Low House Edge Roulette
Thread Rating:
August 11th, 2013 at 10:25:15 AM
permalink
Let us say you have a roulette wheel that pays 1.11:1 on red/black (.05% edge). Min is 1 and max is 25.
What is the best way of turning 500 into 1000? What is the probability you achieve this before going bust?
Initially I thought best way would just to bet 500 on red (because there is till house edge even if small).
But then my friend has this scheme based on betting on both red and black and changing amount based on how much you have left.
What is the right answer?
What is the best way of turning 500 into 1000? What is the probability you achieve this before going bust?
Initially I thought best way would just to bet 500 on red (because there is till house edge even if small).
But then my friend has this scheme based on betting on both red and black and changing amount based on how much you have left.
What is the right answer?
August 11th, 2013 at 10:35:06 AM
permalink
Quote: qweretyqLet us say you have a roulette wheel that pays 1.11:1 on red/black (.05% edge). Min is 1 and max is 25.
What is the best way of turning 500 into 1000? What is the probability you achieve this before going bust?
Initially I thought best way would just to bet 500 on red (because there is till house edge even if small).
But then my friend has this scheme based on betting on both red and black and changing amount based on how much you have left.
What is the right answer?
The less you wager overall, the closer your chances will be to 50% to double your money. But with house edge so small, you will have close to 50% chance of doubling your money no matter how you play.
Note that if you bet 500 on red and win you would actually overshoot your target (because payout > 1x) so to double to 1000 exactly, you should bet 473.933649289 on red. If you miss it you will have 26.066 left to try to reach 1000.
August 11th, 2013 at 10:55:27 AM
permalink
Min and max Bet limits?Quote: qweretyqLet us say you have a roulette wheel that pays 1.11:1 on red/black (.05% edge).
Min is 1 and max is 25.
Not with a max bet of 25Quote: qweretyqInitially I thought best way would just to bet 500 on red
some R code and results for max bet of 25
Bold Play
(bet at each spin what it takes to hit your bankroll target or everything)
1st is a bet on 1# only
2nd is for any 18/38 bet
Note: wager is an integer only (this is reality)
> br = 500 # Starting Bankroll
> goal = 1000 # Target bankroll
> odds = 35 # Payoff Odds
> p = 1/38 # P(win bet) Roulette 1# straight up
> max_bet = 25 # Table max
>
> prob = 0
> p_fail = 1
> count = 0
>
> while ( (br >= 1) & (br < goal) & (count < 1000) ) {
+
+ # Compute probability 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] 0.4281457
> delta
[1] 0
> count
[1] 1000
> br = 500 # Starting Bankroll
> goal = 1000 # Target bankroll
> odds = 1.11 # Payoff Odds
> p = 18/38 # P(win bet) Roulette (Even Money type bet)
> max_bet = 25 # Table max
>
> prob = 0
> p_fail = 1
> count = 0
>
> while ( (br >= 1) & (br < goal) & (count < 1000) ) {
+
+ # Compute probability 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] 1.410215e-06
0.000001410215
1 chance in 709,111.73
> delta
[1] 0
> count
[1] 1000
Bold Play
(bet at each spin what it takes to hit your bankroll target or everything)
1st is a bet on 1# only
2nd is for any 18/38 bet
Note: wager is an integer only (this is reality)
> br = 500 # Starting Bankroll
> goal = 1000 # Target bankroll
> odds = 35 # Payoff Odds
> p = 1/38 # P(win bet) Roulette 1# straight up
> max_bet = 25 # Table max
>
> prob = 0
> p_fail = 1
> count = 0
>
> while ( (br >= 1) & (br < goal) & (count < 1000) ) {
+
+ # Compute probability 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] 0.4281457
> delta
[1] 0
> count
[1] 1000
> br = 500 # Starting Bankroll
> goal = 1000 # Target bankroll
> odds = 1.11 # Payoff Odds
> p = 18/38 # P(win bet) Roulette (Even Money type bet)
> max_bet = 25 # Table max
>
> prob = 0
> p_fail = 1
> count = 0
>
> while ( (br >= 1) & (br < goal) & (count < 1000) ) {
+
+ # Compute probability 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] 1.410215e-06
0.000001410215
1 chance in 709,111.73
> delta
[1] 0
> count
[1] 1000
please start over and state the parameters exactly as imagined
thanks
winsome johnny (not Win some johnny)
August 11th, 2013 at 2:08:37 PM
permalink
Quote: qweretyqLet us say you have a roulette wheel that pays 1.11:1 on red/black (.05% edge). Min is 1 and max is 25.
What is the best way of turning 500 into 1000? What is the probability you achieve this before going bust?
Does only red/black has a 0.05% house edge ? What about the number bets?
In general, for any stop goal with a positive house edge, you want to minimize total bet amount that hits the table.
If only red/black has 0.05% house edge:
Probably the best strategy to turn 500 into 1000 would be to bet table max on red or black (never both!) if you hold 972.25 or less.
If you have more, adjust your bet so that you hit 1000 exactly if you win.
However there is a subtile low threshold where you would actually want to play higher variance bets (even if the house edge is a lot larger).
If all other bets have 0.05% house edge as well:
In general, you would want to play the single number bets with table max, as long as a possible win will not bring you above 1000.
Why the number bets ? Because they have large variance. If you play low variance bets (i.e. table min on red/black), the house edge will grind you down before reaching the goal.
August 11th, 2013 at 3:57:41 PM
permalink
yea sorry obviously you can't bet 500 at once. I meant to say 1 and 25 min and max bet on red/black. Your code definitely helps.
Let me start over with a new problem:
Using any strategy starting with 250, what is the best way of making $4000.
Minimum bet is 1 and maximum bet is 1000.
To make it simple lets just use the odds of this one casino online:
Single Zero Roulette
Wager Placed Casino Payout
Any 1 number 35.65x
Any 2 number 17.32x
Any 3 number 11.21x
Any 4 number 8.16x
Any 6 number 5.11x
Any 12 number 2.06x
Any 18 number 1.04x
The reason I ask is that my friend deposited 250 and made it into 4000. Was just trying to get a gauge of how repeatable this is.
His strategy was basically betting on the dozen with a progression, but if he was up a lot already he would risk more and go further in the progression, and if he fell down he would lower his bet trying to make 100 at a time. That combined with betting 1 red,1black, if you lose 5 red, 5black for 10 turns, lose that 25 red,25 black etc.
I have a feeling he just got really lucky
Let me start over with a new problem:
Using any strategy starting with 250, what is the best way of making $4000.
Minimum bet is 1 and maximum bet is 1000.
To make it simple lets just use the odds of this one casino online:
Single Zero Roulette
Wager Placed Casino Payout
Any 1 number 35.65x
Any 2 number 17.32x
Any 3 number 11.21x
Any 4 number 8.16x
Any 6 number 5.11x
Any 12 number 2.06x
Any 18 number 1.04x
The reason I ask is that my friend deposited 250 and made it into 4000. Was just trying to get a gauge of how repeatable this is.
His strategy was basically betting on the dozen with a progression, but if he was up a lot already he would risk more and go further in the progression, and if he fell down he would lower his bet trying to make 100 at a time. That combined with betting 1 red,1black, if you lose 5 red, 5black for 10 turns, lose that 25 red,25 black etc.
I have a feeling he just got really lucky
