Craps Bet Race

After 3,500 bets for each, which one or ones has the best chance of showing a profit?
Between these 6 bets.

Place 5
Place 6
Pass Line (no odds)
Field Bet (Pays 3X on a 12)
Hardway 6
Fire Bet
(why these??? I heard a conversation between 3 Craps players about this. So I looked it up)

Unlimited casino credit so every bet can be made.
1 unit wager for each bet.

My first thought is a tie between the Pass Line and the Place 6 strictly from a HE point.
It got my vote.

Here is a chart of the 6 bets over 3500 wagers (cumulative)
Maybe it helps

Is this a per bet resolved (so the place bet is counted when it hits or loses, but rolling a 4 on a place 6 doesn't count as a bet)?

Also, how can a bet lose 5000 units, when the total amount bet is 3500 units?

Without doing any math, this is just gut instinct.

Either the Fire Bet, or the Field Bet.

I believe the lower house edge bets will all consistently show the least amount of loss, but the question is which one has the best chance of showing a win.

To do that, we have to have a bet with high variance, coupled with good luck.

The Fire Bet fits that bill.

Edit: I missed the Hard 6 bet as a choice. That too is a high variance bet, but my gut tells me that is not the right answer. Perhaps it should come ahead of the Field bet though.

Is 27.32 the right answer ?

kudos to 7craps for a great thought provoking graph and question.

I am looking forward to the thread conversation on this one.

Quote: thecesspit

Is this a per bet resolved (so the place bet is counted when it hits or loses, but rolling a 4 on a place 6 doesn't count as a bet)?

Also, how can a bet lose 5000 units, when the total amount bet is 3500 units?

Yes, Per bet resolved.
I had $6 as the unit bet for each bet when I made the chart.
The data table shows same action.
I will double-check just to make sure.

Quote: Buzzard

Is 27.32 the right answer ?

Yes, in some circles.
That is actually a strange number you offered.
27 is my fav # (my birth date)
32 is my 2nd fav (Sandy Koufax #)

If I know what I'm talking about (and I could get schooled) the answer is the fire bet.

That's enough events that all the grind strategies are going to lose consistently, and the fire bet still has a chance to win with two big hits.

The others: not much chance at all for most RNG's on a computer.

Trick question, though. And of course, I could get schooled!

Just trying to make a profit on any bet listed flat betting with your rolls is a good way to gauge non-randomness of your outcomes.

Quote: 7craps

Yes, in some circles.
That is actually a strange number you offered.
27 is my fav # (my birth date)
32 is my 2nd fav (Sandy Koufax #)

I made a bet too many years ago to shut a Dodger fan up. Talk about DUMB luck. My hometown Orioles actually beat Sandy in a World Series game. LOL

Of Course Willie Davis making 3 errors in the 5th inning sort of helped !

My guess is :

Orange is fire bet.
Purple is hard six
Teal is passline
Red is Place 5
Green is the Field
Blue is place 6

I'm not 100% sure though

Quote: 7craps

Yes, Per bet resolved.
I had $6 as the unit bet for each bet when I made the chart.
The data table shows same action.
I will double-check just to make sure.

Awesome, cheers, look forward to the answers. I notice how close the orange, blue and teal lines are at the 0 mark... all three have similar chances to end up in the positive.

Some, maybe most, will not know how to "read" that chart.
That makes many just go with the gut or simple brain power.

So far nice observations about the chart.

The conversation I heard about these bets ended up with 2 guys agreeing that the higher payoff type bets
would win out in the long run simply because they paid more than the safer bets that paid the least. The other guy flat out disagreed.
Where they got 3500 bets, I do not know. but the final order is interesting to see.

The actual answers can and have been calculated directly using some Excel code and another program I have
that sums over every possible outcome at each trial.
Both programs came to the same answers as did a quick simulation that was very close to those results.

Using EV and SD to find the answer with the normal curves,
a few that are really skewed just returned a wrong order in half the cases.
But I will also show those numbers as well.

I guess another chart to make would be which bet or bets still has a decent probability of showing a profit, say after
15,000 bets made. Every bet but the Field bet resolves with more than one roll.

We should know and understand that the longer we keep making these -EV bets, the less likely, but not impossible,
we are to come out ahead in the end.

Quote: Ahigh

If I know what I'm talking about (and I could get schooled) the answer is the fire bet.

That's enough events that all the grind strategies are going to lose consistently, and the fire bet still has a chance to win with two big hits.

The others: not much chance at all for most RNG's on a computer.

Trick question, though. And of course, I could get schooled!

Just trying to make a profit on any bet listed flat betting with your rolls is a good way to gauge non-randomness of your outcomes.

I thought the Fire as my second choice knowing it's high variance,
but I also know that the 6pt hit is about 1 in 6,000 so in just 3500 bets, it must be less than a 50% shot to hit it.
I will do the math for that, but that is why I did not choose the Fire Bet. I feel it may have a better chance after say 6,000 trials or more.

5pt hits is about 1 in 600 so the expected number of those is about 6 hits.


So I also have run the numbers for 500, 1k, 2.5k, 5k, 10k and 20k bets

Ah, ha
The order, the bet with the best chance of showing a win,
changes as the more trials are made.
I will add this table in a few days with a final answer.

Quote: 7craps

I thought the Fire as my second choice knowing it's high variance,
but I also know that the 6pt hit is about 1 in 6,000 so in just 3500 bets, it must be less than a 50% shot to hit it.
I will do the math for that, but that is why I did not choose the Fire Bet. I feel it may have a better chance after say 6,000 trials or more.

5pt hits is about 1 in 600 so the expected number of those is about 6 hits.


So I also have run the numbers for 500, 1k, 2.5k, 5k, 10k and 20k bets

Ah, ha
The order, the bet with the best chance of showing a win,
changes as the more trials are made.
I will add this table in a few days with a final answer.

For flat betting, there is a number of bets where the chance of coming out ahead is negligible.

The number of events required is smaller for bets that pay even money.

To have an chance at all, ie nonzero, you are required to have a higher payout bet as the number of trials increases. That in conjunction with luck.

That is my perspective assuming we are talking about random data.

Nothing you will ever do can make lifetime wins just flat betting black on an unbiased Vegas roulette wheel over 100,000 trials. Nothing....

This thread is starting to tax my mental ability to keep track of it. That was my joke for bumping this thread. Hoping an answer shows soon.

I ran all these bets through my C++ program to calculate ev and SD, and I will compare my results to those published. I used "Pay Table 1" for the Fire Bet and the Wizard's table of probabilities. (24, 249, 999 payoffs)

When the answers are given, I will also provide, for each bet, "the other side of the coin", i.e. the loss given the same amount of bad luck as required to break even.
Cheers,
Alan Shank

BTW, pass/DP w/odds bets were not included in this poll, and they would be clear winners, given the low ev and high volatility.

If you know or can calculate the ev and SD for two bets for a given number of decisions, you can figure which bet will do better, depending on how good or bad one's luck is. For example, let's compare $10 pass with $5 pass, double odds for 3500 decisions.

$10 pass $5 pass, double odds
ev -$494.95 -247.47
SD $591.55 $845.23

So, if each player has average luck, the $10 pass player will lose twice as much. However, since the SD is much higher for the $5 w/odds, as the players have worse luck, eventually the odds player will lose more. We can figure the point at which that occurs this way:

initial advantage = 494.95 - 247.47 = 247.48 (rounding)
different in SD = 845.23 - 591.55 = 253.68

IA/diff = 247.48 / 253.68 = .9756

What does this mean? If both players experience "negative variance" to the tune of .9756 standard deviation, they will each lose the same amount, i.e. this is the "crossover point" where the more volatile method starts to lose more. If we visualize a "graph of luck", like this:

---------------------------------------------------
-3 SD -2 SD -1 SD ev +1 SD +2 SD +3 SD

we could plug in numerical outcomes for each bet. We would see that the $5, odds player does better from the right of the graph, left past the ev point to just before the -1 SD point. To the left of that, the $10 pass player does better, i.e. loses, but less.

From this IA/diff figure, we can get the probability of one bet doing better than another for a given number of decisions from the Z table. The portion of the table from the right end to -.98 SD is about 84% of the total area under the curve, so for 3500 bets, the probability is about .84 that the player betting $5 pass and taking double odds will come out ahead of the player betting $10 pass, no odds.
Cheers,
Alan Shank

3500 bets
per bet resolved so if Place 6, then rolling a 4 doesnt count for anything. it's either roll a 6 or 7 to count as one bet.
1 unit wager for each bet starting at $6?

3500 x 6 = $21,000 if he lost 3500 straight bets?

orange is highest loss and win at +/- $5000.
like everyone else, i say orange = firebet and purple = Hard 6


oh, and i dont understand the Y axis (probability %). there's a 100% chance Orange will be +$5000??

It's cumulative frequency. 100% chance that the orange player will end up between -infinity to $5000+

Quote: thecesspit

My guess is :

Orange is fire bet.
Purple is hard six
Teal is passline
Red is Place 5
Green is the Field
Blue is place 6

I'm not 100% sure though

You be right.
from left to right at the bottom of the chart
Fire, Hard6, Place5, Field3X, Place6, Pass

Here is the order for 3500 resolved bets

HE	Finish	Bet	Win prob %	Simulated	Lose prob %
-20.76%	1	Fire	21.59052	22.747%	78.40948
-1.41%	2	Pass	20.61604	20.440%	79.38396
-1.52%	3	Place 6	20.18781	20.307%	79.81219
-2.78%	4	Field 3X	7.64350	7.577%	92.35650
-9.09%	5	Hard 6	3.41365	3.361%	96.58635
-4.00%	6	Place 5	2.19483	2.214%	97.80517

Here is the order at different number of resolved bets
At 2,500 bets, the Fire, Pass and Place 6 are a virtual tie.

# of Bets >>>	500	1k	2.5k	3.5k	5k	10k	20k	50k
Place5	6	6	6	6	6	6	6	6
Field 3X	3	4	4	4	4	4	4	4
Place6	2	2	2	3	3	3	2	2
Hard6	5	5	5	5	5	5	5	5
Fire Bet	4	3	3	1	1	1	1	1
Pass Line (no odds)	1	1	1	2	2	2	3	3

The probabilities at each number of bets and order.
I deleted my file by mistake. I have to re-do the data

EV and SD values for the 3500 wagers
At higher # of trials, the Fire Bet, Field and Hard 6
even/ahead values are way off.
Not really normal distributions
table below is for 1 unit bets.
Original chart used $6 wagers

Type of Bet	sd of he	ev trials	SD trials	unit sd	HE	ev/sd	even/ahead
Place5	1.9875%	-140.0000	69.56126609	1.1758	-4.00%	-2.012614	2.207761%
Field 3X	1.9308%	-97.3000	67.57937936	1.1423	-2.78%	-1.439788	7.496365%
Place6	1.8235%	-53.0303	63.8226687	1.0788	-1.52%	-0.830901	20.301485%
Hard6	4.8593%	-318.1818	170.0754616	2.8748	-9.09%	-1.870827	3.068451%
Fire Bet	27.7643%	-726.6000	971.7516009	16.4256	-20.76%	-0.747722	22.731394%
Pass Line (no odds)	1.6901%	-49.4949	59.15488175	0.9999	-1.41%	-0.836701	20.138032%

OK, the results are in. Here's what I got, just calculating ev, SD and finding the probability of breaking even or better indicated by the ev/SD ratio.



Those losses are if the player has the same degree of bad luck as the degree (% of SD) of good luck to break even.

BTW, a $5 pass bet, single odds (avg. bet $8.56) for 3500 bets has a .3346 probability of breaking even, with a corresponding loss of $495.
Nice thread, 7Craps!
Cheers,
Alan Shank

thanks for the brain teaser 7craps!

and thanks goatcabin for the info about passline WITH even single odds is better than the firebet.
else we'll see a wave of people rushing to donate their $ to firebets w/their insane house edge.

The interesting results, to me at least, is that the pass line and place6 finished just behind the Fire Bet in 3,500 bets.
That is a lot of bets made for the FB. (30,000 dice rolls)

So 3 bets were close to each other (they were about tied at 2500 bets)

and the other 3 were sad finishers.
A lot of luck needed to get profit from them as well as from all the bets over that many wagers.