What is the chance of never being "up"?

What is the chance of never being "up" betting full 345X odds (pass line) assuming bankrolls of 10, 100 and 1000 units?

Not good. At least for 100 and 1000.

Quote: longtimelancer

What is the chance of never being "up" betting full 345X odds (pass line) assuming bankrolls of 10, 100 and 1000 units?

This is dependent on bet size (which you didn't specify) versus bankroll and how long you'll go before giving up trying.

If you only try for one resolution or if your bet size versus bankroll will only allow for one initial loss before busting then your probability of never being up is the same as the probability of losing the passline = 1004/1980 = ~ 50.7%

If you allow for more resolutions, the variance will increase your chances of being up at some point.

I wrote a script (which you can copy/paste) to help find some answers. It queries for bankroll, bet size, # resolutions, and odds.



Looking at $5 flat bets, no odds, and unlimited resolutions (iow run until success or busted) I get the following for your 3 bankroll amounts:

Bankroll	% chance never up
10	34.3
100	6.2
1000	2.8

Same criteria except taking 345x odds, I get:

Bankroll	% chance never up
10	47.7
100	16.2
1000	1.8

I didn't run these sims too long so these are just ballpark figures. Also note that partial odds are taken when remaining bankroll is insufficient for full odds.

Steen

Here is what I get to compare to the simulation results
I take 10,100 and 1000 units as just $1 bet
That way any one can convert their flat bets and bankroll using a units bet

My values are calculated. it really is simple to do.

The flat betting uses the famous Gambler's Ruin formula
It is in prob and stats books and all over the internet if one takes a look for it
here is a post I showed
GR Example
The 345x odds uses a Markov chain approach. I used an all-in bet if the full odds could not be made.
This really does not change the values that much compared to betting what is left as odds.
It actually increases very slightly the chances for success.
One can see the chances between don't pass and pass are very close
I really doubt an average player could see a real difference in actual play.

Of course, I would really hate to be those players that never ever sees a 1 unit gain too.
And from the math we know there must be many of them.
But someones has to be there.

win goal = 1 unit (so FAIL = never being up)
we can see the larger the bankrolls not much of a difference in the overall success/fail rate
edit: data for 1000 and 2000 unit bankroll with Don't Pass 345x odds and
2000 unit bankroll Pass Line with 345x odds
are from a 10 million session simulation.

Bankroll Units	Don't Pass	Fail	1 in	Don't Pass 345x	Fail	1 in	Pass	Fail	1 in	Pass 345x	Fail	1 in
2	65.727%	34.273%	2.92				65.720%	34.280%	2.92
10	89.581%	10.419%	9.60	76.517%	23.483%	4.26	89.570%	10.430%	9.59	74.479%	25.521%	3.92
20	93.786%	6.214%	16.09	84.913%	15.087%	6.63	93.773%	6.227%	16.06	84.868%	15.132%	6.61
100	97.061%	2.939%	34.02	96.247%	3.753%	26.64	97.041%	2.959%	33.80	96.240%	3.760%	26.60
200	97.224%	2.776%	36.02	97.965%	2.035%	49.13	97.202%	2.798%	35.74	97.965%	2.035%	49.14
1000	97.234%	2.766%	36.15	99.380%	0.620%	161.39	97.211%	2.789%	35.86	99.37186%	0.62814%	159.20
2000	97.234%	2.766%	36.15	99.530%	0.470%	212.89	97.211%	2.789%	35.86	99.519%	0.481%	207.96

Sally

I did a quick Monte Carlo of 10,000,000 passes of each bankroll size, and I got:

Bankroll 10: 25.52% (1 time in 4)
Bankroll 100: 3.75% (1 time in 26)
Bankroll 1000: 0.63% (1 time in 159)

Mine are based on the initial bet being 1 (i.e. for "bankroll 10", the bankroll is 10x the pass line bet) with 3/4/5 odds.

Quote: ThatDonGuy

I did a quick Monte Carlo of 10,000,000 passes of each bankroll size, and I got:

Bankroll 1000: 0.63% (1 time in 159)

I agree with your 1000 unit bankroll
my simulation also shows
pass 345x
Bankroll was busted . . = 0.627% of the time ( 62725)
Win goal was met . . . = 99.373% of the time ( 9937275)
dpass 345x
Bankroll was busted . . = 0.620% of the time ( 61960)
Win goal was met . . . = 99.380% of the time ( 9938040)

pass 345x
2000 unit bankroll
Bankroll was busted . . = 0.481% of the time ( 48087) about 1 in 208
Win goal was met . . . = 99.519% of the time ( 9951913)

don't pass 345x
2000 unit bankroll
Bankroll was busted . . = 0.470% of the time ( 46973) about 1 in 213
Win goal was met . . . = 99.530% of the time ( 9953027)

can not find the error in my Markov chain in Excel
added 1 pm: found the error.
I had named a matrix the same as another
can not blame that one on my fat fingers. leftover from copy/paste

Sally

Sally,

Could you fill out your spread sheet with the correct numbers?

Thanks!