Discount Gambling

I wanted to quantify the edge of a count system for the “dice” dealt out of the CSM for the PlayCraps™ game I’ve been talking about. I tried a few simple ideas, based on how I actually play the game at the table. A good method needs to be practical and not mentally taxing. After all, we’re playing craps, and we want to have fun.

I know when a large run of high rolls (both die are >= 4) occurs, the distribution for the next “roll” is skewed towards the 4/5/6, and away from the 8/9/10 points. If the point is on 10, I jack up my don’t pass odds. (See below how I play the 5/9 and 6/8 points.)

In the graphs below, don’t worry about the negative parts of the curves. These are times you’re not laying don’t pass odds. Your flat bet is still a 6:5 favorite on the 6/8, a 3:2 favorite on the 5/9, and a 2:1 favorite on the 4/10, minus the delta shown in the graph. Plus, these are good times to take pass odds on the point (e.g., your friend is pass line, and he jacks up the odds when you take them down).

Don't Pass Odds Advantage vs. Shoe Count

I formalized the strategy by keeping a running count of the last 6 rolls. A roll is high if both die are ⚃, ⚄, or ⚅. A roll is low if both die are ⚀, ⚁, or ⚂. All other rolls are neutral. Then I just keep the hi/lo total for the last 6 rolls. It’s pretty much what we naturally do in our heads anyway. Since every low or high roll significantly distorts the distribution, you get pretty excited to see one. (My eyes perk up every time I see a ⚀ ⚀, or ⚀ ⚁, or ⚁ ⚁, etc. I start looking to lay the no-4. Conversely, if I see ⚅ ⚄ then ⚃ ⚄ then ⚄ ⚄ I get pretty excited about lay no-10, or jacking up my don’t-10 odds.)

This above plot shows the results of simulating this count system, and tracking the distribution of the next “roll” out of the CSM. It clearly shows that the player gains a huge advantage by increasing his don’t pass odds when the count is good, and taking down the don’t pass odds when the count is bad. (The converse applies to the pass line bet. Just flip the graph to get the advantage of taking odds on the point for a given count. When laying don’t pass odds are bad, taking pass odds are good, and visa-versa.) Sometimes, I adjust my don’t pass odds bet on every roll.

This makes for a very good craps game, since this dirt-simple count system buys you from 0.5% to 1.5% on your 4/10 odds bet. The 5/9 aren’t too bad either. See below for the count system for the 6/8 points. The 6-roll window does not need to be exact, by any means. A 5,6,7, or 8 roll wide window produces similar results. They say people can remember about 7 numbers (e.g., telephone numbers). So you’ll end implementing this naturally anyways. Note that the simulation assumed the dealer let about 7 rolls accumulate in the muck before shuffling it into the CSM.

This strategy lets you lay/take odds only when you get an advantage for doing so. Normally, people lay/take odds on the point, and wait until the roll ends (hit the point, or 7-out). But with this counting method, you watch the “rolls” out of the shoe, and change your pass / don’t pass odds accordingly. You get to predict the future, and you actually have a little insight into it.

Update: Here’s how to play the 6/8 points.

The key card for the 6 point is the ⚅. This card can make a 7, but cannot make the point. Just keep track of how many of them you’ve seen in the last 6 or so rolls. Use this count as an index into the below graph. You’ll see that as long as the count is below 3, you still have an edge laying odds against the 6. For counts >= 3, you’d be laying odds at a disadvantage. Take them down, and wait for the count to go back below 3.

A similar approach is used for the 8 point. Here, the key card is the ⚀. This card can make a 7, but cannot make the point. Again, keep track of how many you’ve seen in the last 6 rolls or so. The more that are out, the worse off your don’t-8 odds bet is. See how the return changes from about +0.3% to -1.2% as the count increases from 0 to 7. Again, back off your don’t-8 odds bet when you see too many ⚀ come out.

A/6 Count System for 6/8 Points

2nd Update: Here’s better way to play the 5/9 points.

The key cards for the 5 point are the ⚄ and ⚅. These cards can make a 7, but not the point. So count the number of these cards you see in the last 6 rolls. When the count gets to 5, take your don’t pass odds down. Wait for the neutral (other) cards to flush down the count to 4 or below, then lay your don’t-5 odds again.

The situation is similar for the 9 point, where the key cards are the ⚀ and ⚁.

Don't Pass Odds Advantage vs. Count for 5/9 Points.