Discount Gambling

Card Craps Counting With Pen & Paper @ Viejas

Posted in +EV, card craps by stephenhow on November 5, 2009

I just figured out the perfect way to play card craps at Viejas Casino. I always see Baccarat and Roulette players recording and studying the hand history right at the table, so I figured I’d make real use out of the right to pen & paper at the craps table. I sat down at the CSM craps game tonight, and recorded each roll on paper. That allowed me to look over the last 5-6 rolls, and see if the count was positive for laying odds on my Don’t Pass bet. This took all the guesswork out of counting, and was quite fun and relaxing. Before, I’d have to think back and guess if I saw the key cards for the point. It was inaccurate, and I probably made a lot of mistakes. Now, it’s smooth sailing, and I know exactly when to lay odds.

I had a good winning session (my 3rd in 3 consecutive nights), and played for about an hour or so. The play is pretty fast out of the CSM, and I recorded about 300 rolls (all of them). I played Don’t Pass on 62 points, laying odds on 24 of them (39%). It was really easy to see when the count was good. (Of course, any time the count is positive, I should be laying 10x odds.) When I change my odds, I note it to the right of the roll. I also use exclamation marks (!) to indicate the outcome when I’m laying odds. For example, “win!!!” means I won when laying 3x odds; “lose!” means I lost when laying 1x odds. I use a horizontal line to indicate the come-out roll.

I played with two other semi-regulars tonight (compared to me, everyone else is semi-regular). One guy was playing $5 pass line with 5x-10x odds, and got killed. He watched me vary me odds bet during the roll, and saw I usually won when laying odds, and I usually didn’t have odds when I lost. After he busted out, he brought out another $200, but decided not to play. Instead, he watched what I was doing with the notation. I’m sure he knows that card craps is not normal, and that its possible to count the cards in some way. Of course, you’re not really going to figure it out unless you have a lot of time and energy on your hands. Or find this site. I really hope someone reads this, and understands how good the game is. For crying out loud … you can count with pen and paper right at the table! This is completely and absolutely classic.

Below are photos of my session (I don’t have a scanner). Take a look, and you should see exactly how to play. I highly recommend taking advantage of this method of playing. It’s the only way I’m going to play the game in the future.

card craps rolls 1,2

Card craps session notation, pages 1 & 2


Card craps session notation, pages 3 & 4.

Improved CSM Craps Analysis @ Viejas Casino

Posted in +EV, card craps by stephenhow on September 27, 2009

After some debate and discussions with the (very cool) floor supervisors and dealers at Viejas Casino, I developed a much more accurate model for the CSM, and re-analyzed the effects of counting in the craps game. Initially, my model of the CSM was a conceptual one, and involved a random shuffling of cards in a reservoir, fronted by an continuous, 10 card deep buffer. In fact, after detailed discussions of how the CSM actually works, I re-modeled it after these mechanisms.

The CSM actually consists of an elevator shuffler, which uses 20 slots that holds from 0 to 14 cards. When the dealer feeds the muck into the hopper, it raises/lowers the elevator to select a random slot, then pushes a muck card into a random position within the chosen slot. The buffering consists of dropping an entire slot (of 0 to 14 cards) into the chute, from which the dealer pulls cards, until it empties. Then another random slot is dropped into the buffer for dealing.

Using this model, and the new, no accumulated muck dealing policy (the muck is fed back into the CSM after each roll), I determined that the actual window depth a counter should use is 4 rolls. I.e., your odds decisions should only be based on the last 4 rolls out of the CSM. Of course, if you could open the CSM and see how many cards are still left in the buffer (dropped slot), you’d know the exact distribution of the next roll. But, alas, that’s why there’s an opaque front panel cover, and we don’t know where we are in the dropped slot. So we just run simulations, and look for the best and simplest overall correlations we can devise.

I’m pretty pleased that a 4-roll windowed fair weighted count works out pretty well. The chart below shows an overall lower effect of the count, because we’re averaging in the variability of the buffer depth. But, the overall EV for laying 10x on a positive count is still +1.6% of the flat bet. It’s better than nothing, and the count is even simpler with the smaller window, and is still 100% fun.

CSM Craps Counting Advantage

CSM Craps Counting Advantage

PlayCraps™ @ Viejas: A Counter’s Dream

Posted in +EV, card craps by stephenhow on September 8, 2009

I’m loving the PlayCraps™ (cards-based craps) game @ Viejas Casino. I just love watching each roll out of the CSM change the EV of the odds bet on my Don’t Pass bet. For each +4 change in the count (e.g., a (1,2) roll against a 4 point), I increase my Don’t Odds by 1 unit. Of course, I could just lay 10x odds for any positive count, but I’m really conservative. Still, I often see +16 counts, which gives me over a 1% edge on whatever Don’t Odds I decide to lay.

Since it’s obvious to absolutely everyone that I’m counting (out loud), the casino changed the dealing policy to shuffle in the muck as often as every roll. This changes nothing for me, since I’m dealing with a CSM anyways. As I’ve shown in previous posts, the only important thing to track is a trailing window of approx. 6 rolls. This morning, I started some simulations before heading off to win $80 in 4 hours laying small (1x, 2x, occasionally 3x) odds.

Player edge for laying Don't Pass Odds using a 6-roll windowed, fair-weighted count.

Player edge for laying Don't Pass Odds using a 6-roll windowed, fair-weighted count.

The graph shows the 6-roll windowed count using fair-weighted values (i.e., “good” rolls for the 4/10 points are 4x powerful than “good” rolls for the 6/8 points) is all the info you need for any point. This graph demonstrates the entire essence of advantage play for this game. It’s all you need to see to know the game is clearly beatable, and to see the inherent bias towards the Don’t Pass.

While the overall edge is small (laying 10x odds for any positive count yields 1% of the flat Don’t Pass bet per roll; i.e., $.05 per roll for a $5 Don’t Pass bet), the game is 100% fun. It’s really easy to estimate how good the count is from watching key cards for the point, and remembering back a few rolls. With practice, it’s just a matter of watching for a few key cards, and instantly pumping up, or backing off your Don’t Odds on a roll-by-roll basis. It’s much, much easier, faster, and rewarding than counting at blackjack, which requires an expertise few master. Watching for key dice combinations for a given point is child’s play comparatively.

I’m editing the main PlayCraps™ page, and I need to make some graphical example diagrams. We need more Don’t players at this game; all the pass line players are just donating to the house.

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Simulations For PlayCraps™ @ Viejas Casino, CA

Posted in card craps by stephenhow on August 20, 2009

Using the improved don’t pass counting system, using a trailing six roll window, as described in the previous post:

Point Conditions to lay (max) don’t pass odds
4 running count over the last 6 rolls <= -2
5 seen at most 2 fives or sixes in the last 6 rolls
6 seen at most 1 six in the last 6 rolls
8 seen at most 1 ace in the last 6 rolls
9 seen at most 2 aces or deuces in the last 6 rolls
10 running count over the last 6 rolls >= 2

where the running count is incremented when both die are high (>= 4), and decremented when both die are low (<= 3).

Applying 10x don't pass odds, I simulated the game using my model for the CSM (continuous shuffling machine), and I got the following results:

Macintosh:Debug show$ ./playcraps -a -m14 -n100000000 -r
max muck depth: 14, CSM buffer depth: 10, rolls: 1.0e+08
net: +584729, EV: +0.58% per roll

Macintosh:Debug show$ ./playcraps -a -m20 -n100000000 -r
max muck depth: 20, CSM buffer depth: 10, rolls: 1.0e+08
net: +621717, EV: +0.62% per roll

Macintosh:Debug show$ ./playcraps -a -m20 -b6 -n100000000 -r
max muck depth: 20, CSM buffer depth: 6, rolls: 1.0e+08
net: +646693, EV: +0.65% per roll, +2.18% per come out

meaning that the dealer shuffles the muck back into the CSM when it’s more than 14 cards deep. The CSM is modeled with a buffer depth of 10, meaning that the earliest a card can come back out of the shoe is 10 rolls after any shuffle.
The results show that you’ll win +0.58% of your don’t pass bet, on average, per roll. So, for a $5 don’t pass bet, you’ll make $.029/roll, when laying 10x don’t pass odds according to the above table. Note the results improve a little if the dealer allows the muck to collect a little longer (+0.62%/roll for a 20 max card muck).

Note how the count scheme is insensitive to the buffer depth modeled in the CSM. When I decreased it to 6 rolls (12 cards), the return actually improved a little. In the last simulation, I also calculated the return per come out, which came out to +2.18% of the don’t pass bet. Again, that’s only about $0.10 per $5 don’t pass bet.

It’s not a lot of money. Even at a fast 500 roll/hr, you’re only making $14.50/hr. The bankroll requirements for this strategy are large, because you’re laying $100 to win $50 against the 4/10. It’s probably not an option to try and grind this game out. However, if you like playing don’t pass craps, then at least you’re getting the psychological benefit of a $14.50/hr tailwind 🙂

Note that just playing blind 10x don’t pass odds gives you the same ~2% EV. Employing a count scheme is just reducing your 10x odds variance a little from ~35 to ~32 (its still huge). I enjoy varying my odds with every roll. It only takes a small amount of effort, and it makes me feel like I’m in control.

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Count System for PlayCraps™ @ Viejas Casino, CA

Posted in card craps by stephenhow on August 19, 2009

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

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

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.

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

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