On the other hand, there are a few pluses to the Barona game. First, everyone is playing their hand face up, like they allow in their Mississippi Stud game. As I’ve written about in this blog, that’s worth about a 0.5% reduction in the house edge. Better yet, the Barona Trips paytable is the 9-7-4-3 type (9 for full house, 7 for flush, 4 for straight), which has a very small house edge of 0.9%. (All the other casinos in San Diego have the 8-6-5-3 paytable, which has a 1.9% house edge.) The game also goes quite a bit faster, since the iTable reads all the hands instantly, and makes the correct payouts. Also, I believe they’re able to open up as many UTH tables as they need in the iTable pit, whereas you can easily be locked out of the only UTH table at Viejas, or the two tables at Harrah’s Rincon and Pala. And, the Barona game is only a $5 Ante, even on weekend nights. Since it’s an iTable game, you can also bet $6, $7, etc. (does not have to be multiples of $5). That’s the only amount of pressing that I’m comfortable with

Click on the screenshot below to play:

This shows that even if no one else hits middle or top pair on the board (i.e., players are holding 10 cards that don’t hit middle or top board cards), it’s still worth 10% of the Ante to 2x bet bottom pair on the flop, compared to checking. It was useful to see these results, because it shows the value of the other players hitting the board, as expected. I wasn’t sure about betting bottom pair when everyone else missed, but the simulations show its still a good bet.

By checking marginal copied hands, the session outcome distribution improves as shown below. Assuming a bankroll of 200 Antes, a goal of 20 Antes, and a maximum session length of 250 hands, the improved strategy reduces the probability of busting out from .20% down to .13%. The probability of reaching your 20 Ante win is reduced from 69% to 68%, but the distribution for the in-between cases improves as shown.

Session outcome probabilities for 200 Ante bankroll, 20 Ante goal, 250 max hands.

[Note: the low-variance strategy used for the distribution does not raise any basic strategy preflop checking hands; it is designed to minimize variance, and simulates at 2.2% house edge.]

Practically, this advanced strategy is very intuitive, and you’ll find it agrees with your experience. When no one hits the board, or even has a playable kicker, your chances of winning with a minimum kicker go down considerably. However, when everyone hits the board, sometimes multiply (e.g., full house), your chances increase considerably. The table above quantifies this effect, and shows you the relative strength of your hand for the range of scenarios.

Overall, you’ll find the 3rd nut kicker on a paired board decision comes up about 2.5% of the time. While it’s not really frequent, it’s a decision that most players mull over. Knowing the advanced strategy will help you make your final decision quicker, and with more confidence.

Click on the screenshot below to play the game:

Or you can still play the older but simpler and faster Java game (check that you have Java 1.6):

Ultimate Texas Hold'Em Practice Game (Screenshot)

I’ve calculated the probability distributions for a few session scenarios, given 1) starting bankroll, 2) hit-and-run goal, and 3) maximum number of hands (session length). These distributions are calculated using basic strategy, i.e. betting a hand whenever long-term advantageous. Hopefully, these scenarios will help you understand the possible outcomes of your sessions, and their likelihoods.

100 Ante Bankroll, Leave if Double-Up or Bust-Out, 100 Hands Max

Let’s say you sit down with a bankroll of 100 Antes (i.e. $500 for a $5 Ante game). You decide before hand that you’ll play a maximum of 100 hands (about 3 hours), and that you’ll leave if you double up (+$500 profit), or bust out. In this scenario, you have an equal chance (1.5%) of busting out or doubling up. Otherwise, 97% of the time you’ll end up somewhere in-between, following the distribution below:

Session Distribution for 100 Ante Bankroll/Goal, Max 100 hands

20 Ante Bankroll, Leave if Double-Up or Bust-Out, 100 Hands Max

In this example, say you have only 20 Antes (i.e., $100 total bankroll for a $5 Ante game). You plan to leave if you double-up or bust out, and to play a maximum of 100 hands (~ 3 hours). In this scenario, you’ll have a 33% chance of busting out, a 27% chance of doubling up, and a 40% chance of falling somewhere in-between, following the distribution below:

Session Distribution for 20 Ante Bankroll & Double-Up Goal

200 Ante Bankroll, Leave if Win 20 Antes or Bust-Out, 250 Hands Max

Say you have a big bankroll, are happy to hit-and-run after winning 20 Antes (i.e., $100 in a $5 Ante game), and are willing to grind out 250 hands. In this case, you have a 69% chance of making your $100, an overall 70% chance of winning, and only a 0.2% chance of busting out. The remaining 30% of the time, you’ll fall somewhere in-between, according to the following distribution:

Session Distribution for 200 Ante Bankroll, 20 Ante Goal, Max 250 Hands

Playing “Forever” for 0.8 Antes/hr

Personally, my only goal is to play UTH “forever” and lose (2.3% Ante/hand)(35 hands/hr) = 0.805 Antes/hr. For a $5 Ante game, that’s only a cost of $4/hr. I consider that cheap entertainment, and Casino Pauma gives back more than that in player rewards and cashback. There, your only effective costs are your dealer tokes.

Still, there’s always the risk of running bad, and busting out a limited bankroll. (And the equal chance of running good and doubling your entire bankroll, or hitting a Royal Flush, and becoming a “lifetime winner” for a while). I computed an outcome distribution over 3000 hands, starting out with a 500 Ante bankroll (i.e., $2500 for a$5 Ante game), and adding back $4/hr to your bankroll (either from cashback, or chalking it up to cheap entertainment). For this scenario, there’s still a 3.5% of busting out, and a 3.5% chance of doubling-up. Otherwise, 93% of the time, you’ll end up somewhere in-between according to the following distribution:

Distribution After 3000 Hands, 500 Ante Bankroll, Ignoring House Edge

Conclusions

The probability density function of the outcome of a single basic strategy UTH hand was calculated, and used to compute the session outcome distribution for a scenarios of bankrolls, goals, and session times. In each scenario, the simulated 2.3% Ante/hand house edge is seen, no matter the shape of the distribution.

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.

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.

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.

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.