3 Dice Football

[MonkeyF0cker]

A new dice game called 3 Dice Football was introduced this week at O'Sheas.

The primary objective of the game is to score a touchdown. Three dice are rolled every down (2 green dice, 1 red die). The game begins on the 20 yard line and the player has 3 downs to earn a first down or score a touchdown. A first down is earned by reaching the 10 yard line. If a first down is earned, the player has 3 new downs to score a touchdown.

There are 4 possible outcomes of rolling the dice:

1. Yards gained: Equals the total of the green dice minus the red die.
2. Penalty: When the total of the green dice is less than the red die (except for in the case of a turnover), the result is a 1 yard loss.
3. Trips TD: When all three dice show the same number, the result is an instant touchdown.
4. Turnover: When a red 6 is rolled with either a green 1-1 or green 1-2, you instantly lose.

If a first down or touchdown is not achieved in the appropriate number of downs, the game ends.

If a touchdown is scored, the three dice are rolled once more for an extra point. And just like craps, the same shooter rolls again. If not, the dice pass clockwise to the next player.

The interesting thing here is that I created a spreadsheet to see just how horrific the odds are in this game. While doing so, I seem to have found a pretty significant +EV opportunity. I'm hoping that someone can double check my work on this. Reno?

Full game bets

Touchdown 1:1
Defense 4:5 (no touchdown scored)
Extra Point
1 "1" 1:1
2 "1's" 10:1
3 "1's" 50:1
Any triple 10:1

Single Play Bets

Trips TD 33:1
Penalty 11:1
Turnover 66:1
Cover 3 (Trips TD, Penalty, or Turnover) 7:1
No Gain (0 yards) 5:1
Big Play (7 or more yards) 4:1
Over 4 yards 1:1 (with a Trips TD bonus of 7:1)
Under 4 yards 1:1

 

[MonkeyF0cker]

Well, I guess I can't attach the file. There's a 19k size limit for *.xls files. My spreadsheet is nearly 800k. Can someone fix that (at least temporarily)?

 

[reno cool]

Interesting stuff Monkey. Finding a fucked up table game is a real gem.
Oshea's in particular seems to often come up with these weird twists to traditional games. (hats off to em for doing something different anyway)

I'll count up probabilities on some of these. The easiest ones look negative so far. The probability of a td seems like it would be very hard to calculate (with my tools anyway)... on second read sounds like they only have to go 20 yards to score

trips 35-1
turnover 71-1
no 1's 57.9%
any triple should be like 35:1 they're paying 10

working on the penalty next.

 

[reno cool]

looks like

Cover3 true odds 7.3/1 26 out of 216 possible outcomes

penalty 11.7/1 assuming you don't get paid for a penalty in the case of a turnover. So those are close if I did em right.

 

[reno cool]

getting exactly true odds on under 4. assuming you lose on 4

 

[reno cool]

true odds

no gain 13.4/1
big gain 5.17/1

so those don't look good.

exactly 4 would come 12.5% of the time so the over at 37.5% can't be good even with the bonus.

looks like we're down to the touchdown or no bet.

 

[reno cool]

If any triple at 10/1 refers to the whole round (not just one throw) that could be interesting.

 

[senco78]

how many yards is the field?

 

[MonkeyF0cker]

20 yards, Mike.

 

[rito]

lets get that spreadsheet up here Polaroid

 

[pico]

pretty complicated game. not to be played when hammered

 

[MonkeyF0cker]

Sorry, Reno. The way it was written wasn't entirely clear. Everything under "Extra Point" is paid for an extra point bet. Here is my single roll probability table and single roll bet EV table...

Roll Result Probability
Trips (TD) 6 0.027777778
TO 3 0.013888889
-1 17 0.078703704
0 15 0.069444444
1 20 0.092592593
2 24 0.111111111
3 26 0.12037037
4 26 0.12037037
5 24 0.111111111
6 20 0.092592593
7 15 0.069444444
8 10 0.046296296
9 6 0.027777778
10 3 0.013888889
11 1 0.00462963



Single Play Bets Odds EV
Trips TD 33 -0.055555556
Penalty 11 -0.055555556
Turnover 66 -0.069444444
Cover 3 7 -0.037037037
No Gain 5 -0.027777778
Big Play 4 -0.050925926
Over 4 Yards 1 -0.046296296
(Over TD) 7
Under 4 Yards 1 -0.027777778

 

[MonkeyF0cker]

Wow. That sure looked better when I pasted it. It actually resembled a table.

The first table has columns of Roll Result (touchdown, turnover, or yards), the number of possible combinations (out of 216 total), and the probability.

The second table has columns of each single bet wager, the listed odds of the wager, and the EV.

 

[roguejuror]

Check the limit now, should be up to 2MB now.

 

[MonkeyF0cker]

Obviously, from this you can tell that the +EV that I'm talking about isn't in the single roll bets...

I thought I had perhaps found two +EV situations. However, I have to rework some of it. I currently have two 3 roll subsets that equate to possessions. However, I think I left out some first down probabilities that would have achieved a first down on the first possession prior to a turnover or negative yards (that resulted in less than a first down after three rolls). I tried to avoid creating a six roll combination table since it was 11,390,625 combinations. However, I may need to do that.

 

[MonkeyF0cker]

Thanks, RJ.

 

[reno cool]

So the only multiple roll bets would be the TD or no TD correct? Maybe easier to write a simulator for that one. Doesn't seem very likely they would fok that up. They got a healthy vig built in for them together.

Also I guess the under 4 pays less than true odds because it loses on a triple? I have it at 50%

 

[MonkeyF0cker]

Okay. Here's the spreadsheet. The more that I thought about it, the more that I think there actually is EV in this game since not counting those first downs would seem to increase the probability of a touchdown rather than decrease it. I'm going to create a six roll combination table and make sure, but here is my work on the three roll combinations...