Handed Down Rules

We’re taking a detour from the path previous blogs have been on to describe the value of studying Sheepshead data. Most of us were instructed on how to play Sheepshead by a parent or other relative older than us. For some of us, this took place many years ago. Each player at the table I played on growing up had a different opinion on what is a picking hand and what you should do in a given situation. My grandma would have advocated a much stricter definition of what is a picking hand while my dad would have recommended I pick even on weaker hands.

One of the difficulties with being human is we tend to remember the last thing we saw better than we remember long-run trends over the course of tens of thousands of hands. When you’re at a Sheepshead table, you will hear someone say “I haven’t gone in for awhile. My turn.” These comments are mostly made in jest, but people do occasionally pick because they haven’t had anything close to a picking hand in awhile. Other times, a player might lose two hands in a row where they pick with four trump to the queen of spades. The very next hand they are dealt four trump to the queen of diamonds, another picking hand. This time they don’t pick because of their previous picking losses.

It is better to have a strong sense for what a picking hand is and pick when those conditions are met. Any other behavior will cost us points in the long run.

Another reason we are determining picking rules harkens back to the situation described in the opening paragraph. While everyone at the table has an opinion of what kinds of hands we should be picking on, no one really knows. Until now, there hasn’t been data to use that could determine where the cutoff is.

Deeper Data Dive

Last time, we introduced the data available to us for analyzing the game of Sheepshead. We are ready to combine some of those data sets and look deeper into the data.

Data Preparation

Combining the Picker, Score, and Dealt tables, we have the picking team’s score for each hand, the picker’s hand, and thepicker’s place in the picking order. Our combined data set includes the columns mentioned on the 15,940 completed hands to date.

Once the data are combined, it is still difficult to say much about the picker’s hand with the data in their current format. In order to make much sense of the hand the picker has, we create 32 new indicator variables, one for each card in the deck. As an example, one of these variables is called isQC. It simply tells us whether the picker was dealt the queen of clubs or not. Variables isQS, isQH, and so on exist as well.

These new variables allow us to do things like count the number of trump in the picker’s hand and determine the value of having an individual card in one’s hand.

Analysis

Recall that our end goal is to know whether we are better off picking on a given hand or passing. We won’t be able to do that all at once, but the first step in that process involves building a predictive model that tells us the probability we will win the hand if we pick. Before we starting building a model, we want to examine the data a little closer to see whether there are any abnormalities in the data. We also want to see whether some basic reports tell us anything about what to expect of the model we are building.

The table below tells us the percentage of picking hands that contain the given card. This tells us what players find valuable when determining whether to pick. It doesn’t tell us what actually is valuable. With that said, the information is instructive.







































































































































Card % of Picking Hands
Queen of Clubs 42.5%
Queen of Spades 36.9%
Queen of Hearts 33.1%
Queen of Diamonds 30.0%
Jack of Clubs 25.7%
Jack of Spades 25.0%
Jack of Hearts 24.2%
Jack of Diamonds 10.0%
Ace of Diamonds 22.9%
10 of Diamonds 22.4%
King of Diamonds 21.3%
9 of Diamonds 20.9%
8 of Diamonds 21.0%
7 of Diamonds 20.8%
Ace of Clubs 15.6%
10 of Clubs 14.2%
King of Clubs 13.8%
9 of Clubs 12.9%
8 of Clubs 13.3%
7 of Clubs 12.6%
Ace of Hearts 14.4%
10 of Hearts 13.8%
King of Hearts 13.2%
9 of Hearts 12.6%
8 of Hearts 12.6%
7 of Hearts 12.9%
Ace of Spades 14.6%
10 of Spades 14.2%
King of Spades 13.6%
9 of Spades 13.2%
8 of Spades 12.8%
7 of Spades 13.1%

The first thing we notice is the difference in percentage of picking hands with a queen of clubs stepping down to the jack of hearts. If anything, it is suprising 10% of picking hands contain the jack of diamonds. One might expect that to be lower.

Another thing we notice is there is nearly no difference between having the ace of diamonds and a 7, 8, and 9 of diamonds, but there is a significant difference between an ace of fail and a 7, 8 or 9 of fail. There are a couple potential reasons for this: first, a fail ace is the most powerful card for that suit; second, pickers might plan to bury the ace of fail.

The relationship between the fail ace, fail ten, and the rest of the cards in that suit is constant across fail suits. Remember, this doesn’t tell us that an ace of clubs is more valuable than the 7, 8, and 9 of clubs. It only tells us that players on the website are behaving as if the ace is more valuable.

The table above is univariate. It could be that, by chance, players with an ace of fail have happened to have better than average trump while players with small fail have had worse than average trump. This is very unlikely given how many hands have already been played.











































# Trump Had JD No JD
0 0.2% 0.0%
1 2.1% 0.6%
2 10.5% 5.0%
3 34.2% 17.7%
4 41.0% 42.0%
5 11.2% 29.7%
6 0.8% 5.0%

It’s no suprise that players require more from a picking hand if they have the jack of diamonds. About 77% of picking hands with the jack of diamonds have at least four trump or more. Without the jack of diamonds, only 53% of picking hands have four trump or more.

We are now in great position to built a model that assigns a win probability to a hand prior to picking.

Data Summary

Before we can analyze the data, we should understand what we have and describe it. We have seven different tables to consider. Each of the bullets refer to the data table. The numbered list under each bullet specifies the fields found in that data table. They are

  • Picker:
    1. handID
    2. the picker
    3. the blinds
    4. type of blitz
    5. number of passes before they picked
    6. the partner
  • Result:
    1. handID
    2. the picker
    3. points scored by each player in that hand
  • Score:
    1. handID
    2. score of the picking team (0-120)
  • Dealt:
    1. handID
    2. player
    3. hand dealt
  • Bury:
    1. handID
    2. cards buried
  • Crack:
    1. handID
    2. player who cracked
    3. type of blitz
  • Trick:
    1. handID
    2. trick number
    3. cards played that trick
    4. player that led the trick
    5. player that won the trick
  • Under:
    1. handID
    2. card placed under in a call an ace game

The data described above will allow us to determine many of the things we would like to study, even if they are not kept in the log in their own field. For example, if we wish to study hands where the picker played alone, we can simply check whether the picker name and the partner name are the same in that hand. We could calculate the value of any trick in a hand if we want.

One thing we are regrettably missing are the rules for the hand. For now, it seems over 90% of all hands have been played jack of diamonds partner and blitzes and cracks allowed. We will assume those were the rules for each hand up to this point and track that information going forward.

Data as of 11/30/2017

Up to now, 17,064 hands have been played by 296 different players. When five players play one hand, that counts as one hand, not five.

One of the factors in whether to pick is which position in the picking order you are in. The table below shows the expected number of points and distribution by picking order. Distribution just means the percentage of hands where the picker was in the given position.
































Picking Position Expected Points Distribution
First 1.93 24.6%
Second 1.89 21.0%
Third 1.96 19.1%
Fourth 1.98 17.5%
Fifth 2.07 17.8%

The expected points don’t consider cracks or blitzes. We have simply assigned points for the picking team based on the score for the picking team. This is a simple calculation of the average points scores by the picker. The expected points look close together, but consider the difference between picking second and picking fifth. If you picked second 1,000 times, you would have expected to score about 184 more points if you could have picked fifth in each of those hands.

This is only a small part of the story. One theory is that people already consider their picking position when deciding whether to pick. I know I do. If players pick without considerating for their position in the picking order, you would expect slightly more picking in the first position in the second. The 3.6% difference in distribution we are seeing (24.6% vs 21.0%) is larger than expected if players aren’t more enthusiastic about picking first.

Next, we will rank hands according to how likely the player is to win if they pick. We will then look at the expected value of picking by picking order and by how likely the hand is to be a winner. We should see significant differences in expected value by picking order within hands of the same strength.

Introduction To Sheepshead Research

The goal of this blog is to distribute insights about the game of Sheepshead as learned from the data collected on the get61 Sheepshead site. Most of us grew up playing Sheepshead with our family and have carried a love of the game into adulthood. Through experience, we have created our own strategies for various scenarios we might find ourselves in, not the least of which being a way to determine whether we have a good enough hand to pick on.

Quite possibly the most important decision made in any hand is whether to pick. The decision of whether to pick boils down to only a few things: what cards do I have, where is my position in the picking order, and what is the penalty for picking and losing?

We will spend most of our time, at least at the beginning, studying the decision to pick. These are not intended to be scientific papers, inaccessible to people without a college degree in math, but there are some key concepts one should understand going into future writings.

For now, I will write this blog assuming its readers are Sheepshead players. Therefore, I won’t necessarily define Sheepshead terms like smear and schneider unless I feel there might be confusion even among long-time Sheepshead players. If you are new to Sheepshead and looking for a good resource to learn the game, visit the authority on Sheepshead.

Key Ideas

Strategy

All of us feel we know what a strategy is, but it is necessary to be a bit more formal here. Our Sheepshead strategy is our rules that tell us what card to play, whether to pick or pass, and whether to smear. If Sheepshead were big business, we would create a system of rules that tell us what to do in any situation we might find ourselves in. We have already mentioned our picking strategy as the most important part of our system of rules, but over time, we will investigate things like what to do on defense when the picker leads fail.

When we use the word rules in referring to our strategy, we are not talking about the rules of the game itself. We are only talking about the rules that govern our course of action within the contraints, or rules, of the game.

Expected Value

An expected value is the average result of employing a strategy over the long-term. It is like saying, “If I find myself in this situation 10,000, what would the result be, in terms of points, if I employ Strategy A? What would the result be if I choose Strategy B.” In choosing between strategies, we are looking for the strategy which offers the best possible outcome for oneself.If Strategy A has an expected value of 1, that means every hand I employ Strategy A in the scenario we are talking about, I expect to gain 1 point. Similarly, an expected value of -0.25 means I expect to lose 1/4 of a point, on average, when I employ the strategy in question.

Lets look at an example. Suppose I am dealt the top 6 cards and pick can first. Further suppose the rules at my table are jack of diamonds partner, blitzes, cracks, and no double on the bump. If I pick and bury the two cards in the blind, I am guaranteed I will no trick the other team. For simplicity sake, suppose I know the jack of diamonds is not in the blind. I can do one of three things:

Blitz in (pick and double the points the hand is worth by showing my black or red queens). This strategy has an expected value of 24 since I am guarateed I will win 24 points by doing this.

Pick without blitzing. This strategy has an expected value of 12.

Pass. This strategy has an expected value of 0 since the cards will likely be passed around the table and a new hand dealt as a doubler.

Clearly, in this situation, we should blitz in. The decision of whether or not to pick depends solely on what we think our expected value is if we pick against what it will be if we pass. The data from the site will help us understand when we should pick and when we should pass.

Predictive Model

One might ask, “how can we say what the expected value of picking on a given hand is? Do you plan to take a hand, look it up in all the hands that have been played on the site, and check how well people did when they pick on that hand?” Even if that were possible, it would be a highly inefficient use of the data. Instead, we will build a predictive model that uses each of the hands that have been picked on, the picker’s position in the picking order, and the result of the hand. We will built a predictive model that allows us to score any hand that can come to us in the future, and we will be able to say what the value of that hand is if the player picks in the picking order they are in. We will also be able to estimate the expected value of not picking.