Discount Gambling

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