A Craps Scenario - Need Some Help with the Math

DISCLAIMER: The purpose of this betting strategy is fun, nothing else. I am aware that no betting system will improve EV.

Consider the following craps strategy:

Make $5 Pass Line bets and two continuous $3 Come bets. Take 100x ($500) odds on Pass Line bets if it is the first time that specific point has been established during the session. Take 20x ($100) odds on all subsequent Pass Line bets for that number. Always take 20x ($60) odds on Come bets. End the session once all points have been established at least once, and all outstanding bets have been resolved.

Note 1: There should be a total of six $500 odds bets in the entire session--one on each point.

Note 2: Odds on Come bets are off during the Come Out roll when making a Pass Line bet.

Note 3: If the last Pass Line bet is a loser, the session will end immediately because there will be no outstanding Come bets. However, if the last Pass Line bet is a winner, there will be at least one and possibly two Come bets outstanding. Take 20x ($60) odds on these bets and keep them working during all come out rolls until the bets are resolved. Do not make additional Come bets after the last Pass Line bet has been resolved.

Here come the math questions:

1) What is the EV of this strategy?

2) What is the average number of rolls it will take to complete the session?

3) What is the minimum bankroll requirement to have at most a 10% chance of ruin?

First off, odds don't affect EV.

How big is your bankroll? Three straight seven-outs can put you some $2000 in the hole. And three fast seven-outs in a row happen all the time. 21% chance or so of three staight seven-outs, ignoring non-point come-outs and whether the Come bets win. Getting the exact numbers is probably best calculated by simulating a few million trials, but I have to believe you'd need to survive at least five straight seven-outs on point numbers (7.5% chance of happening).

Quote: 7outlineaway

First off, odds don't affect EV.

How big is your bankroll? Three straight seven-outs can put you some $2000 in the hole. And three fast seven-outs in a row happen all the time.

Odds don't affect EV, but they definitely affect bankroll requirements. I agree that $2K is way too low for this strategy, but I think $4K would get me to the end well over 95% of the time. Unfortunately, I have no math to back that up.

You would need 80 units to have only a ten percent chance of Risk of Ruin during four hours of play at a "Downtown" paced table assuming perfect play without tipping or dealer error.

Quote: dk

... Make $5 Pass Line bets ... Take 100x ($500) odds on Pass Line bets ...

I've never played at a table that would allow 100x free odds, or anything like it, but I have always figured these were not $5 or $10 minimum bet tables? I was wrong?

Quote: dk

DISCLAIMER: The purpose of this betting strategy is fun, nothing else. I am aware that no betting system will improve EV.

Consider the following craps strategy:

Make $5 Pass Line bets and two continuous $3 Come bets. Take 100x ($500) odds on Pass Line bets if it is the first time that specific point has been established during the session. Take 20x ($100) odds on all subsequent Pass Line bets for that number. Always take 20x ($60) odds on Come bets. End the session once all points have been established at least once, and all outstanding bets have been resolved.

Note 1: There should be a total of six $500 odds bets in the entire session--one on each point.

Note 2: Odds on Come bets are off during the Come Out roll when making a Pass Line bet.

Note 3: If the last Pass Line bet is a loser, the session will end immediately because there will be no outstanding Come bets. However, if the last Pass Line bet is a winner, there will be at least one and possibly two Come bets outstanding. Take 20x ($60) odds on these bets and keep them working during all come out rolls until the bets are resolved. Do not make additional Come bets after the last Pass Line bet has been resolved.

Here come the math questions:

1) What is the EV of this strategy?

2) What is the average number of rolls it will take to complete the session?

3) What is the minimum bankroll requirement to have at most a 10% chance of ruin?

Casino Royale in Vegas offers 100x times odds with $3 or $5 minimums.

EV doesn't change because there is no house advantage. In other words, the HA is 1.414% on any pass line bet. The HA is 0% on any odds placed on the pass line.

So, for a $10 pass line bet with zero odds, the expected loss is $10 x 1.414% = $.1414
For a $10 pass line bet with $1000 odds, the expected loss is $10 x 1.414% + $1,000 x 0% = $.1414. The house advantage on the entire bet playing $1,000 odds is not $.1414 / 1,010 because there are there are 24 combinations out of 36 that result in playing the odds.

I can't easily at all answer the other questions.

Quote: dk

2) What is the average number of rolls it will take to complete the session?

I think the average number of rolls is about 82. Here is my logic:

The average number of points required to make at least one of each is about 15.8.

The average number of rolls to establish a point is 1/(2/3) = 1.5.

The average number of rolls to hit the point or seven out is about 3.564.

So to resolve 15.8 points takes on average about (1.5 + 3.564)*15.8 ~ 80 rolls.

However, there may be one or two Come bets outstanding, which averages out to about another 2 rolls for a total of 82.

Note: I realize that the 15.8 and the 3.564 aren't perfectly independent, but I think it's close. If anything, I may be under estimating by 1 or 2 rolls.

Does this sound about right? Any thoughts on questions 1 and 3?

Quote: dk

The average number of points required to make at least one of each is about 15.8.

I calculate an EV of this strategy to be about -$6. Here are my assumptions:

1) As previously stated, odds have no effect on EV.

2) Given 15.8 average rolls, there will be 15.8/2 = 7.9 come out winners/losers without a point being established.

3) The average number of Come bets is 2 per point established (just a guess and the weak link in my calculations).

I calculate an EV of -8.26 on Pass Line points + 4.94 on Pass Line come out rolls for a Pass Line EV = -3.32.

Similarly, -6.61 on Come bet points + 3.95 on the first roll for Come bets for a Come bet EV = -2.66.

Adding the two, I get -5.98.

I tried out this strategy at the Casino Royale on a recent trip. I'm happy to report I got a result on the positive side. I hit 3 of the 6 $500 points (4, 6 & 8). In order of enjoyment, the top 3 things about the experiment were:

1) I won a good chunk of money
2) The bettors next to me making $5 pass line bets (same as me), and posting $5 odds while I put up $500 (so we had the same EV, but I stood to win or lose more). It was fun to see one of them whisper to the other about my pink chip behind my bet.
3) Actually being nervous on my way to play--that hasn't happened in years. (Or maybe I was just still shaking from freezing my tail off at the LV Bowl).

Quote: odiousgambit

I've never played at a table that would allow 100x free odds, or anything like it, but I have always figured these were not $5 or $10 minimum bet tables? I was wrong?

It was a mistaken assumption. A table with 100x is often just a casino promotion since few players actually avail themselves of 100x odds anyway and just play with their usual "emotionally comfortable odds" of 2x to 10x. Casino Royale has 100x odds thought the signage is often confusing. The 100x applies to 5.00 bets but the table may be displaying a sign of 3.00 minimum bet with 10x odds being the limit.

The dice tables at Harrah's Horsehoe in Tunica also routinely offer 100x odds, I believe, but do not know from personal experience.

Most odds in Vegas are 3x4x5x, because this speeds up the game. Other routinely encountered odds are 10x and 20x. A few grind joints are said to limit the odds to 2x and will have low table limits as well.

Even with a flat bet of only 5.00 I have neither the courage nor the bankroll to place a 100x odds bet.

I would wonder at the poster's strategy however. Why bring confusion and calculation efforts into this scheme? Er uh.. strategy! Flat bets will sometimes be 5 and sometimes 3 dollars? Odds bets will sometimes be 20x and sometimes be 100x. Is there some added value to this variation? Is there more value to simplicity?

Quote: FleaStiff

I would wonder at the poster's strategy however. Why bring confusion and calculation efforts into this scheme? Er uh.. strategy! Flat bets will sometimes be 5 and sometimes 3 dollars? Odds bets will sometimes be 20x and sometimes be 100x. Is there some added value to this variation? Is there more value to simplicity?

There was added value for me, which is why I created the "strategy" in the first place. (As a side note, I agree the term strategy may be misleading since it does nothing to improve EV, but "system for determining when/how much to bet in different situations" is cumbersome).

I would recommend flat betting and taking max odds for first time or inexperienced players. I developed this strategy to mix things up a bit, make sure I played for a while, but didn't just play until I lost all my money. I don't like setting a dollar win limit, so instead a set a somewhat randomized time limit. I feel it definitely enhanced my fun, and having to keep track of what numbers required big bets added to my focus and the excitement of the game. YMMV.