Craps Don't Player Challenge - Who wins??

4 poker players who happen to be all Craps players.
Don't players or Dark Siders.

The conversation was heated about doubling a starting bankroll, say 20 units,

by making just
1) don't pass bets with no odds,
2) don't pass bets with a max 1 don't come bet on a number on any roll with no odds
3) don't pass bets with a max 2 don't come bet on a number on any roll with no odds
4) don't pass bets with don't come bets on every roll with no odds

None of the 4 players think the odds bet is a good bet for the Dark Side.
You win less than you bet. That can be for another topic in another thread.

So every bet is $25, no Lay odds, and each buys-in for $500 (20 betting units)
4 playing methods.

They agreed on simulation results to declare the winner
but will take their game to the craps table when they get the chance just for fun and some side bets.
Sim results coming later

Who has the best chance to double their bankroll or go bust trying??

The one with the most money out there has the best chance to do both, in my opinion.

Give me the DP bettor with the continuous DC bets.

Quite a stupid contest. All bets have an identical house edge. The the guy with more money on the table will have more volatility and have a better chance of doubling or busting out quick.

The guy that throws even 1x odds out there is the clear winner. But none of these poker players have the brains to do that?

This is a pretty easy question.

The answer is that all four players have EXACTLY the same chance to double their bankrolls.

Note, you didn't ask who would double his the FASTEST or in the fewest rolls. You only said who has the best chance to eventually double.

It is easy to prove that all four of these options are, in reality, exactly equivalent. Since there is no "race," the number of rolls doesn't matter. Option 4 would have much more money in play than option 1, but for the question at hand, they are the same, because you could just say that option 4 is starting a new virtual don't pass bet with every don't come bet -- and since there is no race, his strategy is equivalent to option 1.

Quote: sodawater

The answer is that all four players have EXACTLY the same chance to double their bankrolls....since there is no race

My thinking went this way and I concur.

Quote: sodawater

This is a pretty easy question.

The answer is that all four players have EXACTLY the same chance to double their bankrolls.

Note, you didn't ask who would double his the FASTEST or in the fewest rolls. You only said who has the best chance to eventually double.

It is easy to prove that all four of these options are, in reality, exactly equivalent. Since there is no "race," the number of rolls doesn't matter. Option 4 would have much more money in play than option 1, but for the question at hand, they are the same, because you could just say that option 4 is starting a new virtual don't pass bet with every don't come bet -- and since there is no race, his strategy is equivalent to option 1.

I don't think this is correct because 4 will have more money on the table per bet resolution. The guy with the best chance is the guy that bets it all on the don't on the first bet. 4 comes closest to that.

would love to hear from the experts on this forum like Math Extremist or miplet as to the correct answer

I can plug it into a Monte Carlo sim and do a bunch of trials.

The short answer from my perspective is the approach that makes the fewest number of bets.

I believe the best way to double your bankroll is with a single bet. The closer you get to that the better chance you have.

If they are all betting the exact same units on the exact same edge, there is no better way according to JUST the math.

A sim would provide the answer though. I would expect they are the same in theory of the math, but seeing as volatility is negatively affected by making additional DC bets, I'm going to say just sticking with the don't pass alone is the best way. It's possible that you get an advantage with two DC's though. I don't see it with one.

Quote: sodawater

Note, you didn't ask who would double his the FASTEST or in the fewest rolls.
You only said who has the best chance to eventually double.

Exactly. The understanding is the more bets you make the faster one can go bust or bouble a bankroll.
For the 20 unit buy-in (that will be $200 with $10 bets on the craps table)
here are the number of rolls and the number of resolved bets (on average) from the sims.

1dpass
rolls:1353.51
bets:389.81

dpass+1dc
rolls:778.54
bets:401.9

dpass+2dc
rolls:590.32
bets:405.26

dpass+ continuous dc
rolls:460.24
bets:428.54


The group has decided that it is OK to actually lay 1x odds. Their reasoning is any more is just a bad bet.
$20 to win $10 for the 4&10 is better than $40 to win $20.
I will also include the results from laying $20 to win $10 for the 4&10, $15 to win $10 for the 5&9 and $12 to win $10 for the 6&8 from different sims.

I do not think the odds will make any difference in who has the better chance at doubling their bankroll,
except a higher overall chance to double the starting bankroll.

I am just doing the sims for them.

Answer to the question for who has the best chance to double a bankroll?

I will also add that making a distinction between these different strategies only has slightly more merit than considering what rolls just recently came out.

The main difference is that anybody can be fooled by gambler's fallacy, but to make a distinction between the above approaches requires that you know something about math and simulators.

In both cases, the short run details of what happens (IE: luck) is going to overshadow any effort of looking at what just happened or which one has the better long-term advantage.

I found myself thinking in the shower this morning that advantage play on a $5 bet is $0.02 per roll or less if my advantage is under 3% (without odds). The argument is hinging on whether or not you can do all this shit ton of work or not that's worth a whole $0.02 per roll from people who think this is an argument about being able to take money from the house by playing with skill.

You have to get to $500 passline bet just to get that skill to translate into $2 per roll even assuming it's possible.

Once you start talking about "free" bets .. your volatility is going to start driving the bus, and none of it matters anyway.

This is one reason I'm working up towards doing $25 bets with no odds, and then $100 bets no odds. I tried to go straight to $100, and I got schooled. But I'm working on doing green chips with no odds.

I think too many people obsess over tiny fractions of edges only to get schooled by volatility combined with bad luck.

I think this is even more common than people who get volatility and good luck and think they are awesome, which happens plenty too.