Prop Plays - What Costs More?

[heavy]

Okay, I'm going to crank up a thread here where I'll pose a question and we'll let you take shots at the answer. Then we'll see if we can come to a consensus at the end of it all. Let's start with a simple one:

Which play costs you more for an hour of continuous play, assuming sixty rolls per hour? $20 in the Field on every toss or $5 each on all the hardways, always working? Yeah, we'll replace those hardways when they fall.

Let's hear it from you guys who know math better than the fat guy.

h

[acpa]

Easy one, hard ways have a larger house advantage than the, even if the field pays triple on either the 2 or 12. With out looking the numbers up the Hards are a worst bet by two or three times the field.

And that is ignoring the occasional casino that pays triple on both the 2-12.

Noah

[heavy]

Agree or disagree? ACPA put a little thought in it, but I am not sure the answer is as simple as he thinks. Or maybe it is . . .

[Maddog]

OOOOhhhh this is a very interesting question. I have done some figuring and believe I have the answer, however I don’t want to post it just yet.

I will say that Heavy is correct that it is not as simple as which bet has the most house advantage. The trick to this question has to do with the number of bet resolutions. The Field bet will be resolved on each roll, so 60 times in this example question. The hardway bets do not resolve on every roll, so you must calculate the expected life of the bet within the 60 rolls (or average HA per roll).

[heavy]

Ba-da-boom. And the resolved Field bet wins or loses $20 on every decision (except on the 2 our 12 where we'll assume we're playing a 2X in the Field layout). Unless a seven knocks them all off, the dice can only knock off one $5 hardway bet per decision. But payoff on those bets range from 7-1 to 9-1. Thorny calculations for the "over sixty" among us with a touch of dementia setting in. Break out the calculators guys. I'd sure like to see some numbers and an explanation of how you came up with them. I think you have a roadmap now.

[Golfer]

Oooooppppps. Calculator is broke. My money is that the Field is better.

[heavy]

Come on, Golfer. Take a shot at it. Let's start with a simple given for a random game. Sixty tosses - ten sevens. That means, assuming you're always working both bets - then you'll lose a total of $200 on each bet.

Now, out of sixty tosses how many losing Field decisions can we expect?

Out of sixty tosses how many losing hardway decisions can we expect (number rolls easy)?

Now let's flip that around and see how many winning Field decisions we can expect?

How many winning hardway decisoins can we expect?

Now make four columns on your pad. Add up the total of wins and losses under each wager.

Net out the numbers and compare results.

Tell me which one wins - the $20 Field Bettor or the $20 Hardway Bettor.

[wudged]

According to wizard of odds http://wizardofodds.com/games/craps/, hardways have a per roll house edge of 2.78%. The field bet has the same edge at 2.78%, on a 2 or 12 pay triple. In this case, they are essentially equal as far as final outcome goes, but with field bet being resolved every single roll, one would expect more variance.

Reducing the field to only double on 2 and 12 gives a house edge of 5.56%, so the hardways is clearly the better bet.

[heavy]

Okay, but are you comparing apples to apples or apples to oranges? The wiz's stated house edge on the hardways per roll is 2.78%. But per resolved wager the house edge is 9.09% on the six and eight and 11.11% on the four and ten. The house edge on the triple the field layout is 2.78% per resolved wager - or 5.56% per resolved wager on the double field layout. This sort of takes me back to my old adage that "you can't spend percentages - only dollars."

By the way, some of you old timers may recall that I proposed a similar question on the old forum many years ago, where we compared a $5 Field bet with a $5 Place bet on the nine. Ask any dealer and he will tell you the place bet on the nine is a better bet. Ask him what the house edge on the nine is and he probably won't know (4%). Then tell him the house edge on the Field bet is only 2.78% so in theory the Field should be a better bet. But again, the Field bet is resolved every toss of the dice - so the house gets it's 2.78% of that $5 on every toss. It only gets it's 4% on the nine place bet when the bet is resolved (wins, where they pay you less than true odds at 7-5, or loses where they take the entire bet). So in that case, even though the house edge was less on the Field bet - the Place bet on the nine was a better wager. But does the same hold true for the $20 Field versus the $20 Hardway bet?

To be completely honest, I haven't even run the numbers yet. But I have given you a template I think that will provide you with the answer.

Yeah, I'm trying to stimulate a few of those brain cells . . . and get you guys to post a bit as well. Let's see if anyone else has a thought. . .

[acpa]

I still stand by my answer as it relates to Randies. Might have a different answer if I am looking at controlled shooter. I not secure the per roll is relevant assuming you have a proper bank roll to support it.

After writing the above I retread the question and with you specifying a time fram then I should the frequency of decision, which HA doesn't do.

Noah

[wudged]

A per roll edge is apples to apples, mathematically.

Let's assume you play for 36 rolls instead of 60, for simplicity. (The percentages will obviously be the same regardless of number of rolls.) Your expected outcomes are: [tr] [td]hardway[/td][td]expected hits[/td][td]win amount[/td][td]expected losses[/td][td]loss amount[/td] [/tr] [tr] [td]4[/td][td]1[/td][td]35[/td][td]8[/td][td]-40[/td] [/tr] [tr] [td]6[/td][td]1[/td][td]45[/td][td]10[/td][td]-50[/td] [/tr] [tr] [td]8[/td][td]1[/td][td]45[/td][td]10[/td][td]-50[/td] [/tr] [tr] [td]10[/td][td]1[/td][td]35[/td][td]8[/td][td]-40[/td] [/tr] [tr] [td]Total[/td][td]4[/td][td]160[/td][td][/td][td]-180[/td] [/tr] This gives a net of -20.

Now for field (triple 12): [tr] [td]Roll[/td][td]expected hits[/td][td]win amount[/td] [/tr] [tr] [td]2[/td][td]1[/td][td]40[/td] [/tr] [tr] [td]3, 4, 9, 10, 11[/td][td]14[/td][td]280[/td] [/tr] [tr] [td]5, 6, 7, 8[/td][td]20[/td][td]-400[/td] [/tr] [tr] [td]12[/td][td]1[/td][td]60[/td] [/tr] [tr] [td]total[/td][td]36[/td][td]-20[/td] [/tr] Again, a net of -20.

Taking the 2.78% edge from wiz, and multiplying it by 36 rolls, we come up with 1. This means your expected loss is going to be 1 unit, which in this case is $20, shown in the calculations above

[heavy]

Very good, wudged. You saved me from having to do the math myself. Everyone on the same page here? Agree or disagree? If we're all good then I'll probably come up with another example for use to play with.

[wudged]

I forgot to mention, unless the very last roll is a 7, you will have money left on the hardways to pick up, if you so wish, as well!

[Mad Professor]

Two other things you'll want to consider when comparing wagers like this, is total-dollar exposure and hand-to-hand volatility.

~In the case of the every-roll $20 Field-bet; you'll be getting a paying-hit, on average, 1-in-2.25 rolls...with total action of $1200 being wagered for every 60-roll hour.

~In the case of the $5 each on all the Hardways wager; you'll be getting a paying-hit, on average, 1-in-9 rolls...with total betting-action of around $333 for every 60-roll hour.



MP

[DeadCat]

My brain hurts.

[Maddog]

What is really interesting about this question is that it makes us think about the effect of bet resolution rate. The Wizard of Odds has given an excellent tool for helping to calculate out the "cost" of bets over time at the following link: Wizard Of Odds - Appendix 2

Using this tool makes the calculations much easier since he has done all the probability work and we just need to plug in the numbers.

Resetting the original question:

60 rolls per hour, betting $5 each on the hardways ($20 total), the expected cost is:
60 * ((5*.0278)+(5*.0278)+(5*.0278)+(5*.0278)) = $33.36 loss per hour

60 rolls per hour, betting $20 on the Field (12 pays Double)
60 * (20*.0556) = $66.72 loss per hour

60 rolls per hour, betting $20 on the Field (12 pays Triple)
60 * (20*.02778) = $33.34 loss per hour

And using the same tool one can look at the expected cost of playing the Iron-Cross (ABS) strategy:
60 rolls per hour, bet $10 on 5, $12 on 6 & 8, $5 in field (12 pays Triple)
60 * ((10*.0111)+(12*.0046)+(12*.0046)+(5*.02778)) = $21.62 loss per hour

Fun huh?

[heavy]

Okay, that was fun. Now, any more comments on the other problem I posted (much easier) at this link:

viewtopic.php?f=4&t=504

[heavy]

A little "re-boot" post for you prop bettors. How much do those bets cost you? Or do they PAY over the long run?

[DanF]

I tried something that works fine lately.

Never bet the field unless it’s lighting up like a litebright.

Place 10$ hardways high on 4&10 only on a comeout winner.

Working not so bad!

[London Shooter]

Over here the hardways bets would lose more slowly. We do have triple on the 12 on the field but we get an extra half unit payout on our hardways.