Simplified Card Craps Counting
Lately, I’ve been drawn back to the card craps (PlayCraps™) game at my local Viejas Casino, mostly because I’m willing to lay more odds now with my newfound bankroll. They’ve changed the constant shuffle machine (CSM) to the ShuffleMaster® 126 model, which has a lot more internal slots than the previous shuffler. I thought this might hurt the don’t pass advantage, but I updated my simulator parameters (now 40 slots, and 312 cards) and the results remained as good as before. Most importantly, I added a MIN_RESERVOIR_DEPTH parameter, which is the minimum number of cards in the chute (reservoir) before the CSM drops another slot. I set it to 5 cards, and experimented with various counting window depths, and max odds to find a strategy I was comfortable with.
I found that a window size between 3 and 6 rolls prior rolls didn’t make much of a difference. This was a nice result, because it’s practically impossible to remember more than two prior rolls, and the management won’t let me record rolls with paper and pen anymore 😦 I also found that laying 5x odds is enough to gain about +0.25% over the house. (10x odds yields an 1.8% edge.) Again, this is nice, because 5x is the limit of my comfort zone. So, I’ll bet $5 on the Don’t Pass line, and use a 3-roll window to determine when to lay 5x odds.
| Point | Roll Values | Lay Conditions | Notes |
|---|---|---|---|
| 4 | +4 if both die <= 3 (“low”) -4 if both die >= 4 (“high”) 0 otherwise (“neutral”) |
count >= 0 in last 3 rolls |
Lay when #(low rolls) >= #(high rolls) in window. |
| 5 | -4 if both die 5 or 6 (“ugly”) -1 if one die 5 or 6 (“bad”) +2 otherwise (“good”) |
count > 0 in last 3 rolls |
Lay if two of last three rolls are “good”. (Two “good” + one “ugly” = no edge.) |
| 6 | -5 if boxcars (“ugly”) -2 if one die 6 (“bad”) +1 otherwise (“good”) |
count >= 0 in last 3 rolls |
Lay if at most one “bad” roll in last 3. (At most one six-spot in last 3 rolls.) |
8 | -5 if snake-eyes (“ugly”) -2 if one Ace (“bad”) +1 otherwise (“good”) |
count >= 0 in last 3 rolls |
Lay if at most one “bad” roll in last 3. (At most one Ace in last 3 rolls.) |
| 9 | -4 if both die 1 or 2 (“ugly”) -1 if one die 1 or 2 (“bad”) +2 otherwise (“good”) |
count > 0 in last 3 rolls |
Lay if two of last three rolls are “good”. (Two “good” + one “ugly” = no edge.) |
| 10 | +4 if both die >= 4 (“high”) -4 if both die <= 3 (“low”) 0 otherwise (“neutral”) |
count >= 0 in last 3 rolls |
Lay when #(high rolls) >= #(low rolls) in window. |
Note that a simple counting scheme emerges from the roll types (“good”, “bad”, “ugly”) and the small window. The 4/10 are very easy to play (i.e., know when to lay DP odds). A neutral count for the 4/10 still yield a +0.15% DP odds edge. If the count gets to +12 (e.g., all three rolls “low”), the DP odds edge averages about +0.5%.
The 5/9 points also work out easily. You need 2 out of the last 3 rolls to be “good”. If there’s one “ugly” roll (-4) and two “good” rolls (+2) in the window, you’re DP odds are neutral. The 5/9 points are “fair” in that a neutral count yields no bias against the point. If all three rolls in the window are “good”, then your +6 count yields about a +0.2% DP odds edge. If you have two “good” rolls (+2), and one “bad” roll (-1) in the window, the +3 count yields about a +0.1% DP odds edge.
Finally, the 6/8 points are very easy to play as well. If two of the last three rolls are “good” (+1) and one is “bad” (-2), the neutral count still yields a DP odds edge of +0.1%. If all three rolls are “good”, the +3 count yields a DP odds edge +0.2%.
You don’t have to worry about being perfectly exact on all your counts. Usually, when I play, I pay attention to how the previous hand ended. That way, I know the roll before the come-out. The important thing is to have an adequate bankroll, and the will to lay against all points when the count is good. You’ll find that things average out well, and a game is enjoyable with enough bankroll and a +0.25% (@ 5x) tailwind.
Discount Gambling 
Very interesting post. Have you written the entire strategy for playing craps with cards in a report that I might read?
Calculating estimated bet percentage should be fairly easy given your estimates too. If you were to use the Kelly Criterion, a 1% bet of total capital would be warranted on 4/10 in .5% +EV situations. I know there is a max. payout of $1,000 at Viejas, so, it’s not scalable.