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s7pete
s7pete
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May 22nd, 2015 at 11:36:42 AM permalink
Sorry if this is repeating. I recently had a friend that wanted to take up Craps and put together a 'beginners guide' and a recommended abbreviated starter strategy. As part of that, I wanted to include a calculation sheet for the House Advantage for Pass given various Odds multiples (1X, 2X, 3X etc). I searched Wizard of Odds, this site, and all over the place and didn't find an explanation on how to calculate it. Lots of places gave the HA (0X 1.41%, 1X 0.85% 2X 0.61% etc) but not the math behind it. When the math was given it was in terms of fractions which make it laborious to calculate each time, so I put together a spreadsheet. Nothing new - the results agree with established casino math exactly, just easier to use.

I previously posted the text version of the spreadsheet but the editor messed up the columns and it wasn't 'operational'. Here's a link to the spreadsheet you can actually use:

Spreadsheet to calculate HE given Pass/Odds bets

Obviously you don't need to know how to calculate HA, but for the math buffs its entertaining.

- enjoy.
mustangsally
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May 22nd, 2015 at 12:15:17 PM permalink


A B C D E F G H I J K L M N
Craps House Advantage Calculator with X Odds input
Roll Ways Pass$Odds$Risk$WtAvg WinEV Analysis LossEV Analysis (uses Risk$)
$10 $20 Risk$ Win$ PrRoll PrWin TotPrWin EVWin$ PrLoss TotPrLoss EVLoss$
2 1 $10 $0 $10 $10.00 0.0278 0.0000 0.0000 1.0000 0.0278 $0.2778
3 2 $10 $0 $10 $20.00 0.0556 0.0000 0.0000 1.0000 0.0556 $0.5556
4 3 $10 $20 $30 $90.00 $50.00 0.0833 0.3333 0.0278 $1.3889 0.6667 0.0556 $1.6667
5 4 $10 $20 $30 $120.00 $40.00 0.1111 0.4000 0.0444 $1.7778 0.6000 0.0667 $2.0000
6 5 $10 $20 $30 $150.00 $34.00 0.1389 0.4545 0.0631 $2.1465 0.5455 0.0758 $2.2727
7 6 $10 $0 $10 $60.00 $10.00 0.1667 1.0000 0.1667 $1.6667 0.0000 0.0000 $0.0000
8 5 $10 $20 $30 $150.00 $34.00 0.1389 0.4545 0.0631 $2.1465 0.5455 0.0758 $2.2727
9 4 $10 $20 $30 $120.00 $40.00 0.1111 0.4000 0.0444 $1.7778 0.6000 0.0667 $2.0000
10 3 $10 $20 $30 $90.00 $50.00 0.0833 0.3333 0.0278 $1.3889 0.6667 0.0556 $1.6667
11 2 $10 $0 $10 $20.00 $10.00 0.0556 1.0000 0.0556 $0.5556 0.0000 0.0000 $0.0000
12 1 $10 $0 $10 $10.00 0.0278 0.0000 0.0000 1.0000 0.0278 $0.2778
Ós > 36 $23.33 1.0000 0.4929 $12.8485 0.5071 $12.99

ok
it looks a bit better

MAYbe try using
code tags
place

code

inside [] at the start of your table
and [/] at the end of the table
[/this-is-where-code-goes]

still requires some better formatting i say

thank you for sharing!
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mustangsally
mustangsally
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May 22nd, 2015 at 12:26:34 PM permalink
Quote: s7pete

I searched Wizard of Odds, this site, and all over the place and didn't find an explanation on how to calculate it. Lots of places gave the HA (0X 1.41%, 1X 0.85% 2X 0.61% etc) but nowhere the math behind it.

i have that info somewhere
but again here

the player edge for a 1 unit bet = -7/495

for 1X odds the numerator = -7

but the denominator will change to
495 * avg bet in units

(1* 1/3) + (2* 2/3) = 1/3 + 4/3 = 5/3

495 * 5/3 = 825
the house edge for 1 with 1x odds = -7/825
same method for others (except 345X odds and the 5&9 points adjustments)

==================
the avg bet is higher
the ev stays the same
the combined house edge goes lower

try it
Sally
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Romes
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May 22nd, 2015 at 12:47:36 PM permalink
I've never been able to "see" why the house edge goes down with an odds bet. It's a 0% HE bet, so in terms of EV, it shouldn't change a thing...

EV = SummationOfAll(Bet*Advantage)

Example of pass line bet with odds... say you have a pass line bet of $10. The point is established at 6, and you put $50 in odds to win $60...

EV = 10*(.0141) + 50*0.00 = 10*(-.0141) = -.141.

From this you can see that it doesn't matter what amount of odds bet you make, if the house edge on the bet is 0, then it won't effect your overall EV.
Playing it correctly means you've already won.
MathExtremist
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May 22nd, 2015 at 1:40:32 PM permalink
They're looking at it in terms of percentages. The 14c loss on a $10 line bet is much less than 1.4% of the total wager when odds are included.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
s7pete
s7pete
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May 23rd, 2015 at 12:34:55 PM permalink
The explanations for how to calculate EV and HA are in the 'Column Explanations' in the chart above (thank you MustangSally for correcting the columns).

HA = (EVWins - EVLosses)/Amount Risked EV = Sum(ProbabilityWin * $Win) or Sum(ProbabilityLoss* $Loss)

For a point of 6:

PrWin = .0631 $Win 0XOdds = $10 $ Win 2XOdds = $ 50 - The probabilities are the same 0X and 2X but the amounts risked and potentially won
PrLoss = .0758 $Loss 0XOdds = $ 20 $Loss 2XOdds =$ 20 - are dramatically different.

Note: You have to use probabilities, not House Advantage or Odds as you put in your formula. Also, you are not allowed to just have the bet resolved if the point is 6 - you have to do the math over all 36 possibilities of coming out roll.

The house is right - the HA for Pass/Come 0X odds is 1.41% and for 2X odds is .61%; but they want you to play more odds because there's more money on the table to pay your space 'rent'.
s7pete
s7pete
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May 23rd, 2015 at 12:40:36 PM permalink
I had this all worked out years ago. Couldn't find my spreadsheet :{ and had to do it all again. Anyway fun to refresh. The numbers all agree with casino numbers. I always use spreadsheets for calcs so fractions fry my brain. tks for your looking into it. I didn't really mention it, but the chart is just the contents of the spreadsheet for 2X odds. the $10 and $20 at the top of the Pass and Odds columns respectively are inputs so one could figure out $ 150 pass, $500 odds if one wanted. It would be possible to enter different odds amounts in the Odds column if you wanted to, say, take single odds on 4/5 and double odds on 6.
odiousgambit
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May 23rd, 2015 at 1:38:01 PM permalink
Quote: Romes

I've never been able to "see" why the house edge goes down with an odds bet. It's a 0% HE bet, so in terms of EV, it shouldn't change a thing...



Care to go another round? LOL

I really am puzzled as to why such a bright guy has such a blind spot.

Quote: Romes

it doesn't matter what amount of odds bet you make, if the house edge on the bet is 0, then it won't effect your overall EV.



This statement is simultaneously correct and also indicative of the problem. Note I say you are correct with the above.

I think there is one bump we have to get past. Can you agree that EV and HE are not the same thing?

I like formulas, and here is a simple one that has both EV and HE in it.

EV = Bet * HE

note that these alterations do not work:

EV = Bet * EV

HE = Bet * HE

Thus I conclude that EV does not equal HE. Do you concur?
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!”   She is, after all, stone deaf. ... Arnold Snyder
odiousgambit
odiousgambit
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May 23rd, 2015 at 1:40:23 PM permalink
Quote: s7pete

they want you to play more odds because there's more money on the table to pay your space 'rent'.



The house would prefer you not play the free odds. The odds increase the variance, which is something you do not desire if you have the odds on your side. The places where they can get away with it will only offer something like 2x odds.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!”   She is, after all, stone deaf. ... Arnold Snyder
odiousgambit
odiousgambit
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May 23rd, 2015 at 3:26:22 PM permalink
Romes, I am going to propose a bet - stay tuned
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!”   She is, after all, stone deaf. ... Arnold Snyder
mustangsally
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May 23rd, 2015 at 4:04:16 PM permalink
Quote: odiousgambit

I like formulas, and here is a simple one that has both EV and HE in it.

EV = Bet * HE

and never forget this one as it can easily apply to more than one bet
i think you will like it too

Advantage = Net $ / Handle $

Sally
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s7pete
s7pete
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May 23rd, 2015 at 5:13:30 PM permalink
MustangSally
I tried your [] text [/] and got nothing. suggestions?
betwthelines
betwthelines
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May 24th, 2015 at 12:25:04 AM permalink
Quote: Romes

I've never been able to "see" why the house edge goes down with an odds bet. It's a 0% HE bet, so in terms of EV, it shouldn't change a thing...


i don't understand it (the math that is) and most of the math here is just beyond me but i think that i am able to "see" it and explain it (to myself anyway!) in plain vernacular: the HE goes down with greater odds simply because you have a higher percentage of your money at 0% than at 1.4%...

this "struck" the Tough Craps player again in particular a couple-a months ago while playing atta place with what i consider an especially good deal: free buys on the 4 & 10, 20x odds, and during certain weekday hours a $1 minimum line bet...given that the bets (initially 3, eventually 4 [6 if you consider p or c with odds as 2 bets, which of course they are]) started out at $10 each (actually $31, then $42 total), and with the Tough Craps relentless pressing strategy it was a quite hot roll, including seven 4s or 10s & eight 6s,8s,5s or 9s (this is known, not from memory, but precisely because the dollar amounts of the bets was noticed), as the TC gambler looked down & noticed that he now had $758 in action (all subject to the devil...the TC player, eyes-wide-open, does NOT "wonder" why he is almost always losing! in his pursuit of the HUGE win!): of this amount $8 was subject to (initial) vig of 1.41% while $750 was subject to 0%...
tom "home runs are often boring" p
"You can't EXPECT to win. But you CAN play Tough"...tom p, 1974
odiousgambit
odiousgambit
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May 24th, 2015 at 2:54:07 AM permalink
Quote: betwthelines

the HE goes down with greater odds simply because you have a higher percentage of your money at 0% than at 1.4%...



This states it pretty well. BTW in the clear light of morning, I haven't thought of a bet yet that anyone would actually take, in case anyone was wondering.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!”   She is, after all, stone deaf. ... Arnold Snyder
s7pete
s7pete
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May 25th, 2015 at 10:38:51 AM permalink
Quote: odiousgambit

The house would prefer you not play the free odds. The odds increase the variance, which is something you do not desire if you have the odds on your side. The places where they can get away with it will only offer something like 2x odds.



I don't know what the casino 'quants' really look at. I assume it breaks down to Net $/Hour for a table netting out win/loss/staff pay etc. I agree about 'odds increase the variance' but question how the casino views it. I believe the 800 lb gorilla in the room is players getting tapped out (house wins it all) which is, in turn, a function of player play AND BANK.

I did a monte carlo simulation to determine a good bank size for SINGLE ODDS, betting each come. It came out to 100X my unit bet, or $1000 for $10 unit, $ 2,500 for $25, etc. It would be much higher for 2X, 3X etc odds. This agreed almost exactly with Frank Scobele Proper Bankroll for Craps . Most sites claim the biggest mistake players make is under capitalization (same true for start up businesses !). I seriously doubt very many players size up their bank to match the increased spread for higher multiple odds.

So that larger variance in the context of the house vs typically under capitalized players, gives the casino a better chance of 'tapping out' the player. This is a huge, 100%, win for the casino, not incremental back and forth at <.5% HE which hardly pays the rent.

It reminds me of the hoopla over black jack card counting and the casinos initially going to 6 decks. The watched the play and realized that the slower play was losing them more money than the very infrequent player counting cards and not getting detected. They went back to double decks to speed up the game - increase 'table rent'.
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