UTH Counting Outs Confusion Question

Board: 7♣ 9♥ K♥ 4♦ 10♥

Me: Q♥ 5♦

When practicing, it told me the correct move was to fold, but I don't see where we get to 21 outs in the play. Thank you

Quote: hostcord

Board: 7♣ 9♥ K♥ 4♦ 10♥

Me: Q♥ 5♦

When practicing, it told me the correct move was to fold, but I don't see where we get to 21 outs in the play. Thank you

AAAA = 4
KKK = 3
777 = 3
999=3 (Originally missed, thanks for the correction, UnJon!)
101010=3
444=3
QQQ + (8/9/J)= (3/45 * 12/44) + (12/45 * 3/44) = 0.03636363636 * 45 = 1.636363 (This is like having 1.636363 more outs)

Now we're at 20.636363

Let's go any two hearts that are both a Jack (or lower) but NOT 7/10/4:

(6/45) * (5/44) = 0.01515151515 * 45 = 0.6818181875

That brings us to about: 21.31818118

We also have a few straight combinations: 6/8 8/J J/Q (We already accounted for QJ, though)

(8/45 * 4/44) + (8/45 * 4/44) = 0.03232323232 * 45 = 1.454545

That brings us to 22.7728634545.

The rest comes down to the probability of a PUSH with a non-qualifying dealer, which would be any Dealer Queen (You have the heart already) combined with a dealer six or less...but not a four, as we already counted it:

(3/45 * 15/44) + (15/45 * 3/44) = 0.04545454545 * 45 = 2.04545454545

That puts us well over 21 possible dealer outs total, and is also covered extensively by Stephen How on Discount Gambling here:

https://discountgambling.net/ultimate-texas-holdem/

Relevant Quote:

Quote:

No pair board
When there’s no pair on the board, you may call with 2nd nut kicker if either both your cards play, or there is no possible flush on board. If there’s a possible flush, then you need nut kicker to call. You can never just play the board. In this case, the most you can win is the 1x call bet, since you can not win the ante bet with nothing. You are hoping to push the ante if the dealer doesn’t qualify, even if he outkicks you. The payoff is good if you win, since you’ll win the 1x bet, and save the Ante and Blind.

The idea here is that your Queen is the second nut kicker, but the problems are twofold:

1.) It fails because both of your cards do NOT play. Your Queen essentially knocks the four off of the board and your five is not superior to the remaining seven.

2.) There IS a possible flush for the dealer on the board, though it does require two cards. Making matters worse is the fact that there are also several two-card straights on the board. In fact, changing the ten of hearts to a three of hearts makes RAISING the better decision, but that's because both fo your kicker cards now play.

NOTE: Grosjean's strategy is also an approximation that will not apply in every possible situation, though it is better than the, "21 count." For example, if the 10H in the dealer's hand were instead a Jack of Hearts, that would take some of the two card straight draws away and make it a slightly better hold:

-1.984848 vs. -2, to be exact.

However, it changes nothing in terms of the, "21 Count," because it neither adds or subtracts any INDIVIDUAL cards that would beat you.

Anyway, fun question and sorry if there are any errors in my stuff. I was just trying to figure out how it becomes more than 21, but again, the 21 is an approximation that simply is correct most of the time anyway. The Grosjean strategy only cares that a flush is possible AND only one of your cards play with second nut (Ace being the first nut kicker).

Mission, your count to 17.6 misses the three 9s that pair the board so should be 20.6.

Using the Wizard's simple strategy (which ignores 2-card dealer hole combos) I only see 19 outs: the 15 cards that would pair the board and the 4 aces that would out-kick the hole queen. But what do I know? The last several times I've played at WoO I lost half my simulated bankroll before I could even blink.

I'm glad you started this thread since (oddly) I was going to pose a simulator UTH question myself. If you have four to a flush after the flop, the Wizard's simple strategy says you should make the x2 raise if you have a hidden 10 or better to that flush. Yet often my pocket will contain two low cards as part of a four to a flush and the game will tell me it's a mistake to check. So, is the strategy page wrong? Is the WoO simulator wrong? Is my phone glitchy (it happens)? Or is the simulator (as in VP) teaching advanced strategy while I'm playing simple? Sadly, I haven't documented any examples.

Quote: unJon

Mission, your count to 17.6 misses the three 9s that pair the board so should be 20.6.

Haha!!! Thanks!

I’m editing that post. The three nines, then everything else I said!

My experience with playing kickers on the river using the 21-out rule on an unpaired board or the 23-out rule on a paired board is that the dealer will draw a better hand more than half the time. I'm pretty much doomed when I get to the river without at least a hidden pair. And basic strategy is what it is - basic.

I put that hand into my Ultimate Texas Hold 'Em calculator and it said to raise.

EV raise = -1.986869
EV fold = -2

There are 19 outs, which is less than 21, so the strategy advises correctly in this play.

Quote: CharmedQuark

My experience with playing kickers on the river using the 21-out rule on an unpaired board or the 23-out rule on a paired board is that the dealer will draw a better hand more than half the time. I'm pretty much doomed when I get to the river without at least a hidden pair. And basic strategy is what it is - basic.

That could be correct, actually. For unpaired kicker play:

1) Player folds = -2 units.

Or

2a) Player bets 1x, dealer doesn't qualify : player saves ante. +1 compared to folding, win or lose.

Player wins, +1 unit on play, save blind.

Dealer wins, -2 units because no qualify.

Hand pushes: save blind and play as well.

2b) Player bets 1x, dealer qualifies: player loses 3 units.

This also applies to a board with a pair or better, but the dealer always qualifies on that, and you're talking about unpaired board kickers particularly, the math is different, so I'm trying to break that out from the rest.

The unpaired kicker strategy isolates those hands on the (very long) table of probabilities and pays (listed on the WoO UTH page) where it is worth doing item 2 above, even if it wins less than 50% of those hands: on average, you will lose less. Maybe the average loss is 1.96 units or something. That's because of the ante push/noqualify, and blind push.

There's a point where the better option is to fold (because you can lose more than -2 units on average), and that's why you're counting the outs, to find whether you're above or below that point.

As a side note, and as a Trips player, this is the edge they take away from you when they force you to bet the Play to collect on Trips. They' (the casino) are stealing EV from you when you collect on a bonus board where the board plays.

In an extreme example, say the board is quad Aces and a deuce. You have a pocket deuces. You should fold the deuces and collect the Trips. (If you're not betting Trips, you should still fold. It's 100% certain you will lose the hand: dealer MUST have at least 1 kicker card higher than a deuce.)

The base game pays separately from Trips. It, and all other sidebets, have a stand-alone EV. SHFL will try and correct this practice with the casino if they hear it's being dealt that way (they have some rights in enforcing correct play of their game), so it's worth letting them know - or avoiding the Trips bet at that House if the casino continues.

Quote: Wizard

I put that hand into my Ultimate Texas Hold 'Em calculator and it said to raise.

EV raise = -1.986869
EV fold = -2

There are 19 outs, which is less than 21, so the strategy advises correctly in this play.

All due respect, but you put the wrong ten. The ten should be a heart. Your hand with the ten of diamonds makes the dealer flush impossible, which is what makes Raising the correct decision in the hand you put.