Probability to Win $100,000 with a $2,000 starting bankroll

Quote: WaltFales

Any assistance that anyone could offer would be greatly appreciated.

Thank you,
Walt

Quote: WaltFales

I am attempting to find a public/free model that would help me better understand the probability a person could achieve a certain win threshold (i.e. $100,000) with a very small bankroll (i.e. $2,000 or approximately 2% of the desired ending total win/bankroll) in order to prove that providing a player with a small, yet immediate, discount or allowance (such as airfare) after a large loss provides the player with but a miniscule chance of recoverying the loss and breaking even.

An over-simplified estimate of the probability would require the bettor to double down until reaching the table maximum and would traditionally require about 9 victories in a row (1 in 512 odds) to achieve such a feat (and that assumed 50/50 odds or no house advantage), but I believe the probablity is actually much smaller assuming the player continues to bet only 2% of their bankroll and would theoretically fall into risk of ruin in the majority of cases well before achieving the desired results.

Lots of examples exist of the probabilities of defined outcomes to certain confidence levels, but I cannot seem to locate one that permits me to adjust the bankroll to such a low amount.

Any assistance that anyone could offer would be greatly appreciated.

Thank you,
Walt

Quote: wroberson

This reminds me of the time I turned 20 bucks into 2500 over a 23 day period.

Quote: varmenti

2500 in 23 days, OMG!!!!

I just did that much over the last two days of playing baccarat.

Quote: GWAE

LOL I was fully ready to write. Why use all 2k on a bet when you can play banker and player at the same time and win 100k in about 6 weeks.

but the lol was interrupted by the man posting in this thread himself.

Quote: varmenti

Especially those who don't know The Game of Baccarat.

Quote: speedycrap

How???

Quote: kewlj

$2000...no, but I turned $4300 into $100,000. Took me 5 years though....lol.

I began supporting myself solely from blackjack play in march 2004, with a bankroll of $4300. :-) Playing red chip level in Atlantic City, I made $32 grand my first 3 years.....that's a total of 32 grand....11,000, 9600, 12,000 respectively. I was 21 years old at the time and lived VERY minimally, single, roommate situation, no car. I could and did live off of $600 - $700 per month. Problem was, I couldn't grow my bank grow much. Finally, year 4, I hit a bit of positive variance which allowed me to grow my bankroll a bit and start moving up in stakes.

I no longer have my exact figures for those early years, but year 4, I made $25 to $30 grand and then year 5, my first 50+ grand year. So it was sometime during year 5, that I hit six figures and can say that I turned $4300 into $100,000. Now in year 10, I can say I turned $4300 into over $500,000. :-) Sometime in the next 4-5 years, I hope to be able to say that I turned $43 into a million dollars. :-) This was actually my original 10 year plan, but those first 3 years and just growing my bankroll to a point that I could begin to move up in stakes, was a much bigger 'hurdle' than I anticipated. But I eventually got there. :-)

Quote: kewlj

$2000...no, but I turned $4300 into $100,000. Took me 5 years though....lol.

I began supporting myself solely from blackjack play in march 2004, with a bankroll of $4300. :-) Playing red chip level in Atlantic City, I made $32 grand my first 3 years.....that's a total of 32 grand....11,000, 9600, 12,000 respectively. I was 21 years old at the time and lived VERY minimally, single, roommate situation, no car. I could and did live off of $600 - $700 per month. Problem was, I couldn't grow my bank grow much. Finally, year 4, I hit a bit of positive variance which allowed me to grow my bankroll a bit and start moving up in stakes.

I no longer have my exact figures for those early years, but year 4, I made $25 to $30 grand and then year 5, my first 50+ grand year. So it was sometime during year 5, that I hit six figures and can say that I turned $4300 into $100,000. Now in year 10, I can say I turned $4300 into over $500,000. :-) Sometime in the next 4-5 years, I hope to be able to say that I turned $4300 into a million dollars. :-) This was actually my original 10 year plan, but those first 3 years and just growing my bankroll to a point that I could begin to move up in stakes, was a much bigger 'hurdle' than I anticipated. But I eventually got there. :-)

Quote: 7craps

Quote: Mosca

I got up, got showered and dressed, and went to work.

Here is Michael Bluejay's system for winning $1,000,000.
It is readily and publicly available on his website.

Interesting how the MB article went from turning $10 into $1 million
to just $10 into $100k with a house limit
Here is what I get
A bit different from his sim results
and I did add in a few Roulette bets (MB thought against it)
these are calculated
(I guess I could PM MB about this
to help him out with his web page data)

using Bold Play
(highest probability of hitting a target in the shortest amount of time.
Craps odds not included
as per the SN Ethier paper 'Improving on Bold Play at Craps" shows this to be the best)

Bet what is needed to hit target goal (or max bet allowed) or go all-in trying
Turn $10 into $100,000
with a max bet of $50,000

*1 in* results
0 Roulette - 1# straight-up: 10,853.08
00 Roulette - 1# straight-up: 11,753.04
Bac Banker: 11,809.54
Bac Player: 12,059.84
Craps Don't Pass: 12,122.74
Craps Pass Line: 12,142.1
0 Roulette - even money bets: 14,528.4
Craps 30 to 1 bet: 15,649.35
00 Roulette - even money bets: 20,908.66

Roulette bets sure look sweet here.

MB also says this:
"That improves our chances to 1 in 125,926 for baccarat and 1 in 128,110 for craps.
(You can't easily calculate that, ..."

Sure one can
(I just removed the 't)

And it is quite easy
(as easy or easier as running a sim IMO)

Show Spoiler

In Excel one can get very accurate results to say 2 to 3 decimal places
with very little effort and simple math.
Turning Excel into some code to run in R for example
lifesaver (time saver too, happy I found it)

it (R code) was done by BruceZ over at 2+2 and matches perfectly with my Excel results
(with way less effort, that I like a lot)
R is a free program

br = 10     # Starting Bankroll
goal = 1000000   # Target bankroll
odds = 1      # Payoff Odds
p = (244/495)       # P(win bet) Pass Line Craps
max_bet = 5000000  # Table max - No max just make higher than goal

prob = 0
p_fail = 1
count = 0

while ( (br >= 1) & (br < goal) & (count < 1000) ) {

# Compute probabity of completing parlay up

  bet = min(br,max_bet)
  consec = 0 
  while (br + bet*odds <= goal) {
    br = br + bet*odds
    consec = consec + 1
    bet = min(br,max_bet)
  }

  p_parlay = p^consec

# Compute probability of reaching goal

  bets = 0
  if (br < goal) {
  while ( min(br,max_bet) >= ceiling((goal-br)/odds) ) {
    br = br - ceiling((goal-br)/odds)
    bets = bets + 1
  }
}

  p_goal = ifelse(bets, 1-(1-p)^bets, 1)

  delta = p_fail*p_parlay*p_goal
  prob = prob + delta
  p_fail = p_fail*p_parlay*(1-p)^bets
  count = count + 1
}

prob   # Probability of reaching goal
1/prob
delta
count

here is another one for those 1/37 or 1/36 type of bets
with a greater accuracy one can change

pdoub = function(br,goal,max_bet,pwin,odds,thresh,prob=1) {
  if (br < 1 | prob < thresh) return(0)
  bet = ceiling((goal-br)/odds)   # bet needed to reach goal
  limit = min(br,max_bet)         # limit = max bet possible
  if ( bet < limit )
    pwin + (1-pwin)*pdoubb(br-bet,goal,max_bet,pwin,odds,thresh,prob*(1-pwin)) 
  else 
    pwin*pdoubb(br+odds*limit,goal,max_bet,pwin,odds,thresh,prob*pwin) + (1-pwin)*pdoubb(br-limit,goal,max_bet,pwin,odds,thresh,prob*(1-pwin)) 
}
require(compiler)
pdoubb = cmpfun(pdoub)

system.time(p <- pdoubb(10,100000,50000,0.49317517,1,0.0000000001))
p
1/p

Pass Line Craps,
Baccarat Player and Banker bets.

$10 into $1 million using Bold Play

Bet what is needed to hit target goal (or max bet allowed) or go all-in trying
Martingale time to start with (10,20,40,80,160,etc) until
hitting the house limit if there is one

Show Spoiler

Craps Pass Line bet, no odds
> br = 10 # Starting Bankroll
> goal = 1000000 # Target bankroll
> odds = 1 # Payoff Odds
> p = (244/495) # P(win bet) Pass Line Craps
> max_bet = 5000000 # Table max - for No table max make value higher than goal
>
> prob # Probability of reaching goal
[1] 7.84834e-06
> 1/prob
[1] 127,415.5
> delta
[1] 0
> count
[1] 1000

> br = 10 # Starting Bankroll
> goal = 1000000 # Target bankroll
> odds = 1 # Payoff Odds
> p = (244/495) # P(win bet) Pass Line Craps
> max_bet = 50000 # Table max
>
> prob # Probability of reaching goal
[1] 2.538923e-10
> 1/prob
[1] 3,938,678,208
> delta
[1] 0
> count
[1] 1000


> br = 10 # Starting Bankroll
> goal = 1000000 # Target bankroll
> odds = 1 # Payoff Odds
> p = 0.49317517 # P(win bet) Bac Player
> max_bet = 5000000 # Table max
>
> prob # Probability of reaching goal
[1] 7.915218e-06
> 1/prob
[1] 126,338.9
> delta
[1] 0
> count
[1] 1000

> br = 10 # Starting Bankroll
> goal = 1000000 # Target bankroll
> odds = 1 # Payoff Odds
> p = 0.49317517 # P(win bet) Bac Player
> max_bet = 50000 # Table max
>
> prob # Probability of reaching goal
[1] 2.579181e-10
> 1/prob
[1] 3,877,199,356
> delta
[1] 0
> count
[1] 1000

> br = 10 # Starting Bankroll
> goal = 1000000 # Target bankroll
> odds = 19/20 # Payoff Odds
> p = 0.50682483 # P(win bet) Banker in Baccarat
> max_bet = 5000000 # Table max
>
> prob # Probability of reaching goal
[1] 8.134146e-06
> 1/prob
[1] 122,938.5
> delta
[1] 0
> count
[1] 1000
>

> br = 10 # Starting Bankroll
> goal = 1000000 # Target bankroll
> odds = 19/20 # Payoff Odds
> p = 0.50682483 # P(win bet) Banker in Baccarat
> max_bet = 50000 # Table max
>
> prob # Probability of reaching goal
[1] 2.466564e-10
> 1/prob
[1] 4,054,223,093
> delta
[1] 0
> count
[1] 1000

lots of MLB and Football this weekend
anyone can and should check my results

Have fun

Quote: WaltFales

I am attempting to find a public/free model that would help me better understand the probability a person could achieve a certain win threshold (i.e. $100,000) with a very small bankroll (i.e. $2,000 or approximately 2% of the desired ending total win/bankroll) in order to prove that providing a player with a small, yet immediate, discount or allowance (such as airfare) after a large loss provides the player with but a miniscule chance of recoverying the loss and breaking even.

Quote: Mosca

I recently turned NOTHING into $2500.

I got up, got showered and dressed, and went to work.

Quote: teddys

LOL, Mosca!

We're not trying to hear that, see? :)

Quote: wroberson

This reminds me of the time I turned 20 bucks into 2500 over a 23 day period.

Quote: rdw4potus

Exactly! Like those folks who bet banker and player at the same time:-)