So i learned something new at the table a few days ago. For those of you that use place bet pressing systems like i do. This is something you may or may not know. Depending if i'm playing on a 5 dollar minimum or 10 dollar minimum table, i like to utilize put bets and get more money for my investment. For example, if i am pressing a place bet on a 5 or 9 to 150 dollars, i make it a 10 dollar put bet (come bet) with 140 in odds. This way i make 220 dollars for my investment instead of 210 if i had a 150 dollar place bet. Or if i had a buy bet on the 5 or 9 for that matter. A 150 dollar buy would pay 225 minus the vig which makes ir 218. I was only making put bets at certain values that offered a 10 dollar cushion because we all know that your flat works on the come out roll and the odds are not. Well i learned that the (if you ask) casino will allow you to make your put bet a place bet for the come out roll and once a point is established you can make it a put bet again. That way you are not risking your flat bets when the shooter is coming out. I have no idea if every casino is like this, but i highly doubt. Just something to think about. Not only is it awesome that i can make a come bet without going through the come, but i can switch from place to put bets whenever i want. Thats a nice perk.

Try to remember this......a casino NEVER allows you to do something, if by doing it, it gives you an advantage. By-pasing the come out roll is not to your advantage ; not being able to remove the put bet is not to your advantage ; a put bet has no financial value to you over a place bet unless you can bet over 5 times odds. 777

Come odds do not work on the comeout by default, but players can call them working if they choose. The dealer then puts an "on" button on them. That is definitely a new one on me! Everywhere I have played a put bet functions exactly as a pass/come bet that has established a point: once the dice have rolled it cannot be reduced, taken down, or called off. I have to wonder how your casino distinguishes a put bet from a place or come bet other than trusting dealers' memory.

You are 100% right. I misunderstood what the dealer was telling me. I recently found out that the reason I was allowed to turn my put bets into place bets is because a seven wiped out my flats. So what I actually did was drop the flat value back on the layout and made them place bets encase a seven showed again. And when a point was established he would just put them back as a flat with odds. Still something different for me. Nice thing to know so I dont loose my flats more than once on the come out. but yes you are right and I know how.come bets work, thats why I was just as surprised to here that as u were I was thinking it was a house rule and allowed that benefit because I didnt go through the come. Now I know

Yeah, you wouldn't want to risk your money when you have a 2:1 advantage, would you? Cheers, Alan Shank Woodland, CA

Goatcabin, I sensed sarcasm in your last comment. Pass line betting is not all its cracked up to be. 2 to 1 advantage is great, but what about the other 24 dice combinations that establish a point. When i risk my money i like to be in control of what numbers i bet on. And i like to get more money for my investment. None of which is controlled with a pass line bet. Wouldn't you rather get payed 39 dollars on a 20 dollar 4 or 10 as apposed to lets say a 10 dollar pass line bet with 10 dollars in odds, which pays 30. I'll take the extra 9 dollars thank you very much. Or 29 dollars on a 20 dollar buy bet on the 5 or 9 (especially if you dont have to pay the vig up front). As opposed to 25 for a 10 dollar pass line bet with single odds. If we are talking 2 to 1 advantage, 24 point combinations, 4 crap, and 8 pass line winner, i'd say thats a 2 to 1 that a point is gonna be established instead of a PL winner or crap. This is the same reason i dont make come bets. No control, i'd have to hedge every come bet with an any crap, and i'm still locking my self into even money. Hence the reason i only make put bets when the investment value to payoff amount is in my benefit. The idea of not betting pass line is enforced even more when the table is 3x 4x 5x odds. Your handcuffed with pressing and the payoff to investment amount isnt in your favor. Matter of fact, the only time i will ever have a "flat" bet working for me is when the table is 100x odds and i was lucky enough to press that high, or im throwing the dice. If you were referring to the 24 to 12 dice combinations as my 2 to 1 advantage. That would only be the case if i had the entire across working with put bets. In that case, yes it would be an advantage for me. However, it isn't very often that i get multiple numbers up to put bet value. Given only one number has a working flat, their is no advantage for me considering the seven is throw more ways that any other one number on the dice. And if i've already lost my flats on one or more put bets, im not going to risk it all again.

Very perceptive! > When the pass bet is not resolved on the comeout, you get a point that is just as likely to win as a place bet on the same number. Yes, it's even money now, but you have the option of taking odds, which have true payouts. It's simply ignorant to compare a line bet, after a point is established, with a place or buy bet, ignoring the 1/3 of the decisions on the comeout. That is a definite advantage of place/buy/lay bets, if you believe in things like "trends", "controlled shooting", the seven being "due", etc. For myself, I'm quite content to let the dice decide the point. That's true, 2/3 of the time the passline goes to a point. However, you then completely ignore the other 1/3, as though it didn't happen. BTW, this thread is about put bets, not buy bets. Buy bets, under certain circumstances, can actually have a lower HA than line bets, but you have to be able to bet $30 a pop at a casino that collects only on wins. However, that' only comparing to the flat bet; the odds bets, of course, carry no expected loss. Huh? Why would you HAVE to hedge a come bet with a craps bet? You're paying for that craps bet, 11%, and cutting into your winnings on the come bet. Let's take your original example of a $10 put bet, $140 odds on 5. Your expected loss is $2, and you have to be at a casino that allows 20X odds in order to make that bet. If you make a $10 pass bet and take odds of $140, your expected loss is 14 cents. The reason your expected loss is so much higher with the put bet is that you are making an even-money bet with only a 40% chance to win. Look here: win $10 * 4 = $40 lose $10 * 6 = -$60 net -$20, divided by 10 = -$2 The $10 bet on the pass line has a 49.29% chance to win. Do you understand that? You combine the 33.3% player advantage on the comeout, 1/3 of the time, with the 18.8% casino advantage, 2/3 of the time, and they combine for that 1.414% HA. When you make a $10 put bet, it's like throwing away $3.33. In both cases, the odds bets have zero expected value. The key here is that when you bet the line and take odds, the 1.414% applies ONLY to the flat portion of the bet, so if you bet $10 on the line and $150 (or whatever) on odds, your expected loss is still only 14 cents. A $150 place bet on 6 has an expected loss of over $2.25, and a $10 put with $140 odds on 6 has an expected loss of 91 cents. In my view, that's a lot to pay for being able to pick your number. Cheers, Alan Shank Woodland, CA

Goatcabin, You said, "Yes, it’s even money now, but you have the option of taking odds, which have true payouts." This statement is ridiculous considering in my last post i proved that even money flats and true odds pay less up to a certain value. 4 and 10, Buy bet for 200 pays 390, 10 dollar flat with 190 odds pays 390. 5 and 9, 100 dollar buy pays 145, and 10 dollar flat with 90 odds pays 145. So if you are telling me that you have a bankroll large enough to start off betting 200 + dollars on the 4 or 10 and 100 + on the 5 and 9. Then sure i say make PL bets all day long, but you should take odds greater than the value above or else you are just losing money. And yes this is given a 10 dollar table and paying the vig after you win the number. I personally do not have a bankroll that large. I usually start off with an average bet of 44 inside or 66 inside. So with that being said, I avoid the passline, because i would lose money on the point number for every hit until i press up to the above value amounts or higher. And even then, i am handcuffed with a 3x 4x 5x odds table. Has to be 20x or higher as you stated. As far as being ignorant to compare place and buy bets to PL bets after the comeout, i think i proved the benefit to not locking yourself into even money for the average player that doesnt have an extremely large bankroll. Sure you could win a PL bet before the point is established, but we agreed their is something like a 77 percent chance you wont win. and a 66 percent chance ur gonna get stuck recieving less payout for your investment then you could have. Plus you just locked in ten dollars for that slim chance you want to call off or remove your bets. And anyone who doesnt want to be in control of what numbers they bet on, is just playing like a novice. And i'm not saying you dont understand the game, but why in gods name would you accept a 4 or 10 over a 5 or 9. When basic math tells us that 5's and 9's roll much more often than 4's or 10's. And thats just keeping it simple. And once again, the only way i see this not being a significant issue, is if you plan on covering the entire across anyways and you bet the value of 200 + on the 4 and 10, and 100 + on the 5 and 9. And thats right after the point is established. If thats not done, i don't see any benefit to just accepting any point number rolled. I know what this thread is about, i started it. And i dont see why buy bets can't be compared to put bets. These are all viable options on a dice table. So why not brainstorm options and compare all possibilities. Goatcabin "Buy bets, under certain circumstances, can actually have a lower HA than line bets, but you have to be able to bet $30 a pop at a casino that collects only on wins. However, that’ only comparing to the flat bet; the odds bets, of course, carry no expected loss." I dont understand this statement. Lets use a 30 dollar 5 or 9. Pays 44 dollars. If its bought. If we only compare to a flat bet, the place bets and buy bets are always a better payout because flats are even money only. So lets compare to a 10 dollar PL bet and 20 in odds. Pays 40. My buy bet just made me 4 dollars more for the same risk, and i could remove my entire investment if i wanted. The statement where you said the odds bets, of course, carry no expected loss. I dont see how, any bet on the table can be lost. Truthfully goatcabin, you like to raddle off crazy numbers and really over think this game. Its simple, your risking 30 to get payed 40 and im risking the same to get payed 44. I dont see the argument. Even if you removed your odds, then your flat has a better chance of being lost than won, no matter what number its on. The statement about hedging, is probably more of just a preference than a decision i make based on odds or advantage. I hate betting the PL (obviously), so when im throwing i like to hedge my passline with an any craps. And after 5 years of throwing. Which i know isnt as much as you im sure. I benefit from the small hedge more than you would think. I just find it extremely aggravating to lose money before i even start the game. So i hedge, so the only way i lose money is when the point is established right away. Which is often, but hey its only two dollars. This is the only hedge i will ever make in the game. I do know that hedging can minimize losses, but also minimize ur wins. But in this case, its minimal. All of the expected loss and HA and percentage talk is just great. I truthfully think you dove way too far into a book and aren't keeping it as simple as it should be. And yes i've read some advanced craps books and i didn't think all those numbers held a significant amount of difference in order to make me change my style of play. What i think you were missing, is that you would have to take odds at that value in order to make that comparision. And still, you better be at a table that allows 20x odds or higher. I dont care what the expected loss is. If you arent taking odds up at that significant cross over point. Where the flat and odds starts paying more than the buy bets, then you are losing so much more than the petty couple dollars that you are talking about. Because i couldnt care less bout 1/3 or 2/3. If i can only afford to make a 20 or 30 dollar bet on a number. And i may not even have enough money to bet all numbers. You better believe im gonna be in control, and im gonna get more money for my return. Plain and simple. Trust me, im not trying to change your style of play. I could care less. I just dont see the benefit to PL betting and feel other parties that read these posts should get each view and make their own decisions.

MY PERSONAL OPINION ONLY TO ALL THAT READ THIS THREAD... always look for a table with a low minimum bet and high maximum, good odds availability (20x-500x), a casino that accepts vig after the bet is won, not upfront(if this is the case, please start buying the 5 and 9 at 20 dollars), and depending on your PL betting preference, ONLY bet it when you are throwing the dice for the table minimum. THANKS LUCKY4688

Here's my quote:"When the pass bet is not resolved on the comeout, you get a point that is just as likely to win as a place bet on the same number. Yes, it’s even money now, but you have the option of taking odds, which have true payouts. It’s simply ignorant to compare a line bet, after a point is established, with a place or buy bet, ignoring the 1/3 of the decisions on the comeout." Then you turn right around and do it again, comparing the post-point pass bet with a place, put or buy bet as though they were parallel. This is like an ostrich hiding his head in the sand! I was just pointing out that the buy bets do not have the same disadvantage that a put bet has. You obviously do not understand the concept "expected loss". "No expected loss" does not mean the bet cannot be lost; it means that the payout exactly balances the probability of winning. Here again, you persist in comparing bets that are not comparable. A line bet has two ways to resolve; a place, put or buy bet only one. It's simple, all right; you simply cannot understand that the pass line bet must be analyzed in both its parts. As you point out, you cannot assume that a pass bet will end up on a point of 5, or any other specific point. 1/3 of the time, it will be resolved on the comeout, winning twice as often as losing. Your comparison is meaningless. (more to follow) Cheers, Alan Shank Woodland, CA

It's clear that you failed to understand what you read, since you have no conception of how to evaluate a line bet, with or without odds. Without that information, you are totally incompetent to compare line bets with any other type of bet. I'm gonna try this one more time. A passline bet can have several different outcomes; you have to consider them all, and their relative probabilities to have anything intelligent to say about them. Look at this: win comeout 440 lose comeout 220 win on 6 125 lose on 6 150 win on 8 125 lose on 8 150 win on 5 88 lose on 5 132 win on 9 88 lose on 9 132 win on 4 55 lose on 4 110 win on 10 55 lose on 10 110 add up to 1980 OTOH, a place bet really is simple; there's one way to win and one way to lose: place 6 win 5 lose 6 The passline bet is at an advantage on the comeout, at a disadvantage after a point has been established. When you make a put bet, you accept the disadvantage without every having had the advantage. This is the situation where you have to take at least 5X odds to get the same or better payout as a place bet. I have NEVER made a put bet, nor will I. Buy bets can, under the bet conditions, be low-HA, but you still have to pay the vig based on the whole bet. With pass + odds, the HA is only on the line part. This is why the expected loss is much lower if you keep the line bet small. If you want to increase your bet, you can increase the odds part without accepting any further expected loss. $5 pass line with single odds -- expected loss $.07/bet win a few more than you lose increase to double odds " win a few more than you lose increase to 3X, or to 3, 4, 5X " Then, if you want to bet more and the table is just 3, 4, 5X, you need to increase the flat part, which involves another $.07 of expected loss per bet. Now, compare to starting out with $6 each on 6 and 8. The expected loss is $.09 on each per bet. win a few more than you lose increase to $12 each, expected loss doubles, too, $.18 on each win a few more than you lose increase to $18 each, expected loss goes to $27 on each Every increase adds expected loss. Cheers, Alan Shank Woodland, CA

I hate to sound dumb, what is a put bet? i know what a place bet, and a come bet with odds are, but I have no idea what a put bet is? Also I'd like to know there's a 90% chance I have my odds working on my come bets on the come out roll (unless its a controlled shooter doing the all 7's set).

A put bet functions in exactly the same way as a come bet that established a point. The only difference is that the player, rather than the dice on the comeout roll, decides which point the bet has established. The bet is made the same way a place or buy bet is made, by putting the cheques on the table and telling the dealer what number the bet is to be put on and how the wager is to be split (between flat and odds). This last part is what distinguishes the bet from its place and buy counterparts: because it functions the same way as an established come bet part, or maybe even all, of the bet will be paid at even money. The advantage of put bets over place and buy bets is realized at table which allow high odds multiples. At greater than 4x odds (5x on 6 and 8) put bets pay better than place bets. What level of odds must be taken to pay better than a buy bet on the same number depends on the amounts being bet, when the vig gets taken, and how far you can push the house (i.e. how much over a $20 increment you can go for the same vig). Not all houses and jurisdictions allow put bets. In Atlantic City, for example, a player cannot make or add to a Pass Line bet after a line point is established, an action which would in effect be a put bet. (That said, however, I have seen players at a $5 table allowed to add $1 to bring a line bet up to $6 so they could take $15 odds on points of 6 and 8.) I don't know what you're asking here. By default come odds do not work on line comeout rolls, but players can override that default (and have the odds working) by so telling the dealer, who should then put an "on" button on the bet, so I don't know what "90%" refers to. One thing you cannot do is have some of your come odds and place bets working and some not. It takes too long to mark multiple bets individually, so everything either works or not. If you do want to turn bets on selectively then those that you do not want working must be taken down (and if desired put back up after the line comeout roll), which is not going to make you very popular with dealers absent generous tipping.

If I were you, Jeremiahj, I would not assume any control of a dice outcome by any shooter, no matter what set is used. Watch the dice bounce when they hit the table and then the back wall. Do you really think there's any relationship between the way they were set and the way they end up? As far as having your come odds working on the comeout, they are just as likely to win or lose then as any other time. If they are good bets, they are good bets. When I was making come bets, I always had my odds working, and a good dealer will remember and always put the ON button on (one of) them. I stopped making come bets, for two reasons: 1) When 3, 4, 5X odds became the norm, I decided I would rather put more money on odds, with no expected loss, than on come, where there's a 1.4% "tax". 2) When I had one or more come bets outstanding and a passline bet, I experienced "mixed feelings" about the comeout roll -- a seven would win the passline, but lose my come bets and odds. I decided I wanted to root for the seven wholeheartedly on the comeout and against it on point rolls. Of course, this second reason has nothing to do with the math of the game; it's just about my enjoyment of the game. I, like Midnight, don't know what you mean by "90% sure". Cheers, Alan Shank Woodland, CA

goatcabin, I always understood what you were saying about comparing the place bets/buy bets/put bets to PL bets. However, we agreed that their is 8 ways to win a pass line bet, 4 ways to lose, and 24 ways to establish a point. Which is 66.6 percent of the time your PL bet will not win or lose on the comeout and just become an even money wager which limits your profits. I look at those numbers as not in the players favor. Wouldnt you? The 2 to 1 advantage for me gets set aside and not as much attention when their is 24 other ways to get stuck with EVEN MONEY RETURN. I understand there is action on a PL bet prior to the bets i make. Which may change HA %, expected loss, and all the other stuff you were chattin away about. But how about this, i cover the across on the come out (working) and then we compare your PL bet to the other wagers i placed. I GUARANTEE you i get more money in return for my investments. When you say a PL bet has two ways to resolve, a place/buy/ and put only one. Do you mean two ways because the flat already was working on the comeout and theirfore added a "second way" for your PL bet with odds to be determined. And i knew that when you said "expected loss" that you were referring to a more complicated concept. I will admit, i dont know how YOU determine expected loss, nor have i ever tried to figure it out. However, i stand bye what i said, If i bet 20 dollars, i stand to lose 20 dollars. And if im gonna risk a certain amount, im gonna get the most for my money. Your right, 5x odds is necessary, however we are a little more advanced here, lets get back to buy bets. Examples: 10 dollar 4 with 50 dollars in odds pays 110, whether it is a put or PL bet with odds. A 60 dollar place bet pays 108. Heres a solution, buy it and get payed 117. 5 and 9: 10 dollar flat with 50 in odds pays 85, place bet pays 84, heres an idea buy it for 60 and get payed 87. Apparently you dont buy numbers at all. (and if the casino allows a vig after you win, then the vig argument is out the window). So if a PL bet with odds pays the same as put bet with odds, (ONCE AGAIN) unless your bankroll supports initial wagers of values that high, then you are simply losing money. This is a concept you have not addressed yet. Setting aside the come out roll, because we already stated ill just work my numbers. I'm simply gonna make more money than your pass line wager if you dont have high value bets. Ok so lets assume every increase adds expected loss. lets compare a 10 dollar PL bet with 10 dollars in odds on the 5 and 9. pays 25 right. if you place it, it pays 28. You make 3 dollars more. The expected loss is, it cant be more than that. And if you buy it you make 29, 4 dollars more. So whats the argument. So even if their is an expected loss because i didnt risk a flat on the come out and get the 1/3 possibility of winning, im still making more money for my investment. how did you come up with 55 to 110, 440 to 220,etc.,? I think i understand the ratio but not why you used those exact numbers. I want to understand your concept fully now, because i've done a lot of math on these numbers, and played at alot of casinos. I've been told by dice instructors and many dealers that my concepts are very accurate. So im intrigued, but still cannot find one idea you have come up with to show me that betting a flat even money wager on the come out is worth it.

lucky4688, Just to quickly answer your question as to how those numbers came about without stepping on Alan's toes (I'm sure he has a more elegamt way of doing it). They are derived from the 1980 rolls. Divide the 1980 by the 36 we are so familiar with and you have 55. For the CO results just individually take the 2, 3, 12, 7 & 11 number of ways and multiply by 55. The 7 has 6 ways times 55 = 330, the 11 has 2 ways times 55 = 110 and together the possible CO wins total 440 for the 1980 rolls. The Point numbers are a little different. You have to consider both the ways to win plus the ways to lose. For the 4 or 10 there are 3 ways to win and 6 ways to lose (the 7) for a total of 9 events. Take the number of ways for the specific number to be made times the 55 and divide by the number of event (that number's ways to make plus ways to make a 7). Now take the result and multiple by the number of ways to make the number to see the wins or multiply by the number of ways to lose (6 ways of the 7) to see the losses. For the 4 or 10 it's 3x55/9x3 for wins or 3x55/9x6 for losses, for 5 or 9 it's 4x55/10x4 for wins or 4x55/10x6 for losses, for 6 or 8 it's 5x55/11x5 for wins or 5x55/11x6 for losses. Hope I was clear and this helps. Wilken

Thank you for saving me the time to explain in complete detail the attached spread sheet showing how the house advantage on a pass line bet is determined. Just to clarify, let's take the "Make point 9" row as an example. There are 4 ways out of 36, or 220 ways out of 1980, for a PL bet to establish a point of 9. We know that once a point of 9 is established it will make 4 times for every 6 times it misses, or 40% of the time over all. 220*.4=88 times a point of 9 will make in a theoretically distributed set of 1980 trials. Why do we use 1980 trials? Because that is the lowest number of trials (55 sets of 36 theoretically distributed rolls of two six-sided dice) that produce an integer number of occurrences for every possible resolution. As the spreadsheet shows, the house expects to win 1.4141...% of every dollar bet on the Pass Line. Now let me address lucky4688 and compare a $32 Pass Line bet to $32 across, always working. 1.41414% of $32 is $0.4525. For the $32 across we have to break the bet up into its separate numbers and apply the house advantage to each, as follows. Code: Numbers House Amount Expected Placed Advantage Bet Loss 4/10 6.6667% $10 $0.66667 5/9 4.0000% $10 $0.40000 6/8 1.5152% $12 $0.18182 Total $32 $1.24849 Liars figure but figures don't lie. By placing $32 across you are expected to lose 2.759 times as much as a $32 Pass Line bettor. Comeout decisions do matter. [Edit: The last two lines of the attached spreadsheet should of course be for a point of 10, not 4.]

Let's talk about that 2:1 ratio, I mean 1/3 comeout resolutions vs. 2/3 points. You dismiss the comeout resolutions as unimportant, as though they just didn't happen. OK, imagine you had a three-sided fair coin with two faces showing heads and one tails. Since the heads should come up 2/3 of the time, you dismiss the possibility of getting tails and offer your friend 3:1 odds, you betting on heads, he on tails. Unless you are VERY lucky, you are going to get hammered, because 1/3 of the time you are paying him $3 while 2/3 of the time he is paying you $1. Now, here is a little lesson on expected loss for you. Code: ways result product 1 * -3 = -3 2 * +1 = +2 net -1 So, you are expected to lose a unit every three bets. This would not be very smart, but it is essentially what you are doing when you dismiss the comeout roll for the line bets. So, how much do you bet across? Tell me, and I will come up with a "commensurate risk" pass/odds bet and compare them. Of course, you understand that you are going to lose your entire spread on a comeout seven, while I will win my flat bet, so you start out with a very serious handicap. I determine expected loss just like everyone else who understands a bit of probability does. In craps, you take the number of ways you can win and the number of ways you can lose times the payoff, add them up and divide by the total number of ways. Here's an example for a place bet on six: Code: ways result product 5 * +7 35 6 * -6 -36 add products - 1 So, on average, for every 11 place six bets, you expect to lose 1 unit. The expected loss, then, is 1/11 of a unit per bet. If your unit is $1, then the expected loss is $1 / 11 = $.0909. Since your base bet is $6, the percentage (house advantage) is .0909 / 6 = .01515, or 1.515% If you look in any craps book, you will see that figure quoted for place bets on 6 and 8, probably rounded to 1.52%. It's not a secret and it's not rocket science. As I showed above and have stated over and over, you cannot set aside the comeout roll and make any kind of valid comparison between line bets and place, put or buy bets. The "perfect 1980" is the lowest number of decisions that allow all the possible outcomes to be expressed as integers (whole numbers). You start out like this: comeout win 8 ways comeout loss 4 ways point established 24 ways But, if you want to know how many times the point is 6, say, and how many times it wins and loses, you have to go to bigger numbers. For example: point six established 5 ways But the probability of a point of six winning is 5/11, and 5/11 * 5 doesn't come out to an even number. Anyway, you keep multiplying until all the possibilities come out as integers and you end up with 1980. There are some interesting things you can figure from the "perfect 1980". For example, if you add up all the winning outcomes you get 976, and 1004 losing outcomes. Divide 976 by 1980 and you get .492929.... Divide 1004 by 1980 and you get .50707..., which is the same as (1 - .492929). Subtract .492929 from .50707 and you get .01414, or 1.414%. Look that up in your craps books. That is the often-quoted house advantage on the pass and come bets. That's another way to figure the house advantage, but it only works for even-money bets (1:1 payoff). Add up the ways to win on points and you get 536, vs. 784 ways to lose, totalling 1320. Divide 536 by 1320 and you get .40606, which tells you that the average probability of winning a point is .406. Of course, this is the same as the average probability of winning a place, put or buy bet. If you divide 784 by 1980, you get .395959..., which is the probability that the shooter will seven out on any decision. You can use these numbers to figure the average number of decisions before a shooter sevens out, 2.5255. Since the average number of rolls for a decision is 3.375, this means that the average "hand" is 3.375 * 2.5255 = 8.52 rolls. There's a lot of good stuff in there, lucky. So, you tell me what your across spread, working on the comeout is, and I'll prove to you that you're expected to lose a lot more money than I am. BTW, thanks to Jacob for increasing the character limit so that I don't have to use two posts to cover my points. I promise not to exceed 20,000 characters! > Cheers, Alan Shank Woodland, CA

goatcabin, Thanks for taking the time to try and explain what you feel so strongly about. I am not convinced yet, but humbled. I read it, but im gonna have to take some time and monkey with the numbers on paper. You were asking what i cover across. I'll just explain the way i've been playing for quite some time. I always bypass the comeout. I'll wait for a point. I'll cover the inside for 44 or 66 depending on how much i brought with me. Sometimes, i cover the across. If i do, its for 64. I always take the first three or four hits and once my initial investment is back, i start to press. I use a few different pressing systems depending on table rules, however its safe to say its about a 50% press. I only press the numbers hit and i never remove bets or call them off. If i'm throwing, the only difference is that i bet table minimum on pass line and hedge with an any craps. I press the odds on the point as close to 50% as i can. Unless im in vegas im usually at a table with 100x odds, 10 dollar minimum, and allows me to pay the vig after. What is your style of play? Other than PL betting

Excellent work Alan. Calculating expected value (loss) is important so one can compare different types of bets. A Binomial Distribution table can also show what can happen betting 11 place 6 bets. You can see at 5 wins it is the most probable outcome at a net loss of $1. But you also have a 37.86% chance of winning 6 or more place bets for a profit of $12 to $77. Variance works both ways. You also have a 38.53% chance of winning 4 or less place bets for a net loss of $14 to $66. Code: wins (or less) exactly (or more) NET 0 0.13% 0.1272% 100.00% -$66.00 1 1.29% 1.1656% 99.87% -$53.00 2 6.15% 4.8567% 98.71% -$40.00 3 18.29% 12.1418% 93.85% -$27.00 4 38.53% 20.2364% 81.71% -$14.00 5 62.14% 23.6091% 61.47% -$1.00 6 81.81% 19.6743% 37.86% $12.00 7 93.52% 11.7109% 18.19% $25.00 8 98.40% 4.8795% 6.48% $38.00 9 99.76% 1.3554% 1.60% $51.00 10 99.98% 0.2259% 0.24% $64.00 11 100.00% 0.0171% 0.02% $77.00 What I like about these distribution tables is what I had seen in 40 years of dealing and playing dice. As easy as it is to win only 1 place bet in 11 tries and lose $53, you have a very slightly better chance of winning 9 place bets for a $51 profit. Without doing too much math, I leave that fun to Alan, if you understand normal distribution and standard deviation, the SD for 11 place 6 bets would be 1.65 and for 11-$6 place bets on the 6 would be $19.82. I was so much younger back in 1982.