# Discount Gambling

## 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.