Laying the 4 or 10 with a hardway hedge. Martingale Style

In several of the Las Vegas Casinos they have upped table limits to 50k (Caesars, and the Bellagio and a few others will per request) This gives the player more room to utilize the Martingale system. I am trying to figure the odds of me blowing my bankroll by the system described below. My bankroll is approximately 54k. My goal is to win 2k each time I play and walk. Here is my system.

Try #1 Lay the 4 @ $100---Pay 5% vig @ $5---Hedge Hard 4 @ $14
This is a $119 bet to win $50----------If the 1&3 hit before the 7 I'll be out for a total of $119 (The 1&3 is the only combination that can hurt me)

Try #2 Lay the 4 @ $240---Pay 5% vig @ $12---Hedge Hard 4 @ $34
This is a $286 bet to win $119---------If the 1&3 hit before the 7 a second time I'll be out for a total of $405

Try #3 Lay the 4 @ $810---Pay 5% vig @ $40---Hedge Hard 4 @ $115
This is a $965 bet to win $405---------If the 1&3 hit before the 7 a third time I'll be out for a total of $1370

Try #4 Lay the 4 @ $2740---Pay 5% vig @ $137---Hedge Hard 4 @ $391
This is a $3268 bet to win $1634---------If the 1&3 hit before the 7 a fourth time I'll be out for a total of $4638

Try #5 Lay the 4 @ $9276---Pay 5% vig @ $463---Hedge Hard 4 @ $1325
This is a $11064 bet to win $5532---------If the 1&3 hit before the 7 a fifth time I'll be out for a total of $15702

Try #6 Lay the 4 @ $31404---Pay 5% @ $1570---Hedge Hard 4 @ $4486
This is a $37460 bet to win $18730---------If the 1&3 hit before the 7 a sixth time I'll be out for a total of $53162 (my entire bankroll)

I stopped at Try #6 because it reaches most place-bet maximums, it also exceeds my bankroll, and since I'm seeking council I hate to seem redundant.

Can anyone calculate the odds of losing the entire roll? Rolling out 6 (1/3's) before a 7 seems like a very difficult feat. In order to walk away with the $2000 intended goal I will have to hit 40 7's. Which isn't a difficult task. I'm just worried how difficult or easy it would be to lose it all. I'm certainly capable of making mistakes so I welcome any critiques or insight on my proposed system. Thank you.

1-in-guaranteed to happen

On a more "serious" note, the odds of hitting 1-3 before 2-2 or any 7 is 2/9
(2/9) ^ 6 = 0.012% = 1 in 8304

No doubt on the "1-in-guaranteed to happen".

Thanks for doing the math. I'd be ok with the 2-2. Losing it all to would be the toughest pill to swallow.

Still 1 in 8304 is tempting.

Quote: 410HEDGE

In several of the Las Vegas Casinos they have upped table limits to 50k (Caesars, and the Bellagio and a few others will per request) This gives the player more room to utilize the Martingale system. I am trying to figure the odds of me blowing my bankroll by the system described below. My bankroll is approximately 54k. My goal is to win 2k each time I play and walk. Here is my system.

Try #1 Lay the 4 @ $100---Pay 5% vig @ $5---Hedge Hard 4 @ $14
This is a $119 bet to win $50----------If the 1&3 hit before the 7 I'll be out for a total of $119 (The 1&3 is the only combination that can hurt me)

Try #2 Lay the 4 @ $240---Pay 5% vig @ $12---Hedge Hard 4 @ $34
This is a $286 bet to win $119---------If the 1&3 hit before the 7 a second time I'll be out for a total of $405

Try #3 Lay the 4 @ $810---Pay 5% vig @ $40---Hedge Hard 4 @ $115
This is a $965 bet to win $405---------If the 1&3 hit before the 7 a third time I'll be out for a total of $1370

Try #4 Lay the 4 @ $2740---Pay 5% vig @ $137---Hedge Hard 4 @ $391
This is a $3268 bet to win $1634---------If the 1&3 hit before the 7 a fourth time I'll be out for a total of $4638

Try #5 Lay the 4 @ $9276---Pay 5% vig @ $463---Hedge Hard 4 @ $1325
This is a $11064 bet to win $5532---------If the 1&3 hit before the 7 a fifth time I'll be out for a total of $15702

Try #6 Lay the 4 @ $31404---Pay 5% @ $1570---Hedge Hard 4 @ $4486
This is a $37460 bet to win $18730---------If the 1&3 hit before the 7 a sixth time I'll be out for a total of $53162 (my entire bankroll)

I stopped at Try #6 because it reaches most place-bet maximums, it also exceeds my bankroll, and since I'm seeking council I hate to seem redundant.

Can anyone calculate the odds of losing the entire roll? Rolling out 6 (1/3's) before a 7 seems like a very difficult feat. In order to walk away with the $2000 intended goal I will have to hit 40 7's. Which isn't a difficult task. I'm just worried how difficult or easy it would be to lose it all. I'm certainly capable of making mistakes so I welcome any critiques or insight on my proposed system. Thank you.

For the math, split it up into two pieces: average bet size for the system, and edge per roll for the system. This is how much you will lose given enough events. You can still get lucky and win with any system, but with enough events you will track the line of the average cost per roll for the system.

$119 will pay $50-5-14 = $31 in 6 out of 9 resolutions
$119 will lose $119-112 = $7 in 1 out of 9 resolutions
$119 will lose $119 in 2 out of 9 resolutions

31 * (6/9) + 7 * (1/9) - 119 * (2/9) = -5 average loss per bet resolved.

Average edge per bet resolved is 5/119 = 4.2%
Chance of winning is 66%
Chance of losing a $7 loss is 11.11%
Chance of catastrophic loss is 22.22%
Rolls to resolve bet is 36/9 = 4. Average edge per roll is 1.05% or $1.25 cost on average for each throw of the dice at $119.

This is your most common scenario. So you're looking at a minimum of expecting to lose $125 per hour with this strategy in the long run. It will go up as your bet size goes up, though. I hope this serves as a starting point. You can follow how I did this math and come up with the cost per roll for the other 5 legs. Then by coming up with the probable chance of being on that leg, you can come up with the average cost per roll that will be higher than $1.25 per roll and plot a chart that will follow a line downward off a cliff. If you are truly interested to see what it looks like, I could simulate it in my Monte Carlo craps simulator and give you a chart showing you exactly what it looks like for hundreds of thousands of randomly generated throws compared to a line of the expected average loss.

Any math guy here could tell you though that it's going to be more than a buck twenty five per roll. Your money would work better for you at the bar. The Wizard advocates flat betting with max odds for maximum entertainment value and the best chance to win. To put it more clearly, the cost of this strategy in the long run would be the same as $304 on the pass line or $320 on the don't pass and however much odds or lay odds you wanted to take. If you want a good chance to win, I would think you would be better off with just $100 on the pass line and be prepared to lay as much up to $600 to get what you want to have the best short-term chance to win at no cost when the four or the ten shows up.

Quote: 410HEDGE

No doubt on the "1-in-guaranteed to happen".

Thanks for doing the math. I'd be ok with the 2-2. Losing it all to would be the toughest pill to swallow.

Still 1 in 8304 is tempting.

It's not really 1 in 8304 unless you are stopping after win #1, which would likely only be $50. if you want to win $2000, it's going to be much worse than 1 in 8304.

Quote: cclub79

It's not really 1 in 8304 unless you are stopping after win #1, which would likely only be $50. if you want to win $2000, it's going to be much worse than 1 in 8304.

Ah, you're right. I misread the original question. The actual math to determine busting the full bankroll is a lot more work.

Quote: 410HEDGE

Try #1 Lay the 4 @ $100---Pay 5% vig @ $5---Hedge Hard 4 @ $14
This is a $119 bet to win $50----------If the 1&3 hit before the 7 I'll be out for a total of $119
(The 1&3 is the only combination that can hurt me)

You Lay the 4 for $100 and do not mind paying a $5 vig for that bet.
well good news, it costs you less than $5 to Lay a 4 or 10 for $100.

do you see why?

Quote: 410HEDGE

In order to walk away with the $2000 intended goal I will have to hit 40 7's.
Which isn't a difficult task.
I'm just worried how difficult or easy it would be to lose it all.
I'm certainly capable of making mistakes so I welcome any critiques or insight on my proposed system.
Thank you.

You need more than 40 7s.

Now the bad news.
Your bankroll will not increase $50 each time you win at step #1.
Sure you win $50 for a $100 Lay4
but you have expenses

I see $50 - $3 - $14 = $net (not $50)
you will need way more than 40 7s to hit the $2k win goal.

I take it you stay at the same step when a hard 4 rolls.

for the probability of hitting a $2k win goal before busting or having to abort
(not having enough $$$ to continue
making the proper step wagers)

I would really just simulate this so
no math would be needed at all.
(when the math is no longer fun)
too easy to make mistakes using math.

BTW,
this system is not new
it is very, very old

Quote: 7craps

You Lay the 4 for $100 and do not mind paying a $5 vig for that bet.
well good news, it costs you less than $5 to Lay a 4 or 10 for $100.

do you see why?
You need more than 40 7s.

Now the bad news.
Your bankroll will not increase $50 each time you win at step #1.
Sure you win $50 for a $100 Lay4
but you have expenses

I see $50 - $3 - $14 = $net (not $50)
you will need way more than 40 7s to hit the $2k win goal.

I take it you stay at the same step when a hard 4 rolls.

for the probability of hitting a $2k win goal before busting or having to abort
(not having enough $$$ to continue
making the proper step wagers)

I would really just simulate this so
no math would be needed at all.
(when the math is no longer fun)
too easy to make mistakes using math.

BTW,
this system is not new
it is very, very old

My wife and I played Craps the other day and she was very excited to have rolled the dice for the very first time. Althouh we lost our $100.00, she managed to have rolled the 4 four times in a row followed by another shooter at the same table rolled 3 fours and 2 tens. I would have to say that this game period is a "Bad Bet" but had you parlayed the fours you could have made on buying a 25.00 bet, 50.00 then 150, then 450, the 1350.00 on that single quarter bet.

Quote: varmenti

I would have to say that this game period is a "Bad Bet"

Why is craps a bad bet?? Can't you beat it by having a positive attitude?

Quote: Beethoven9th

Why is craps a bad bet?? Can't you beat it by having a positive attitude?

Duh! You can only win betting both sides when there's commission/vig charged only on one side. Not like in craps where you pay the vig on both buying and laying the 4/10.

deleted

Quote: wudged

Duh! You can only win betting both sides when there's commission/vig charged only on one side. Not like in craps where you pay the vig on both buying and laying the 4/10.

Well played, sir

Those bac guys really got it easy

If you do want to leverage more money to win less money more often, do it on the free lay odds bet. Find a 10x odds table and bet minimum don'ts and be prepared to lay enough to get to your target until you hit, and reset. The cost is generally $0.02 per roll plus some patience for each $50 or less that you are trying to win. So if you are chasing and trying to win $1000, that's 20 * 0.02 per roll or only 40 cents. That's a lot better than 1% per roll.

https://wizardofodds.com/games/craps/

Comparing edge per roll for a chase system leveraging maximum chance to win per event, I think you would be much more likely to win with 0.037% edge per roll than 1.05% edge per roll. The difference in cost is about 28x in the most extreme case of taking max odds on a 10x table.

What happens is that you end up not just chasing from bad luck, but a combination of bad luck plus the house edge. When this effect compounds you get trapped very quickly and easily.

If you are truly going to put a big bank behind your decision to do this, and are only using luck and math to win, do your homework on how to play the don't pass with lay odds. The Wizard also has answers to these type of questions as they get asked frequently.

Quote: Wizard

For the player who puts a priority on minimizing the overall house edge, the best strategy is to make combinations of pass, don't pass, come, and don't come bets, and always take the maximum allowable odds.

If you are going to chase losses, you better cut the edge to the minimum so you're chasing mostly bad luck instead of bad luck plus the losses from high edge bets like hardways.

If you disagree with this, go try a chase system hopping the hardways and you can learn real quickly how hard it is to win chasing losses from a high house edge bet. If you do this with a smaller bankroll to learn first hand how impossible it is to chase losses on high edge bets, that might be a good motivator to learn how to use the lower edge bets and not use hardways.

Also remember: don't hedge! That hardway idea is a high edge hedge. Not really a good idea at all in the long run. And systems are more vulnerable to these long run gotchas if you keep using them.

GOOD LUCK!

Quote: Tanko

Everything looks better on paper.

Just a few a few hours ago at Mohegan, I saw the 4 hit four times before the seven. Then it hit twice more before the seven on the next hand. No hardways.

In the past, I have seen the ten hit five times in a row before the seven.

In another session, I saw the ten hit five times before the seven, and then hit three more times before the next seven.

Save your money.

I was playing at a local tribal casino and a guy started with $5 on each number. When the 4 hit he toss out a dollar and pressed it to $15. He powered pressed it up to the table limit of $1000 and it hit again - the 7th 4 before a 7 was rolled. All of that in a roll that didn't last 15 minutes and the guy made only one pass. I think I made about $30 on the roll with the pass line winner and a couple of 6's and 8's hit. It would have killed someone laying the 4 even with the hard way hedge bet since most weren't hard 4's.

One night I got the dice after the guy before me and sevened out almost immediately so he went on the don't pass for $500. My first roll was a 4 so he put $2000 on odds and threw in a $200 hard 4 hedge bet. I hit the 4 with a 3 and 1 for a $2700 loss for him. Ouch. I made $45 for the win. This same guy will try to hedge his place bets with a large lay on the 4 or 10 usually $800 to $1000. Of course when that 4 or 10 that he layed hits it's a big loss. His system is to only leave the lay bet up until one of his place bets hits then he'll lower all of the place bets by at least half. It amazes me how much he can lose very quickly betting that way. I think his worst night is something like $12 to $15 grand.

Its got "hedge" and "martingale" in the title and you want us to vote FOR ??

Put you money down,,, take your chance... be right or wrong all the way...not a teensy weensy little of each.

Martingale + hedge = expensive lesson

The only variable in the equation is how long it takes to learn the lesson and how much it costs.

The lucky people die before learning.