Discount Gambling

2nd Nut Kicker on Unpaired Board (UTH)

Posted in collusion, ultimate texas hold'em by stephenhow on January 31, 2010

A lot of times when playing Ultimate Texas Hold’em, you’ll be faced with a 1x river call with a bare minimum kicker. It probably occurs to you that the strength of your call depends on how much of the board the other players have hit. For example, say you’re looking at 1x calling an unpaired board with 2nd nut kicker. Basic strategy says to call if it’s not a scare board, nor gutshot board, and there’s no possible flush on board, or if both your kickers play. (This situation occurs 1.3% of the time if you play basic strategy, and more frequently if you play less aggressively than basic strategy.) Your odds are better if the players at the table connected with the board (made a lot of pairs) than if everyone missed. I ran some simulations to quantify this effect, to show how you can use table information to improve this call.

1x call vs. fold for 2nd nut kicker on unpaired board, given table pair information (simulated)
total
players
total pairs notes
0 1 2 3 4
2 +1.3% +11% +17% always call
3 -3.4% +5.3% +12% +21% +33% fold if no pairs
4 -5.3% -0.0% +7.8% +16% +26% fold if < 2 pairs
5 -16% -5.8% -1.4% +11% +21% fold if < 3 pairs
6 -28% -16% -4.7% +4.9% +14% fold if < 3 pairs

So, for example, say you have Jh 2s and the board is Ah Ks Th 9d 3s. With no more information, the odds are that you should call (+19.1%). However, if you’re at a full table (6 players), and all the other players only made 2 pairs with the board, then you should fold. The percentages of the table don’t exactly apply to this specific case, but are averages over 20 million hands, and all cases where basic strategy said to call with 2nd nut kicker.

Practical Collusion for Ultimate Texas Hold’em

Posted in collusion, ultimate texas hold'em by stephenhow on January 15, 2010

Most casinos that spread Ultimate Texas Hold’em don’t really mind when players discretely show their hands to their neighbors, or even flash the entire table. This is because overall, a player can’t gain much advantage by doing so. While the player will definitely pick up an edge WHEN possessing a borderline hand AND partner information indicates to alter basic strategy, these conditions don’t occur frequently enough to make much of a difference.

How To Collude

Collusion helps only on borderline cases. When you have a solid hand (e.g., 55’s, KTo, A7o, etc.) don’t bother trying to get neighbor info, just raise. If you have a marginal raising hand (J8s, JTo, Q6s, Q8o, K2s, K5o) then it helps to see your immediate neighbor’s cards, or ideally, see if two of your outs are held by the entire table. Finally, if you have a hand just below the raising threshold, or a pair less than 5’s, then you need full table information before raising.

Using Immediate Neighbors

Sometimes, it’s only practical to see the cards of your immediate neighbors, or otherwise communicate with them. This is very helpful for the marginal raising hands. The tables below show that you should only raise the marginal hands if your immediate neighbors (up to 3 of them) don’t have any of your outs. For example, if you know that among 4 hands (yours included), you have the only K and 5, then 4x raising K5o is worth +14% (of the Ante) than checking it. However, if your neighbors have a K or 5, then 4x raising is a mistake. The same pattern is seen for all the marginal raising hands.

When you only have access to immediate neighbors, then use the column of the tables below for the number of hands you have information for. It doesn’t matter what the other’s players (“dark hands” you can’t see) are holding. It just means you can only use the 4-player or 3-player columns in the tables.

Asking The Whole Table

In some cases (say you’ve filled the table with your friends), you can test the whole table for your outs. If communication with the table is good, you can ask “Should I raise K5o?”. This really means, “Does anyone have a K or 5?”. If you get just one response (meaning, “Yes I have one”), then go ahead and raise, you’re still better off by +7.5% to raise 4x than check). However, if you get two responses, then two of your outs are gone, and you should not raise, since it’s 7.5% better to check. If no one has any of your outs, then raising is worth +22% more than checking.

You can use the whole table for advanced collusion play. There are a set of hands a few notches below the minimum raising threshold that are actually good to raise when all their outs are still in the deck. These hands are listed in the table below under “Marginal Checking Hands”. For example, you would ask the table, “Should I raise K4o?”. Of course, basic strategy says to check this hand, and you’re really asking, “Does anyone have a K or 4?”. If you find no one has your outs, then it’s worth raising, by a long shot (e.g., +18% at a full table, +8.9% for 4 players).

Pocket Pairs

Basic strategy says to raise all pocket pairs except deuces. However, for 2’s thru 5’s, knowing how many outs are already gone (in the players hands) will allow you to make a better decision. The below table shows you the difference between checking and raising 4x for these pairs, given the number of players at the table, and how many of your outs are seen. Note that for 5’s or higher, you should still raise even if all your outs have been seen.

Total Players @ Table
Hand 2 3 4 5 6 information
22 -8.1% -5.1% -2.0% +0.8% +4.7% no outs seen
-40% -39% -37% -34% -32% one out seen
33 +12% +15% +18% +20% +24% no outs seen
-16% -14% -13% -11% -9.6% one out seen
44 +31% +34% +36% +38% +41% no outs seen
+6.4% +7.8% +9.5% +11% +12% one out seen
-21% -21% -21% -21% -21% both outs seen
55 +47% +48% +50% +53% +55% no outs seen
+27% +28% +29% +30% +31% one out seen
+4.5% +4.5% +4.5% +4.5% +4.5% both outs seen
66 +55% +56% +58% +59% +61% no outs seen
+39% +39% +40% +41% +42% one out seen
+21% +21% +21% +21% +21% both outs seen

Marginal Raising Hands

The following table shows the marginal raising hands according to basic strategy, and the difference between raising 4x and checking these hands given table information concerning your outs. Note that the value of a nominal raising hand increases tremendously at a full table when not copied (all outs remain). E.g., with no other information, raising Q8o preflop instead of checking is worth about 2.3% of the Ante bet. However, at a full table (6 players), when no one has any Q or 8, then the value of raising vs. checking is +26% of the Ante. On the other hand, it is much better to check Q8o if your table is 4-handed or less, and someone has a Q or 8.

Total Players @ Table
Hand 2 3 4 5 6 information
JTo +12% +16% +21% +27% +33% no outs seen
-6.8% -1.9% +3.0% +7.9% +14% one high out seen
-6.6% -1.9% +2.6% +7.8% +14% one low out seen
-26% -22% -18% -13% -8.0% one high & one low out seen
Q8o +6.9% +11% +16% +20% +26% no outs seen
-9.0% -5.0% -1.1% +3.8% +8.2% one high out seen
-9.7% -5.7% -2.1% +2.6% +7.8% one low out seen
-26% -23% -19% -15% -11% one high & one low out seen
Q9o +15% +20% +24% +29% +34% no outs seen
-0.8% +3.0% +7.5% +12% +17% one high out seen
-1.0% +2.9% +6.9% +11% +17% one low out seen
K5o +7.1% +9.7% +14% +18% +22% no outs seen
-6.9% -3.5% -0.1% +3.7% +7.5% one high out seen
-6.2% -3.2% +0.1% +4.0% +7.7% one low out seen
-20% -17% -14% -11% -7.4% one high & one low out seen
K6o +12% +15% +19% +23% +28% no outs seen
-2.1% +1.1% +4.9% +9.0% +13% one high out seen
-2.1% +1.0% +5.0% +8.2% +12% one low out seen
A2o +16% +19% +22% +25% +29% no outs seen
+3.1% 5.8% +9.2% +13% +16% one high out seen
+4.5% +7.5% +9.6% +13% +17% one low out seen
-7.4% -5.6% -2.9% -0.1% +3.1% one high & one low out seen

Marginal Checking Hands

The hands in the table below are normally checking hands in basic strategy, but if none of your outs are seen by the table, they may be more advantageous to raise. The table shows the difference between raising 4x and checking these hands, given the table information concerning your outs.

Total Players @ Table
Hand 2 3 4 5 6 information
T9o -9.8% -4.4% +1.2% +6.7% +13% no outs seen
J8o -7.2% -2.9% +2.8% +8.1% +14% no outs seen
J9o +1.9% +6.8% +12% +17% +23% no outs seen
Q5o -11.5% -7.4% -3.1% +1.6% +6.5% no outs seen
Q6o -6.0% -2.5% +2.1% +6.5% +12% no outs seen
Q7o -2.7% +1.5% +5.9% +11% +16% no outs seen
K2o -9.2% -5.0% -0.9% +3.7% +8.4% no outs seen
K3o -3.6% -0.1% +4.2% +8.3% +13.1% no outs seen
K4o +1.0% +4.8% +8.9% +13% +18% no outs seen
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