Theoretical Win and Pass/Don't Pass Combined Edge
that is NOT what the dispute is about. Ask the Wizard was this againQuote: unJonWe must be using the word “average” differently. Here’s what I mean: Both players have the same EV. Nothing more.
""Hi, if person A makes 1000 consecutive bets on the pass line without backing up his bet, and person B makes 1000 consecutive bets on the pass line and he takes 100X odds whenever possible, doesn’t each person lose the same amount of money?
BLAKE HAAS FROM THOUSAND OAKS
answer: Yes"
Blake even added later in a different post it was NOT about %
actual average loss
I say most do not understand how powerful variance is
over 1k pass line wagers at 100x odds
here
one can see what happens as the odds go up
and the average loss goes down
8 craps players all at the same table
look and see their avg change of ending bankroll
I gave them 1 million betting units for each of the 1k sessions (so they could make every bet)
Simulation of Craps Pass Line Wagers
Odds Multiplier . . . . = 0
Avg (mean) end bankroll = 999985.89 (change of -14.11)
Odds Multiplier . . . . = 1
Avg (mean) end bankroll = 999985.92 (change of -14.08)
Odds Multiplier . . . . = 2
Avg (mean) end bankroll = 999985.95 (change of -14.05)
Odds Multiplier . . . . = 3x, 4x, 5x
Avg (mean) end bankroll = 999986.00 (change of -14.00)
Odds Multiplier . . . . = 5
Avg (mean) end bankroll = 999986.05 (change of -13.95)
Odds Multiplier . . . . = 10
Avg (mean) end bankroll = 999986.20 (change of -13.80)
Odds Multiplier . . . . = 20
Avg (mean) end bankroll = 999986.52 (change of -13.48)
Odds Multiplier . . . . = 100
Avg (mean) end bankroll = 999989.06 (change of -10.94)
the EV 'is all that matters"
folks
cant grasp the variance concept (they are in the majority)
just the ev
that is still better than most
data from all 8 simulations
Simulation of Craps Pass Line Wagers
Odds Multiplier . . . . = 0
Session Bankroll . . . = 1000000.00
Win goal to quit session= 1000000.00
Max. Decisions to quit = 1000
No. Sessions simulated = 1000000
Starting Random seed . = 54321
------------------------------------
All bets are a single unit
------------------------------------
Simulation Results per Session
------------------------------------
Avg. No. games played . = 1000.00
Avg. No. games won . . = 492.94
Avg. No. games lost . . = 507.06
Avg. No. dice rolls . . = 3375.71
Avg. Total amount bet . = 1000.00
Bankroll was busted . . = 0.000% of the time ( 0)
Win goal was met . . . = 0.000% of the time ( 0)
Bankroll decreased . . = 66.067% of the time
Bankroll increased . . = 31.637% of the time
Avg (mean) end bankroll = 999985.89 (change of -14.11)
Simulation of Craps Pass Line Wagers
Odds Multiplier . . . . = 1
Session Bankroll . . . = 1000000.00
Win goal to quit session= 1000000.00
Max. Decisions to quit = 1000
No. Sessions simulated = 1000000
Starting Random seed . = 54321
------------------------------------
All bets are a single unit
------------------------------------
Simulation Results per Session
------------------------------------
Avg. No. games played . = 1000.00
Avg. No. games won . . = 492.94
Avg. No. games lost . . = 507.06
Avg. No. dice rolls . . = 3375.71
Avg. Total amount bet . = 1000.00
Avg. amount bet on Odds = 666.65
Bankroll was busted . . = 0.000% of the time ( 0)
Win goal was met . . . = 0.000% of the time ( 0)
Bankroll decreased . . = 59.303% of the time
Bankroll increased . . = 40.635% of the time
Avg (mean) end bankroll = 999985.92 (change of -14.08)
Simulation of Craps Pass Line Wagers
Odds Multiplier . . . . = 2
Session Bankroll . . . = 1000000.00
Win goal to quit session= 1000000.00
Max. Decisions to quit = 1000
No. Sessions simulated = 1000000
Starting Random seed . = 54321
------------------------------------
All bets are a single unit
------------------------------------
Simulation Results per Session
------------------------------------
Avg. No. games played . = 1000.00
Avg. No. games won . . = 492.94
Avg. No. games lost . . = 507.06
Avg. No. dice rolls . . = 3375.71
Avg. Total amount bet . = 1000.00
Avg. amount bet on Odds = 1333.30
Bankroll was busted . . = 0.000% of the time ( 0)
Win goal was met . . . = 0.000% of the time ( 0)
Bankroll decreased . . = 56.190% of the time
Bankroll increased . . = 43.726% of the time
Avg (mean) end bankroll = 999985.95 (change of -14.05)
Simulation of Craps Pass Line Wagers
Odds Multiplier . . . . = 3x, 4x, 5x
Session Bankroll . . . = 1000000.00
Win goal to quit session= 1000000.00
Max. Decisions to quit = 1000
No. Sessions simulated = 1000000
Starting Random seed . = 54321
------------------------------------
All bets are a single unit
------------------------------------
Simulation Results per Session
------------------------------------
Avg. No. games played . = 1000.00
Avg. No. games won . . = 492.94
Avg. No. games lost . . = 507.06
Avg. No. dice rolls . . = 3375.71
Avg. Total amount bet . = 1000.00
Avg. amount bet on Odds = 2777.69
Bankroll was busted . . = 0.000% of the time ( 0)
Win goal was met . . . = 0.000% of the time ( 0)
Bankroll decreased . . = 53.509% of the time
Bankroll increased . . = 46.238% of the time
Avg (mean) end bankroll = 999986.00 (change of -14.00)
Simulation of Craps Pass Line Wagers
Odds Multiplier . . . . = 5
Session Bankroll . . . = 1000000.00
Win goal to quit session= 1000000.00
Max. Decisions to quit = 1000
No. Sessions simulated = 1000000
Starting Random seed . = 54321
------------------------------------
All bets are a single unit
------------------------------------
Simulation Results per Session
------------------------------------
Avg. No. games played . = 1000.00
Avg. No. games won . . = 492.94
Avg. No. games lost . . = 507.06
Avg. No. dice rolls . . = 3375.71
Avg. Total amount bet . = 1000.00
Avg. amount bet on Odds = 3333.24
Bankroll was busted . . = 0.000% of the time ( 0)
Win goal was met . . . = 0.000% of the time ( 0)
Bankroll decreased . . = 53.058% of the time
Bankroll increased . . = 46.839% of the time
Avg (mean) end bankroll = 999986.05 (change of -13.95)
Simulation of Craps Pass Line Wagers
Odds Multiplier . . . . = 10
Session Bankroll . . . = 1000000.00
Win goal to quit session= 1000000.00
Max. Decisions to quit = 1000
No. Sessions simulated = 1000000
Starting Random seed . = 54321
------------------------------------
All bets are a single unit
------------------------------------
Simulation Results per Session
------------------------------------
Avg. No. games played . = 1000.00
Avg. No. games won . . = 492.94
Avg. No. games lost . . = 507.06
Avg. No. dice rolls . . = 3375.71
Avg. Total amount bet . = 1000.00
Avg. amount bet on Odds = 6666.48
Bankroll was busted . . = 0.000% of the time ( 0)
Win goal was met . . . = 0.000% of the time ( 0)
Bankroll decreased . . = 51.658% of the time
Bankroll increased . . = 48.232% of the time
Avg (mean) end bankroll = 999986.20 (change of -13.80)
Simulation of Craps Pass Line Wagers
Odds Multiplier . . . . = 20
Session Bankroll . . . = 1000000.00
Win goal to quit session= 1000000.00
Max. Decisions to quit = 1000
No. Sessions simulated = 1000000
Starting Random seed . = 54321
------------------------------------
All bets are a single unit
------------------------------------
Simulation Results per Session
------------------------------------
Avg. No. games played . = 1000.00
Avg. No. games won . . = 492.94
Avg. No. games lost . . = 507.06
Avg. No. dice rolls . . = 3375.71
Avg. Total amount bet . = 1000.00
Avg. amount bet on Odds = 13332.96
Bankroll was busted . . = 0.000% of the time ( 0)
Win goal was met . . . = 0.000% of the time ( 0)
Bankroll decreased . . = 50.862% of the time
Bankroll increased . . = 49.012% of the time
Avg (mean) end bankroll = 999986.52 (change of -13.48)
Simulation of Craps Pass Line Wagers
Odds Multiplier . . . . = 100
Session Bankroll . . . = 1000000.00
Win goal to quit session= 1000000.00
Max. Decisions to quit = 1000
No. Sessions simulated = 1000000
Starting Random seed . = 54321
------------------------------------
All bets are a single unit
------------------------------------
Simulation Results per Session
------------------------------------
Avg. No. games played . = 1000.00
Avg. No. games won . . = 492.94
Avg. No. games lost . . = 507.06
Avg. No. dice rolls . . = 3375.71
Avg. Total amount bet . = 1000.00
Avg. amount bet on Odds = 66664.80
Bankroll was busted . . = 0.000% of the time ( 0)
Win goal was met . . . = 0.000% of the time ( 0)
Bankroll decreased . . = 50.229% of the time
Bankroll increased . . = 49.747% of the time
Avg (mean) end bankroll = 999989.06 (change of -10.94)
was that not Jimmy 'the Greek” Snyder 1st. He is very well known (or at least was)Quote: DeMango7Craps; Correct if wrong, I think we are walking into John Patrick territory who espoused never laying odds.
nice catch.Quote: DeMangoYour sim seems to say, the more you lay, the more you lose.
and that should be correct as you CAN lose more betting more.
It was a simulation of 1000 dpass wagers in a session done 1 million times.
interesting that player lost so much over 1 Billion wagers. (variance still rules at times over ev)
I doubt any would consider that to be normal (or close to it)
there is lots of variance using 100x lay odds as there is with 100x taking odds.
I might during some basketball tonite do the same with 8 dpass players at the same table and see what we get.
many have and still do say, "stay away from laying the odds"
up to them, I just say "watch out for variance"
Quote: DeMango7Craps; Correct if wrong, I think we are walking into John Patrick territory who espoused never laying odds. Your sim seems to say, the more you lay, the more you lose.
I think the sims were all done for the players on the same rolls. So all the odds bets will be perfectly correlated. So if over all the sims the odds bets were losers, then it would necessarily follow the pattern that the more odds taken the more lost. And the reverse would be true if the odds bets were aggregate winners over the course of the simulation.
It does seem that the sims provided so far all show odds bets as losers over the course of all the sims. I assume that’s just negative variance, since in any given sim the odds bets should be as likely to win money as to lose money.
My view is no one should be dumb enough to ask “if I bet $1 and someone else bets $101, are we gonna lose the same amount?” and expect Wizard or some mathematician to be like, “Good thing you asked! I can tell the future....”
now for DeMango and interested bystandersQuote: 7crapsIt was a simulation of 1000 dpass wagers in a session done 1 million times.
interesting that player lost so much over 1 Billion wagers. (variance still rules at times over ev)
I doubt any would consider that to be normal (or close to it)
there is lots of variance using 100x lay odds as there is with 100x taking odds.
100x odds player only lost $8.89 million
while his friend 0 odds lost $13.57 million
(not for the ev believers that say,
with NO hesitation,
both players WILL lose the same amount of money after 1000 pass line wagers. Remember the Wizard answer to that question was a flat out YES.)
recall
ev= -3/220*$1*1Billion
they did not come close to losing the same amount of actual money.
another sim for the dpass players
1 BILLION bets
Simulation of Craps Don't Pass Wagers
Odds Multiplier . . . . = 0
Bankroll decreased . . = 66.202% of the time
Bankroll increased . . = 32.611% of the time
Avg (mean) end bankroll = 999986.43 (change of -13.57)
Simulation of Craps Don't Pass Wagers
Odds Multiplier . . . . = 100
Bankroll decreased . . = 50.030% of the time
Bankroll increased . . = 49.957% of the time
Avg (mean) end bankroll = 999991.11 (change of -8.89)
data
Simulation of Craps Don't Pass Wagers
Odds Multiplier . . . . = 0
Session Bankroll . . . = 1000000.00
Win goal to quit session= 1000000.00
Max. Decisions to quit = 1000
No. Sessions simulated = 1000000
Starting Random seed . = 246810
------------------------------------
All bets are a single unit
------------------------------------
Simulation Results per Session
------------------------------------
Avg. No. games played . = 1000.00
Avg. No. games won . . = 479.33
Avg. No. games lost . . = 492.90
Avg. No. games tied . . = 27.77
Avg. No. dice rolls . . = 3375.98
Avg. Total amount bet . = 972.23
Bankroll was busted . . = 0.000% of the time ( 0)
Win goal was met . . . = 0.000% of the time ( 0)
Bankroll decreased . . = 66.202% of the time
Bankroll increased . . = 32.611% of the time
Avg (mean) end bankroll = 999986.43 (change of -13.57)
Simulation of Craps Don't Pass Wagers
Odds Multiplier . . . . = 100
Session Bankroll . . . = 1000000.00
Win goal to quit session= 1000000.00
Max. Decisions to quit = 1000
No. Sessions simulated = 1000000
Starting Random seed . = 246810
------------------------------------
All bets are a single unit
------------------------------------
Simulation Results per Session
------------------------------------
Avg. No. games played . = 1000.00
Avg. No. games won . . = 479.33
Avg. No. games lost . . = 492.90
Avg. No. games tied . . = 27.77
Avg. No. dice rolls . . = 3375.98
Avg. Total amount bet . = 972.23
Avg. amount bet on Odds = 100001.02
Bankroll was busted . . = 0.000% of the time ( 0)
Win goal was met . . . = 0.000% of the time ( 0)
Bankroll decreased . . = 50.030% of the time
Bankroll increased . . = 49.957% of the time
Avg (mean) end bankroll = 999991.11 (change of -8.89)
from the OP
"Hi, if person A makes 1000 consecutive bets on the pass line without backing up his bet, and person B makes 1000 consecutive bets on the pass line and he takes 100X odds whenever possible, doesn’t each person lose the same amount of money?
BLAKE HAAS FROM THOUSAND OAKS
The Wizard answers
Yes.
https://wizardofvegas.com/forum/gambling/craps/8329-craps-pass-no-odds-or-pass-100x-odds-same-loss-revisited/#post123111
the Ask the Wizard asker (jamminbeh)
replied in another thread and says this, that is actually not right, not correct.
a total misunderstanding what variance is all about
"if $5 was bet on the pass line every time,
you will lose the same amount (not percentage) of money on average whether you back the bet up or not.
Backing the bet up has no house edge and no player edge,
so it won't affect the amount of money won or lost.
That's all the wizard was saying and that's all I was asking about."
"
what last 50 pagers? you mean 50 posts?Quote: RSSo basically the last 50 pages are based on how you interpret the question.
what do you mean exactly?
and what IS there to interpret in the question
"Hi, if person A makes 1000 consecutive bets on the pass line without backing up his bet, and person B makes 1000 consecutive bets on the pass line and he takes 100X odds whenever possible, doesn’t each person lose the same amount of money?
BLAKE HAAS FROM THOUSAND OAKS
The Wizard answers
Yes.
actual answer would be something like this from simulation data
only about 1 in 5000 sessions would they actually lose the same amount of money. 1000 wagers for the 100x odds player is way too low to have the -ev totally swamp the standard deviation. so no they do not lose the same amount of money most attempts (4999 out of 5000)
for future finders of this properly worded question (from Ask the Wizard)
good luck understanding all the hidden meanings and messages and
interpreting the question
LOL
Quote: AsheThank you all for your help. I believe I am coming to see how it works. Appreciate your time and efforts!
All the books about craps that I read when I was learning said the same thing about line bets/odds, combining the house edge on the total bet handle. It's correct, but very misleading. The fact is that, although you must make a line bet to take or lay odds, they are still separate bets, one with a 1.4% edge, the other with no edge. Therefore, the expectation is no different, whether a player takes/lays odds or not.
pass line: $5 bet, expected loss $.0707
pass line plus odds: $5 bet, $10 odds, expected loss $.0707
pass line plus odds: $5 bet, $50 odds, expected loss $.0707
This is why expectation is a clearer way to express this than edge.
So, why take or lay odds? To increase variance (volatility), which is the only thing that gives a player a chance to win (some of the time). Taking or laying odds means that players will win and lose more, depending on their luck.
Risk of ruin depends on initial bankroll and volatility, so you need a larger bankroll to stay at the table if you're making odds bets than if you're not; OTOH, if your luck is good, you will win more by taking/laying odds. Here's an illustration:
for 60 $5 pass bets, the expected loss is $4.24, standard deviation $38.73. You have about a 70% chance of ending up between $35 ahead and $43 behind, and you have about a 45% probability of being even or ahead.
for 60 $5 pass bets taking 3,4,5 times odds, the expectation is still -$4.24, but the standard deviation is $190.37, so you have about a 70% chance to come out between $186 ahead and $195 behind, with about a 49% chance of being even or ahead.
for 60 pass bets taking 10X odds, same expectation, but SD $418.63, so 70% chance of ending up between $414 ahead and $423 behind. The probability of being even or ahead goes up to .496.
The more volatility, the less lucky you have to be (defined as positive variance) to overcome the expected loss. OTOH, the more volatility, the more you will lose if your variance is on the negative side.
Cheers,
Alan Shank
P S I am still alive!
Quote: goatcabinAll the books about craps that I read when I was learning said the same thing about line bets/odds, combining the house edge on the total bet handle. It's correct, but very misleading. The fact is that, although you must make a line bet to take or lay odds, they are still separate bets, one with a 1.4% edge, the other with no edge. Therefore, the expectation is no different, whether a player takes/lays odds or not.
pass line: $5 bet, expected loss $.0707
pass line plus odds: $5 bet, $10 odds, expected loss $.0707
pass line plus odds: $5 bet, $50 odds, expected loss $.0707
This is why expectation is a clearer way to express this than edge.
So, why take or lay odds? To increase variance (volatility), which is the only thing that gives a player a chance to win (some of the time). Taking or laying odds means that players will win and lose more, depending on their luck.
Risk of ruin depends on initial bankroll and volatility, so you need a larger bankroll to stay at the table if you're making odds bets than if you're not; OTOH, if your luck is good, you will win more by taking/laying odds. Here's an illustration:
for 60 $5 pass bets, the expected loss is $4.24, standard deviation $38.73. You have about a 70% chance of ending up between $35 ahead and $43 behind, and you have about a 45% probability of being even or ahead.
for 60 $5 pass bets taking 3,4,5 times odds, the expectation is still -$4.24, but the standard deviation is $190.37, so you have about a 70% chance to come out between $186 ahead and $195 behind, with about a 49% chance of being even or ahead.
for 60 pass bets taking 10X odds, same expectation, but SD $418.63, so 70% chance of ending up between $414 ahead and $423 behind. The probability of being even or ahead goes up to .496.
The more volatility, the less lucky you have to be (defined as positive variance) to overcome the expected loss. OTOH, the more volatility, the more you will lose if your variance is on the negative side.
Cheers,
Alan Shank
P S I am still alive!
Bold mine. Answer is BS in my opinion. Why take odds? Because you are in a casino playing craps, so obviously the type of person ok making a negative EV bet. If you are at the table playing negative EV, you should be encouraged to sped your “gambling money” on bets that are less negative. The odds bet is exactly that bet.
Spend you bankroll, that you’ve self selected as being willing to risk on a negative EV PL or DP, instead on the odds bet. Why is this so difficult to accept?
Quote: unJonQuote: goatcabinAll the books about craps that I read when I was learning said the same thing about line bets/odds, combining the house edge on the total bet handle. It's correct, but very misleading. The fact is that, although you must make a line bet to take or lay odds, they are still separate bets, one with a 1.4% edge, the other with no edge. Therefore, the expectation is no different, whether a player takes/lays odds or not.
pass line: $5 bet, expected loss $.0707
pass line plus odds: $5 bet, $10 odds, expected loss $.0707
pass line plus odds: $5 bet, $50 odds, expected loss $.0707
This is why expectation is a clearer way to express this than edge.
So, why take or lay odds? To increase variance (volatility), which is the only thing that gives a player a chance to win (some of the time). Taking or laying odds means that players will win and lose more, depending on their luck.
Risk of ruin depends on initial bankroll and volatility, so you need a larger bankroll to stay at the table if you're making odds bets than if you're not; OTOH, if your luck is good, you will win more by taking/laying odds. Here's an illustration:
for 60 $5 pass bets, the expected loss is $4.24, standard deviation $38.73. You have about a 70% chance of ending up between $35 ahead and $43 behind, and you have about a 45% probability of being even or ahead.
for 60 $5 pass bets taking 3,4,5 times odds, the expectation is still -$4.24, but the standard deviation is $190.37, so you have about a 70% chance to come out between $186 ahead and $195 behind, with about a 49% chance of being even or ahead.
for 60 pass bets taking 10X odds, same expectation, but SD $418.63, so 70% chance of ending up between $414 ahead and $423 behind. The probability of being even or ahead goes up to .496.
The more volatility, the less lucky you have to be (defined as positive variance) to overcome the expected loss. OTOH, the more volatility, the more you will lose if your variance is on the negative side.
Cheers,
Alan Shank
P S I am still alive!
Bold mine. Answer is BS in my opinion. Why take odds? Because you are in a casino playing craps, so obviously the type of person ok making a negative EV bet. If you are at the table playing negative EV, you should be encouraged to sped your “gambling money” on bets that are less negative. The odds bet is exactly that bet.
Spend you bankroll, that you’ve self selected as being willing to risk on a negative EV PL or DP, instead on the odds bet. Why is this so difficult to accept?
Congratulations! You have managed to completely mis-interpret my post!
Cheers,
Alan Shank
You are right of course. My apologies.Quote: goatcabinQuote: unJonQuote: goatcabinAll the books about craps that I read when I was learning said the same thing about line bets/odds, combining the house edge on the total bet handle. It's correct, but very misleading. The fact is that, although you must make a line bet to take or lay odds, they are still separate bets, one with a 1.4% edge, the other with no edge. Therefore, the expectation is no different, whether a player takes/lays odds or not.
pass line: $5 bet, expected loss $.0707
pass line plus odds: $5 bet, $10 odds, expected loss $.0707
pass line plus odds: $5 bet, $50 odds, expected loss $.0707
This is why expectation is a clearer way to express this than edge.
So, why take or lay odds? To increase variance (volatility), which is the only thing that gives a player a chance to win (some of the time). Taking or laying odds means that players will win and lose more, depending on their luck.
Risk of ruin depends on initial bankroll and volatility, so you need a larger bankroll to stay at the table if you're making odds bets than if you're not; OTOH, if your luck is good, you will win more by taking/laying odds. Here's an illustration:
for 60 $5 pass bets, the expected loss is $4.24, standard deviation $38.73. You have about a 70% chance of ending up between $35 ahead and $43 behind, and you have about a 45% probability of being even or ahead.
for 60 $5 pass bets taking 3,4,5 times odds, the expectation is still -$4.24, but the standard deviation is $190.37, so you have about a 70% chance to come out between $186 ahead and $195 behind, with about a 49% chance of being even or ahead.
for 60 pass bets taking 10X odds, same expectation, but SD $418.63, so 70% chance of ending up between $414 ahead and $423 behind. The probability of being even or ahead goes up to .496.
The more volatility, the less lucky you have to be (defined as positive variance) to overcome the expected loss. OTOH, the more volatility, the more you will lose if your variance is on the negative side.
Cheers,
Alan Shank
P S I am still alive!
Bold mine. Answer is BS in my opinion. Why take odds? Because you are in a casino playing craps, so obviously the type of person ok making a negative EV bet. If you are at the table playing negative EV, you should be encouraged to sped your “gambling money” on bets that are less negative. The odds bet is exactly that bet.
Spend you bankroll, that you’ve self selected as being willing to risk on a negative EV PL or DP, instead on the odds bet. Why is this so difficult to accept?
Congratulations! You have managed to completely mis-interpret my post!
Cheers,
Alan Shank
Quote: beachbumbabsNice to see you again, Alan!
Thank you.
Cheers,
Alan Shank
Hey Alan,Quote: goatcabinRisk of ruin depends on initial bankroll and volatility, so you need a larger bankroll to stay at the table if you're making odds bets than if you're not; OTOH, if your luck is good, you will win more by taking/laying odds. Here's an illustration:
for 60 $5 pass bets, the expected loss is $4.24, standard deviation $38.73. You have about a 70% chance of ending up between $35 ahead and $43 behind, and you have about a 45% probability of being even or ahead.
for 60 $5 pass bets taking 3,4,5 times odds, the expectation is still -$4.24, but the standard deviation is $190.37, so you have about a 70% chance to come out between $186 ahead and $195 behind, with about a 49% chance of being even or ahead.
for 60 pass bets taking 10X odds, same expectation, but SD $418.63, so 70% chance of ending up between $414 ahead and $423 behind. The probability of being even or ahead goes up to .496.
alive and hopefully well.
They say grass when it is blue is actually green. But looks blue. Hope your music is still fun to play and makes many smile.
some numbers for your illustration
all values calculated using a Markov chain (in R) except as noted.
(I also did intervals in my code but do not show it here. for later on.)
| 60 PL wagers | 0x | 1x | 2x | 345x | 10x |
|---|---|---|---|---|---|
| loss | 0.49245177 | 0.52334309 | 0.51619337 | 0.50635396 | 0.50597095 |
| win | 0.40558368 | 0.47400793 | 0.48029745 | 0.4832091 | 0.48928245 |
| even | 0.10196455 | 0.00264898 | 0.00350906 | 0.01043694 | 0.0047466 |
| even/win | 0.50754823 | 0.47863537 | 0.48380651 | 0.49364604 | 0.49402905 |
| . | . | . | . | . | . |
| unit stake/ruin | 0x | 1x | 2x | 3x4x5x | 10x (sims) |
| 60 | 1 in 496,465,011,794,733,589 | 1 in 30,883 | 1 in 159 | 11.43% | 46.62% |
| 50 | 1 in 87,855,174,751 | 1 in 1,567 | 1 in 42 | 19.00% | 54.63% |
| 40 | 1 in 5,882,353 | 1 in 142 | 7.40% | 29.65% | 62.83% |
| 30 | 1 in 747 | 4.68% | 18.55% | 43.59% | 72.19% |
| 20 | 1 in 77 | 19.45% | 38.49% | 60.55% | 81.72% |
| 10 | 22.96% | 53.23% | 67.18% | 79.79% | 90.46% |
| 5 | 55.57% | 76.32% | 83.54% | 89.95% | 95.18% |
| 4 | 64.31% | 81.14% | 86.86% | 91.94% | 96.14% |
| 3 | 72.81% | 85.94% | 90.18% | 93.95% | 97.14% |
| 2 | 82.01% | 90.72% | 93.47% | 95.99% | 98.33% |
| 1 | 90.97% | 95.38% | 96.75% | 98.01% | 99.03% |
unit stake is not steak (sounds good right now)
just your betting units
example: $100 buy-in
$10 pass line bets
100/10 = 10 betting units
$5 pass line bets
100/5 = 20 betting units
I have already placed my 2 cents for 100x odds
and how 2 players (0x and 100x over 1k wagers) do not lose the same amount of money.
