Discount Gambling

Basic Strategy Card for Ultimate Texas Hold’em

Posted in ultimate texas hold'em by stephenhow on September 28, 2009

ultimate-texas-hold-emI didn’t find any basic strategy online for ShuffleMaster’s Ultimate Texas Hold’em, so I developed my own. The following table should yield very close to the 2.2% theoretical house edge. I’ve only played the game a few times, but it seems there are a few cases when you need to know if a small pair, or a kicker, or a draw is good enough to bet.

Update: I started playing the game, and I really enjoy it. I find that people play very differently than basic strategy, and these mistakes often costs more than 20% of the ante bet (e.g., 20% of a $5 ante is $1). I’ve written up an entire page on the game, and explain how to play near-optimal strategy.

Basic Strategy Card for Ultimate Texas Hold'em.

Basic Strategy Card for Ultimate Texas Hold'em.

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

Strategy Card For Mississippi Stud @ Barona Casino

Posted in +EV, mississippi stud by stephenhow on September 26, 2009

I finally got around to making a nice, colourful strategy card for Mississippi Stud, as it’s played at Barona Casino near San Diego (i.e., where you get to see all the players hands). I’ve been playing with an awful print out of my strategy table, and it would sometimes slow the game down. We won again last night, thanks to a full house on the last hand!

Mississippi Stud Strategy Table

Mississippi Stud strategy table when all 6 hands seen.

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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