Discount Gambling

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

2009 UTH Win/Loss Statement

Posted in ultimate texas hold'em by stephenhow on December 21, 2009

I just learned that all casinos are required to provide a player with an annual win/loss statement on request. This is to provide a player with an estimate of his net win or loss at the casino for the calendar year, in case you need to write off gambling losses against a W2-G win. The casinos seem to take this regulation pretty seriously, since I see that every $100 buy-in needs supervisor approval, as does every color-out at the end of a session. The floor supervisor enters the data at the console (usually attached to the table), and everyone is tracked.

So yesterday, I was playing Ultimate Texas Hold’em (UTH) as usual, at Harrah’s, on my usual route of the four north San Diego county casinos (Harrah’s, Pauma, Pala, and sometimes Pechanga). I’d been playing exclusively UTH at these casinos for about three months now, logging in about 300 hours total. I’d been doing well, and I knew I wasn’t just donating to the casino (i.e., ATM -> UTH -> casino). So, I just decided to see if I could get my 2009 Win/Loss Statement at each of these casinos.

My 2009 UTH Win/Loss Statement by Casino
Casino Buy-In Cash-Out Net
Harrah’s Rincon -$9.74
Casino Pauma $17,840.55 $18,001.30 +$160.75
Pala +$170
Pechanga +$300
Total +$621.01

As far as discount gambling goes, I’m claiming success. On average, I should lose about $3.50/hr ($.12/hand), so my 300 hours in 2009 should have totaled to a $1000 loss. So I’m way ahead of the mean here. Also, from what I see at the tables, I’m sure most players don’t want to see their win/loss statements for the year. That’s because most people are afraid to 4x raise preflop according to basic strategy. They’re constantly checking monsters like ATo, KJo, 66, QJo, etc. Then they still check their pairs on the flop, I guess waiting for their hands to improve at the river. They make so many mistakes, they’re probably giving the house an average 10%+ edge. They never bet their hands, and they forfeit the huge +46% Play bet edge. I just see people play passively, re-buying until they bust out. And these people are regulars, who see me all the time, but they won’t stop checking. Maybe if they read this post, they’ll start betting.

A Few Refinements for UTH Basic Strategy

Posted in ultimate texas hold'em by stephenhow on December 3, 2009

I’ve been doing fine playing UTH over the last two weeks, and I’m also finding Six Card Dealer Bluff fun and fair to play. I’ve noticed that in UTH I often have a decision to call at the river with 2nd nut kicker on an unpaired board. It looked at little weird to call sometimes, especially against a board with a possible flush. So I tried out a few cases, and found that I shouldn’t call with 2nd nut kicker unless there was no possible flush, or if both my cards played. I updated this to the main Ultimate Texas Hold’em page, and the basic strategy card.

I also checked that calling 1x with 5th nut kicker against a double-paired board is okay, as long as the pairs are 7’s up or better. Otherwise, for 6’s up, you need 4th nut kicker to call.

Finally, I found that on the flop, you can bet 2x with nut kicker, as long as you have a gutshot straight draw.

Two-Player Collusion for Ultimate Texas Hold’em

Posted in collusion, ultimate texas hold'em by stephenhow on October 16, 2009

After completing basic strategy for Ultimate Texas Hold’em (UTH), I thought I’d look into the effect of knowing your neighbor’s cards. My program computes the EV for a players down cards, the board, and any known cards, so it’s really easy to analyze the effect of collusion. I didn’t think there’d be much EV gain by sharing info with a partner, because the Ante bet requires dealer to qualify, and the Blind bet pays only for straights and better. Furthermore, you’re only getting even money return on your Play bet; the effect of collusion might be greater for a paytable with odds, like in Mississippi Stud.

I broke the rough analysis into the three decision points, preflop, flop, and river. I kept the analysis to two players, since it’s hard to manage and rely on more than one other player. Also, its harder to formulate a collusion strategy for multiple players.

Overall, collusion only helps when you have a borderline decision, and your partner also happens to have cards that helps your decision. In these relatively rare cases, you’ll pick up an EV gain of about 10% of your Ante bet. So, if you experience these conditions in 1% of your hands, you’ll only gain an overall EV boost of (.01)(.10) = 0.1%, which is negligible. However, it’ll make you feel better when you don’t raise K6o when your friend has a K or 6, and you end up saving 3 Ante bets (the hand is likely to call 1x anyway).

Preflop

The following table shows some examples of using partner info to change your preflop decision. Each table entry takes me around 16 hours of compute time to analyze. For pairs, partner info can only slow down your raise for pocket 3’s. Otherwise, pocket pair decisions are not affected. Borderline raising cases are influenced by partner cards if you’re within 2 kicker levels of the raising threshold. E.g., K5o +/- 2 means consider raising K3o if partner has an Ace; conversely, consider checking K7o if your partner has a K or 7.

hand partner EV(check) EV(4x) Notes
Kh 4d Ac 7h -0.1285 -0.0870 raise K4o when Ace seen
Ks 2c Ad 7h -0.2168 -0.2615 check K2o even if Ace seen
Qh 5d Ad Kc -0.1817 -0.2378 two overs aren’t enough to make Q5o a raising hand
Qh 6d Ad Kc -0.1243 -0.1238 two overs make Q6o a raising hand
Ks 7d 7h 6s -0.2019 -0.2020 kicker copy increases raising threshold
3s 3h 3d 8c -0.4135 -0.5515 check pocket 3’s if your friend has a 3
4s 4h 4c 8s -0.2033 -0.1467 raise with pocket 4’s, even if your friend has a 4
Ks 7d Kh 6s -0.2257 -0.2218 raise with K7o, even if your friend has a K
Ac 2s Ah 5d -0.2397 -0.2129 still raise A2o if Ace seen

Flop

There are very few situations where knowledge of your partner’s hand will change the way you play your hand on the flop. Such cases will rarely come up in actual play (e.g., minimum flush draw bets).

hand partner board EV(check) EV(2x) Notes
2s 3d 2h 9h Kh -0.8182 -0.9389 check bottom pair no kicker/draw on a suited board
2s 3d Ah Qh 2h 9h Kh -0.6946 -0.7530 still check even if partner has two overcards and flush
2s 3d Kd 9s 2h 9h Kh -0.7569 -0.8189 still check even if partner has top two pairs
Ts 3s 2s 9s Kh +0.1865 +0.2069 bet 5th nut flush draw with board undercard
Ts 3s 4s 7h 2s 9s Kh +0.0895 +0.0600 check minimum raising draw if partner has one flush out
Js 3s 4s 7s 2s 9s Kh +0.0102 +0.0435 still bet 4th nut draw if partner has two flush outs
2d 3s 2h 3d 2s 9s Kh -0.5499 -0.5163 still bet bottom pair if partner has identical hand
2d 3s 2h 2c 2s 9s Kh -0.5499 -0.4871 still bet bottom pair if partner has two of your outs
Jd Th Qh 6d 8s 9h 2s -0.1535 -0.1725 check JT98 if partner has one of your outs
Jd Qh Kh 8d Ts 9h 2s -0.1730 -0.1352 still bet QJT9 if partner has two of your outs

River

Partner information may occasionally help your minimum kicker requirements on the river. If the board is paired (i.e., qualifies the Ante bet), when your partner has 2 keys cards, you may decrease your kicker requirements by one.

hand partner board EV(fold) EV(call) Notes
Qs Jd Ts 9h 7c 2d 3h -2.0000 -2.1162 fold without 2nd nut kicker on unpaired board
Qs Jd As Kd Ts 9h 7c 2d 3h -2.0000 -2.0875 fold 3rd nut kicker even if partner has 2 overs
Qs Jd 2c 3d Ts 9h 7c 2d 3h -2.0000 -2.0310 fold 3rd nut kicker even if partner has 2 pairs
Ts Jd 9s 9h 7c 2d 3h -2.0000 -2.0030 fold 4th nut kicker on paired board
Ts Jd As Kd 9s 9h 7c 2d 3h -2.0000 -1.9070 call 4th nut kicker if partner has 2 overs
Ts Jd 2c 3s 9s 9h 7c 2d 3h -2.0000 -1.9070 call 4th nut kicker if partner has 2 dealer outs
Ts 8d 9s 9h 9c 2d 3h -2.0000 -2.0030 fold 5th nut kicker on trips board
Ts 8d As Kd 9s 9h 9c 2d 3h -2.0000 -1.9070 call 5th nut kicker on trips board if partner has 2 overs
Ts 8d As 2c 9s 9h 9c 2d 3h -2.0000 -1.9070 call 5th nut kicker on trips board if partner has 2 key cards
6s 7d Js Jd Kh Ks 2c -2.0000 -2.0697 fold 6th nut kicker on 2 pair board
6s 7d Ad Qh Js Jd Kh Ks 2c -2.0000 -1.9801 call 6th nut kicker on 2 pair board if partner has 2 overs

A Week Of Ultimate Texas Hold’em

Posted in ultimate texas hold'em by stephenhow on October 12, 2009

I finished my first week of playing Shuffle Master’s Ultimate Texas Hold’em in 4 of the casinos in Temecula Valley, and thought I’d post my take on the game. Of course, I was playing as I always do: grinding out minimum bets ($5 Ante and $5 Blind) and near-optimal EV decisions. I played every day, drove a lot, stayed up late, and probably logged around 40 hours of playing time. Usually when I play some game like this, I end up losing some amount near the house expected house edge. But UTH played so well, I just kept accumulating winning sessions, and I ended up net +$2000 for the week.

I’ve never had as much success with a game as I have with Ultimate Texas Hold’em. I notice the game plays very well, since you bet when you’re ahead (either with a good starting hand, or with a made hand), and you check otherwise. But I was really surprised that I won like this. Some of it’s due to session management. I’d end a session when I was up a few hundred. I might drive down the road to another casino and start another session, but I’d make a point to log a session win.

I saw that no one else played correctly, and they preferred to bet the bonus Trips bet instead of raising 4x preflop with good hands. They all thought I was crazy playing basic strategy. Of course they lost, not because of their Trips bets (only a 1.9% house edge), but because they wouldn’t bet their hands (Play bet). They refuse to raise 4x preflop without some monster like QQ or AKs. When you show them a basic strategy card (raise K5s, JTo, Q6s, 33, etc.), they just think you’re crazier. They don’t want a copy of the card, they just want your seat when you leave a winner.

I’d sit for hours and play. On the weekend sessions, I’d play all day, and find a time to leave when I was up. I never got stuck worse than $200 in a session, and that was rare.

While I just grinded away, I played two sessions with my friend G, a high-limit blackjack player (average $100-$200 bets). In UTH, he played $25 Ante bets, and grinded out one session for an $800 win. In the other session, he grinded for a few hours at this level, but at the end pressed his bets to $50 Antes. He hit a good streak of winning a few 4x ($200 Play bet) hands, then cashed out $1450 ahead.

So, my take on the game is that its good for the grinder, using session management. The game plays well, with a lot lower variance than blackjack, because you bet more when you have a good hand. It’s also good for hit and run play, for the same reason. And with an overall element-of-risk of about 0.5%, it’s a better game than blackjack, even though the house considers it a carnival game.

UTH is my new favorite game. I’ve never had success with a table game like this. Unfortunately, I have to drive about 50 minutes to reach the game, so I probably will stop playing it during the week. It’s not like the game is +EV or anything, I just got lucky, and cashed out winners. But if I do go, I’ll choose to play at Casino Pauma, essentially a tiny local’s casino, because the hand rate is much, much faster there, as you’re typically heads-up with the dealer. The worst thing about UTH at a busy casino is the game is slowed down tremendously by people entering and leaving the game, buying in and coloring out, and by inexperienced dealers and players. It can get painfully slow at a table full of these delays. Otherwise, I highly recommend you learn basic strategy, and try the game out.

Basic Strategy Card for Ultimate Texas Hold’em

Posted in ultimate texas hold'em by stephenhow on September 28, 2009

ultimate-texas-hold-emI didn’t find any basic strategy online for ShuffleMaster’s Ultimate Texas Hold’em, so I developed my own. The following table should yield very close to the 2.2% theoretical house edge. I’ve only played the game a few times, but it seems there are a few cases when you need to know if a small pair, or a kicker, or a draw is good enough to bet.

Update: I started playing the game, and I really enjoy it. I find that people play very differently than basic strategy, and these mistakes often costs more than 20% of the ante bet (e.g., 20% of a $5 ante is $1). I’ve written up an entire page on the game, and explain how to play near-optimal strategy.

Basic Strategy Card for Ultimate Texas Hold'em.

Basic Strategy Card for Ultimate Texas Hold'em.