of folding = -2.000000

I would just add that the Wizards practice game is an invaluable resource, especially if you can see the E.V.'s for each hand. Make sure you have the right version of Java. (chrome isn't supporting Java anymore.)

Quote: teddys

I would just add that the Wizards practice game is an invaluable resource, especially if you can see the E.V.'s for each hand. Make sure you have the right version of Java. (chrome isn't supporting Java anymore.)

oddly, using the latest version of Firefox, I get the warning now without the EV data

I agree though ... very reassuring to be able to play with few warnings

Quote: Wizard

Here is my new example.



There are 5*3=15 cards that will pair up the dealer. Then there are 2*4=8 jacks and queens that will outkick the player. So we can see 23 single cards that will beat the dealer. 23>=21, so we fold.

We don't count the other three nines, because those don't beat the player, but result in a push.

We also don't count combinations, like two spades, or a pocket pair. Just single cards.

EV of raising = -2.136364
EV of folding = -2.000000

edit this? "So, because there are only 23 outs (21 or more), we fold" I suggest remove the word 'only'

>>>>>>

A test for my count down method: since there are no pairs etc. King or better is automatically good as your kicker. I'll count down from there. There is an Ace and a King in the community cards - as part of the first 15 outs, don't count them again as 'other' outs in this method. Seeing the Ace and King, now the count down 'goes like' this: King, Queen, Jack. Meaning if the player had a Jack or better kicker, he would bet, but a 10 he folds [but see below, a 10 pairs]. This goes fast at the table, somewhat important to me.

Testing with J.B's calculator:

Test #1: Changing the 10 in community to a 5 of hearts so a 10 will not pair, and testing with 10 kicker in player's hand [not the 9 kicker shown]

Average value of raising -2.214141
Average value of folding -2.000000

Test #2: no changes except a jack of diamonds being made best kicker in player's hand

Average value of raising -1.914141
Average value of folding -2.000000

So the count down method worked here, Jack or better for Kicker bets the 1X, 10 folds [except in the Wizard's example it would pair of course]

I'm not sure that is easy to follow. Works for me as counting the outs is a slow process, perhaps another person does that quickly.

Speaking of "counting down methods," here's one, although I'm not 100% sure about some of these decisions:

This assumes that neither of the hole cards in your hand "improve" the board (the five up cards); if they do (e.g. there is a pair on the board, but one of your hole cards makes it two pair or three of a kind), then always bet.

If the board does not have a pair, 4/straight, or 4/flush:
15 cards make a pair, leaving 6 outs before reaching the "fold point."
If there are no ranks that are both not on the board and higher than your high card, then there are only 15 outs, so bet.
If there is one such rank, then there are 19 outs, and you still bet.
If there are two (or more) ranks, then there are 23 (or more) outs, so fold.

If there is a pair on the board:
2 cards make 3 of a kind, and 9 cards make 2 pair, so that's 11 outs.
If there are 3 or more ranks not on the board and higher than your high card, fold; otherwise, bet.

If there are two pair on the board, and the fifth card's rank is lower than the lower pair (e.g. K-K-9-9-2):
4 cards make a full house, so that's 4 outs. (The dealer having a 2 is meaningless.)
If there are 5 or more ranks not on the board and higher than both the unpaired card on the board and your high card, fold; otherwise, bet.

If there are two pair on the board, and the fifth card's rank is higher than the lower pair (e.g. K-K-9-9-A, or K-K-2-2-9):
4 cards make a full house, and 3 cards make a higher two pair, so that's 7 outs.
If there are 4 or more ranks not on the board and higher than both the unpaired card on the board and your high card, fold; otherwise, bet.

If there is 3 of a kind on the board:
1 card makes 4 of a kind, and 6 cards make a full house, so that's 7 outs.
If there are 4 ranks higher than both your high card and the lower card not in the three of a kind, fold; otherwise, bet

If there is 4/open-ended straight on the board and the fifth card does not make a pair:
15 cards make a pair, and 8 make the straight, so that's 23 outs; fold.

If there is 4/open-ended straight on the board and the fifth card makes a pair:
2 cards make three of a kind, 9 make two pair, and 8 make the flush, so that's 19 outs
If there are 1 or more ranks not on the board and not completing the straight that are higher than your high card, fold; otherwise, bet.

If there is 4/inside or closed-ended (AKQJ or 432A) straight on the board and the fifth card does not make a pair:
15 cards make a pair, and 4 make the straight, so that's 19 outs.
If there are 1 or more ranks not on the board and not completing the straight that are higher than your high card, fold; otherwise, bet.

If there is 4/inside or closed-ended (AKQJ or 432A) straight on the board and the fifth card makes a pair:
2 cards make three of a kind, 9 make two pair, and 4 make the flush, so that's 15 outs
If there are 2 or more ranks not on the board and not completing the straight that are higher than your high card, fold; otherwise, bet.

If there is 4/flush on the board and the fifth card does not make a pair:
15 cards make a pair, and 9 make the flush, so that's 24 outs; fold.

If there is 4/flush on the board and the fifth card makes a pair:
2 cards make three of a kind, 9 make two pair, and 9 make the flush, so that's 20 outs
If there are 1 or more ranks not on the board and higher than your high card, fold; otherwise, bet.

If there is a straight or flush on the board:
Always bet - the only way to lose is if the dealer has a higher card in the straight (3 cards, or 0 if it;s A-K-Q-J-10) or any card in flush that is higher than the lowest card (no more than 9 cards, or 15 if there's a straight flush chance - with 8765 of spades, there are four 9s, four 4s, and seven remaining spades that would beat you).
"But what if the dealer makes a pair?" The pair is irrelevant as the dealer's hand will be the straight/flush on the board.
This is one of the ones I'm not 100% confident of - you're making a bet you can't possibly win in order to "save" your Ante and Blind bets

If there is a full house on the board:
Always bet - there can't be 21 outs in this case.

If there is a four of a kind on the board:
The only way to lose is if the dealer has a card higher than both your high card and the fifth card on the board.
If there are 6 or more ranks not on the board and higher than both the card not in the four of a kind and your high card, fold; otherwise, bet.
For example, if the board is A-A-A-A-3 and you have 7-2, then you lose if the dealer has anything from 8 to King, which is 24 outs.
On the other hand, if it's A-A-A-A-9 and you have 7-2, only 10 through King beats you (a 9 or less and both of you have A-A-A-A-9, so you push), which is only 16 outs.
Then again, shouldn't we take the increased payout of the blind bet if you win into account?
Example: the board is 3-3-3-3-7, and you have 8-5
Of the combin(45,2) = 990 pairs the dealer can have:
combin(24,2) = 276 are both cards 9 or better; you lose 3
24 x 21 = 504 are one card 9 or better; you lose 3
3 are a pair of 8s; push
3 x 18 = 54 are an 8 and something smaller; push
The remaining combin(18,2) = 153 are both cards 7 or lower; you win 1 on the ante, 1 on the play, and 10 on the blind
EV of playing = (153 x 12 - 780 x 3)/990 = -28/55
EV of folding = -2

If there is four to a straight flush on the board:
Even if there is a pair as well (e.g. 9-8-7-6 suited, and another 7), there are 2 cards that make 3 of a kind, 9 that make two pair, 9 that make a flush, and at least 4 that make a straight, so that's at least 24 outs; fold (even with an inside or close-ended straight).

If there is a straight flush (or royal flush) on the board:
Bet - at worst, there will be only one card that can beat you.

Great explanations on the 1X bet!

Not sure if this should be in another thread or not but I wanted to ask about the Trips bet since it's a common question. I play it a lot when I can find a lower HE paytable; I like the chance of a big hit since I usually only play short sessions. What are folks' comments about the amount of Trips bet vs Ante bet? I see most folks tend to match it with some adding even more...

Quote: JohnnyComet

Not sure if this should be in another thread or not but I wanted to ask about the Trips bet since it's a common question.

Since the Element of Risk of the base game is 0.53%, I would bet $0 on the Trips under any pay table. However, if you can find a 9-7 Trips pay table (house edge of 0.90%), then I wouldn't make you do too many push-ups for betting it.

Quote: Wizard

Since the Element of Risk of the base game is 0.53%, I would bet $0 on the Trips under any pay table. However, if you can find a 9-7 Trips pay table (house edge of 0.90%), then I wouldn't make you do too many push-ups for betting it.

That's great. :)

So in that case, is it better to have the Trips bet 1/2 or less of the Ante so that you have some chance on making money from all the 1X non-qualifying hands? Just wondering how much $ is lost to all the even money hands when the bets are even...

Quote: Wizard

...I would bet $0 on the Trips under any pay table. However, if you can find a 9-7 Trips pay table (house edge of 0.90%), then I wouldn't make you do too many push-ups for betting it.

I've only seen it at home in MGM Detroit.

Quote: ThatDonGuy

(his post generally)

interesting. I find that, say, a pair in the community roughly equals a higher kicker than mine being in the community

Quote:

Then again, shouldn't we take the increased payout of the blind bet if you win into account?

There's no doubt in my mind J.B.'s calculator does. It's highly desirable to get in on the 4 oak [in community] at least as a tie but especially as a win .... enough to really take a chance on it. I'd be winging it on the decision myself.

Quote: Wizard

Since the Element of Risk of the base game is 0.53%, I would bet $0 on the Trips under any pay table. However, if you can find a 9-7 Trips pay table (house edge of 0.90%), then I wouldn't make you do too many push-ups for betting it.

I certainly would find that paytable irresistible LOL. However, my feeling otherwise is that the variance in the game is sufficiently high for me - a matter of personal taste - so I have pretty much decided not to go with the Trips bet. On the other hand I can be mightily tempted for side bets in those games where the variance is low and would wish to avoid the Wizardly gaze and subsequent punishment.

Here is my "simplified counting strategy" to determine whether or not to bet after seeing all five board (face-up) cards if you reach the "count the number of outs" step.

The number next to each hand indicates the minimum number of ranks that do not appear on the board and that are higher than both your higher hole card and the lowest card on the board that does not appear more than once and does not complete a straight, needed for you to fold.

"Four to a closed straight" is an inside straight (for example, 9-8-7-5), A-K-Q-J, and 4-3-2-A.

No pair - 2
Pair - 3
Two Pair, fifth card lower than low pair - 5
Two Pair, fifth card higher than low pair - 4
Three of a kind - 4
4/Open Straight, no pair - always fold
4/Open Straight & Pair - 1
4/Closed Straight, no pair - 1
4/Closed Straight & Pair - 2
4/Flush, no pair - always fold
4/Flush & Pair - 1
Straight - always bet
Flush - always bet
Full House - always bet
Four of a Kind - correction (see this post):
Fold if the fifth card on the board (the one not in the four of a kind) is 8 or lower, or 9 if the four of a kind is 8s or lower, and your higher hole card is any of:
(a) lower than the fifth card;
(b) 2-5;
(c) 6, if the four of a kind is 5s or lower
4/Straight Flush (open or closed, and with or without pair) - always fold
Straight Flush - always bet

For example, if the board is K-9-9-8-5 of three different suits, and you have 10-3 (and don't have 4 to a flush), your highest hole card is 10, and the lowest card appearing once on the board is 5, so count how many ranks higher than 10 are not on the board; there are three (A, Q, J), and the "fold number" for a pair is 3, so you fold.
(Count the number of outs: four Aces, three Kings, four Queens, four Jacks, two 9s, three 8s, and three 5s = 23.)

On the other hand, if you had J-3 instead of 10-3, there are only two ranks higher than J missing from the board, and the "fold number" is 3, so you bet.
(Again, count the number of outs: four Aces, three Kings, four Queens, two 9s, three 8s, and three 5s = 19.)

Also, if the board is Q-J-10-7-7, and you have 8-3, the higher hole card is 7, and the lowest card appearing once on the board is 10; there are only 2 ranks higher than J missing from the board (A and K), which is less than 3, so you bet. The fact that 9 is missing from the board and is higher than your higher hole card is irrelevant; both players would have hands of 7-7-Q-J-10.

good stuff

Quote: ThatDonGuy

Four of a Kind - always bet

what if you have, say, 3-2?

Quote: odiousgambit

what if you have, say, 3-2?

You mean, if your hole cards are 3-2?

Good question. The only way you can win is if the dealer has 2-2 - but it also depends on what the fifth card is on the board. If the board is, say, 4-4-4-4-A, then it's going to be a push, so you bet in order to not lose your ante and blind bets.

Also, if neither of your hole cards are higher than the fifth card on the board (the one not in the four of a kind), the best you can do is push, in which case, the "fold number" is 6 (if the board is 7-7-7-7-8 and your two hole cards are less than 9, then any of the 24 cards Ace through 9 wins, so there are 24 outs).

Here is the strategy for a four of a kind on the board:
Fold if the fifth card on the board (the one not in the four of a kind) is 8 or lower, or 9 if the four of a kind is 8s or lower, and your higher hole card is any of:
(a) lower than the fifth card;
(b) 2-5;
(c) 6, if the four of a kind is 5s or lower

"Why do you bet if the board is, say, 5-5-5-5-10, even if both of your hole cards are lower than 10, so you can't win?"
To protect your Ante and Blind bets.
Of the 990 possible pairs of dealer hole cards:
6 are A-A
164 (4 Aces, 41 lower than Ace) are Ace and something lower
6 are K-K
148 (4 Kings, 37 lower than King) are King and something lower
6 are Q-Q
132 (4 Queens, 33 lower than Queen) are Queen and something lower
6 are J-J
116 (4 Jacks, 29 lower than Jack) are Jack and something lower
There are a total of 584 pairs of hole cards that lose for the player.
Any of the other 406 pairs results in a push, as both the player and dealer have 5-5-5-5-9 as their hands.
Since you lose 3 (1 ante, 1 blind, 1 play) by betting, the EV is -3 x 584/990 = -1752/990
However, if you fold, the EV is -2 = -1980/990.

Quote: ThatDonGuy

You mean, if your hole cards are 3-2?

Good question. The only way you can win is if the dealer has 2-2 - but it also depends on what the fifth card is on the board. If the board is, say, 4-4-4-4-A, then it's going to be a push, so you bet in order to not lose your ante and blind bets.

Also, if neither of your hole cards are higher than the fifth card on the board (the one not in the four of a kind), the best you can do is push, in which case, the "fold number" is 6 (if the board is 7-7-7-7-8 and your two hole cards are less than 9, then any of the 24 cards Ace through 9 wins, so there are 24 outs).

Here is the strategy for a four of a kind on the board:
Fold if the fifth card on the board (the one not in the four of a kind) is 8 or lower, or 9 if the four of a kind is 8s or lower, and your higher hole card is any of:
(a) lower than the fifth card;
(b) 2-5;
(c) 6, if the four of a kind is 5s or lower

"Why do you bet if the board is, say, 5-5-5-5-10, even if both of your hole cards are lower than 10, so you can't win?"
To protect your Ante and Blind bets.
Of the 990 possible pairs of dealer hole cards:
6 are A-A
164 (4 Aces, 41 lower than Ace) are Ace and something lower
6 are K-K
148 (4 Kings, 37 lower than King) are King and something lower
6 are Q-Q
132 (4 Queens, 33 lower than Queen) are Queen and something lower
6 are J-J
116 (4 Jacks, 29 lower than Jack) are Jack and something lower
There are a total of 584 pairs of hole cards that lose for the player.
Any of the other 406 pairs results in a push, as both the player and dealer have 5-5-5-5-9 as their hands.
Since you lose 3 (1 ante, 1 blind, 1 play) by betting, the EV is -3 x 584/990 = -1752/990
However, if you fold, the EV is -2 = -1980/990.

Be aware, that if playing the Trips bet, some places force you to make a play bet in order to get paid on that Trips bet.

Quote: Ibeatyouraces

Be aware, that if playing the Trips bet, some places force you to make a play bet in order to get paid on that Trips bet.

I don't take the Trips bet into account - just the Ante, Blind, and Play bets. The Blind bet pays 10-1 for a four of a kind (if your hand wins), doesn't it?

Quote: ThatDonGuy

I don't take the Trips bet into account - just the Ante, Blind, and Play bets. The Blind bet pays 10-1 for a four of a kind (if your hand wins), doesn't it?

I know that and you know that, but not everyone does. Still good to know this info whether you play the trips or not.

What's the house edge for betting everything including trips? And what's the difference between EV and house edge? I noticed the Wizard discussed that there was a difference between the two but I wasn't sure what the difference was.

Quote: HotBlonde

What's the house edge for betting everything including trips?

Depends on the paytable, and also depends on what the average bet is on the regular game. Worst paytable Wizard shows has a 6.2% edge and I believe you would use an Element of Risk of 0.58% for the average bet in the regular game. I would estimate, using that paytable, that the overall is around 3%. Hopefully somebody can calculate it accurately and with more confidence than me.

Quote: HotBlonde

What's the house edge for betting everything including trips? And what's the difference between EV and house edge? I noticed the Wizard discussed that there was a difference between the two but I wasn't sure what the difference was.

I assume you know the basic definitions.

IMO the best reason to talk about EV instead of HE is that it sometimes brings clarity. But it also is easier to calculate. Someone can calculate the combined HE of your first question a lot quicker and with less chance of error than me, but we all can calculate quickly the EV of a bet on the Trips. You have been betting $10 on it I believe? You need to know the paytable of course. Where I have been playing it would mean 10 * -0.034979 = -35 cents a bet, rounding. I can just decide if I am happy with the idea of making about a 100 of those or not. It increases the variance at a cost, and I have decided the variance of the regular game is excellent and personally I do not need the action of the side bet.

PS: it might be worth checking out Ibeatyouraces' contention. If it is the case with your game, I would cease making the bet as a matter of protest.

3% with trips actually isn't too bad. If anyone knows the exact number ease let me know. I thought it would be worse. 3-Card Poker is over 7% with the 6-card Bonus, isn't it?

Quote: HotBlonde

3% with trips actually isn't too bad. If anyone knows the exact number ease let me know. I thought it would be worse. 3-Card Poker is over 7% with the 6-card Bonus, isn't it?

have you checked out the paytable?

and are you still in Vegas?

Most UTH tables on the strip I've seen are the 8-7-4-3 (3.5%) with the occasional 8-6-5-4 (1.9%).

I'd also like someone with better math skills than I to do HE/Risk including trips, assuming you are a) placing equal on Ante/Play/Trips, or b) placing 50% less than Ante/Play on Trips... I like the chance of hitting a monster hand during my short play sessions, but realize a lot of cash has likely gone into the Trips hopper.

Quote: odiousgambit

have you checked out the paytable?

and are you still in Vegas?

im still here. What I do do you need? Info from the trips pay table?

Quote: HotBlonde

im still here. What I do do you need? Info from the trips pay table?

Yes. For your next level of achievement in smarter gambling, to make the Wizard proud, start investigating the paytables.

I just walked up to a table to get the pay table for its trips payout and someone hit a royal flush!!!

Pics here:
http://pixady.com/image/55u/
http://pixady.com/image/55v/
http://pixady.com/image/55w/

Unbelievable!!

Anyway, here's the pay table for trips here at Bellagio. Now help me analyze the house edge. Thanks!

http://pixady.com/image/55x/

Nice of them to let you take the picture!

So we go to the Wizard's page at WoO [see link] and see that this is pay table 3 = -0.034979 or an HE of about 3.5%
not bad for the variance it gives, but it will guarantee losing a lot in the long run

Nobody is stepping up to crunch any numbers so that means you are stuck with me for that. Hopefully someone will at least spot errors.

After further thought I think the easy way to calculate the overall HE is to stick to the regular HE [not the element of risk]. With $10 each on ante, blind, and trips we ignore the variation in bets on the 'play' [if I understand it all correctly]. Winging it, my easily remembered formula is HE = EV/bet .

The EV of the trips bet is -0.34979, and the EV of the regular betting is -0.437 [using Wizard's 2.185% HE]

0.34979 + 0.437 = total EV of 0.78679 [dropping minus signs]

$30 was bet

so 0.78679/30 = 0.0262263333333333

I get a HE of 2.6%

sounds about right so I have a modicum of confidence LOL


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

PS: I'd say this is a case where looking at the increase in EV tells you more than the change in HE. I admit it is debatable, considering increase in variance. However, the picture of the element of risk is also complicating the decision; there is a big change in HE considering that [and no I would not be able to do an element of risk for the combined bet]

3.5% isn't too bad. It's not great, but it could be worse.

Quote: HotBlonde

3.5% isn't too bad. It's not great, but it could be worse.

??? 3.5 Is horrible. Especially if you know better. I'm not saying don't play it, but one shouldn't ever say 3.5% isn't too bad. That's like saying date rape isn't too bad, It's not great, but it could be worse.

That's one reason we have games like 6:5 6:5 isn't too bad. It's not great, but it could be worse("checks change $1000")

You make a decent point but I might not have used that particular analogy...



Getting back to the conversation- http://www.table-games-online.com/ultimate-texas-holdem/ saves stats including separate win/loss between the ante/play and the trips with the option to reset the days stats. Note I am not affiliated with that site at all.

It's eye opening to see how much more you typically lose when playing Trips with the same bet.