ANATOMY OF A BANKROLL MURDER: HOW IT HAPPENS

The total probability of complementary events is exactly 1, so the probability here is: P(X ≤ 26) = 1 - 0.02 = 0.98. When to use dice probability calculator? There are a lot of board games where you take turns to roll a die (or dice), and the results may be used in numerous contexts. Home Craps Discussion Advanced Craps playing 5 days a week and trying to win a $100 a day, how to bet? Discussion in ' Advanced Craps ' started by scott22, Mar 1, 2015.

In Part 1, I explained why the theoretical becomes reality and why you can’t avoid the theoretical house edge. Let’s now look at how the typical loss happens and then add the element of tilt to our play. Note: if you only want to see the final numbers, look to the bold text. I included the explanations so that you may double check and critique my math, if you are so inclined.

Tilt: what is it?

First, let’s discuss this issue of tilt. It’s broader than you may think.

• An odds bet is paid at your true odds of winning (explained in next section). This differs from other craps wagers, which are usually paid at slightly less than your true odds. For example, pass line offers 251:244 true odds. But you’re only paid at 1:1 for a win, which is where the casino gets its house edge.
• House odds and true odds aren't hard concepts to understand. They're fundamental to gambling games, though. Casinos make their profits by paying bets off at less than the odds of winning. This holds true for every bet in the casino. Understanding how odds work is a fundamental step in becoming an educated gambler.

Tilt is simply any stimulus that causes a gambler to deviate from his normal play. It’s really that simple and broad. While most people associate tilt with loser’s tilt – where a gambler chases after his loses by increasing his bets or making more bets – there are many forms of tilt.

All the forms of tilt also have a similar element in common: they compel the player to bet more, exposing more of his bankroll to the house edge. Here are some forms of tilt.

Winner’s tilt

Winner’s tilt is when the high and rush of winning compels the bettor to bet more. Winner’s tilt has the same effect as loser’s tilt in that the player will bet more because he is winning. Winner’s tilt also has the added danger of causing the player to start wasting his bankroll away from the table. Tilt doesn’t always just end when the player leaves the table.

FOMO tilt

There is what I call FOMO tilt, meaning the Fear Of Missing Out, where the bettor starts making bets because he is afraid of missing out on a win. The player normally would not make these bets, but since he’s already been making the bet, he must continue making the bet. He is afraid that once he stops, it might just hit. He has a fear of missing out.

Frustration Tilt

Our player is place betting the inside numbers and the outside numbers are hitting. Joe Gambler then switches to the outside numbers, and the inside numbers start hitting. Out of frustration, he now bets across, which is something he usually does not do.

It’s not wining or losing that’s setting off the gambler, it’s frustration.

Alcohol Induced Tilt

Alcohol should have its’ own tilt category, due to its’ availability in a casino. When players become drunk and start betting more, they not betting more because they’re happy, sad, frustrated, winning, or losing; rather, they’re just betting more because they’re drunk and have a false sense of bravado for no good reason.

The result is the same: player bets more or differently than they would have bet if they had not been drunk.

All forms of tilt do one very dangerous thing: expose more of the bankroll to the house edge.

Tilt acts as amplifier to the house edge. Tilt is an accomplice to the bankroll murder. That’s why in this anatomy of a murder, it’s not proper to solely blame tilt. If the player were to play a positive expectation game, and he started doubling his bet because of loser’s tilt, it would mean that the player would have double the expected gain per bet (assuming the player did not make adverse decisions that reduced his expectation).

It’s not difficult to imagine a craps game – or any casino game – with a positive expectation: just look at the game from the casino’s perspective. The casino is effectively playing craps with a positive expectation. The casino owner might get drunk, make a rash decision and triple his maximum limits. Oh no, the poor casino owner is going to have his clocked cleaned by the martingale bettors. Yea, not really.

Tilt is not a problem until the negative expectation from the house edge is added to the equation.

Let me show you how the house edge and tilt work by breaking down the cost inflicted by the house hedge, and then show you the cost when various levels of tilt is added. Have you ever wondered, ‘what is this hardways bet costing me’?

The House Edge, In Action

Let’s break down the amount of the loss attributable to the house edge.

Let’s say that Gambler Joe likes to play craps, and he is going on vacation. Joe takes a $2o00 bankroll with him. His plan is to play for 4 hours per day, and his vacation is for 5 days in beautiful Las Vegas. In effect, he will play a total of 20 hours of craps during his vacation.

Assuming at the average craps table there will be 100 rolls per hour (note that the Hard Rock Real Craps game, which lasts approximately one hour, has 110 rolls https://youtu.be/7KL8H91s28I). This means that Joe will play about 2000 rolls.

Let’s breakdown his play, and see what it should theoretically cost Joe to play craps on his vacation.

Without tilt and sticking to his normal play

This is how Joe likes to play. Based on my observations at the table, this is a common way for many players to play. So that Joe has a reasonable chance of not being broke in the middle of his vacation, he will bring a $2000 bankroll…

• $10 pass line + $20 odds
• $5 on the hard ways 6 and 8
• $5 craps on the come out
• Place bet of $12 on the 6 and 8

Let’s now do the math on his expected loss per bet over the course of his trip. You can just look to the bold print for the final figure of each bet.

• $10 pass line + $20 odds
  • House edge of 1.41% on the pass line, and considering the average number of rolls per pass line bet, the house edge per roll is .42% (citation, Wizard of Odds). We will ignore the odds bet, since there is no house edge. On an expected loss per roll, the expected loss per roll can be broken down into 4.2 cents per roll.
  • The average number of rolls for a pass line bet to settle is 3.38 (citation, Wizard of Odds).
  • At 100 rolls per hour, his expected loss per hour from pass line betting is $4.20.
• $5 each on the hard ways 6 and 8
  • House edge of 9.09%, which is 2.78% per roll, considering it takes on average 3.27 rolls to settle the bet (citation, Wizard of Odds). This works out to an expected loss of 13.9 cents per roll, per number.
  • The average number of rolls for a hard ways bet to settle is 3.27 (citation, Wizard of Odds).
  • At 100 rolls an hour, his expected loss per hour from betting both the hard ways 6 and 8 is $27.80 ($13.90 per number).
  • Note that Joe could reduce his expected hourly losses by turning the hard ways off on the come out.
• $5 Any Craps on the come out
  • One roll bet, so the house edge is 11.11% per bet and per roll.
  • Since this bet is on the come out only, assuming a new pass line bet every 3.38 rolls, this bet will be made around 29 times in an hour. His expected loss per Any Craps bet is 55.55 cents per roll.
  • At 29 Any Craps bets per hour, his expected loss per hour from betting the Any Craps is $16.10
• $12 each on the Place bet of 6 and 8
  • House edge is 1.51%, which is .46% per roll, considering the average number of rolls to settle the bet. Thus the expected loss per roll is 5.5 cents per roll, per number.
  • The average number of rolls for a Place bet to settle is 3.27 (citation, Wizard of Odds).
  • At 100 rolls an hour, his expected loss per hour from betting both the Place 6 and 8 is $11.04 ($5.50 per number).

Expected loss with normal play

Gambler Joe is going to play over 20 hours. This is his expected loss over the vacation for each bet.

• $10 pass line + $20 odds
  • Expected loss over the vacation is $84.
• $5 each on the hard ways 6 and 8
  • Expected loss over the vacation is $560.
    • Note: Now do you understand why the casino allows a $1 or $5 hard ways when the table minimum is $10+?
• $5 Any Craps on the come out
  • Expected loss over the vacation is $322.
• $12 each on the Place bet of 6 and 8
  • Expected loss over the vacation is $220.

So the grand total of all his gambling over 5 days is that itcosts Gambler Joe a theoretical $1,186.

If Gambler Joe’s were to cut out the hard ways and the prop betting, his gambling vacation would be relatively cheap at $304.

Theoretical Probability Of Winning Craps Odds

Even if Joe were to stick to his betting because he loves the hard ways, one could argue that $1,186 as the cost of gambling over a 5-day vacation is not that bad.

So let’s add tilt into Joe’s gambling; not a lot of tilt, just a little.

With mild tilt

While Joe has put a dent into his bankroll, he hasn’t lost his entire bankroll.

This is now the story of how Joe loses his entire bankroll, propping him to consider quitting.

Joe has a bad session or a bad day, and now, he increases his bets.

Joe is not going to play on tilt all of the time. Let’s say that he only goes on tilt, 1/3 of the time (rounded up to 34%). Let’s take his exact play from above, and start increasing his bets because he tilts. Assume 100 rolls per hour, and on 66 of those rolls, he plays his usual game (his ‘normal’ rolls), but he adds to his bet, hoping to chase his losses and bets more (’tilt’ rolls). It doesn’t matter when he presses the bets, because the effect is the same whether he presses in intervals, all at the end, or in the middle of the game.

• $10 pass line + $20 odds
  • Tilt causes Joe to increase his pass line bet to $25 because he is at a table that allows a max of 3x, 4x, 5x. He cannot increase his odds without increasing his pass line bet.
  • 100 total rolls an hour, of which 66 are normal play, and 34 are on tilt play.
  • At 66 normal rolls, expected loss per hour is $2.77
  • At 34 tilt rolls, expected loss per hour is $3.57
  • At 100 rolls per hour, Joe’s expected loss per hour from pass line betting with tilt is $6.34.
• $5 each on the hard ways 6 and 8
  • Joe starts losing or is dazzled by the hard ways constantly rolling in front of him, so he presses or parlays his bets. ‘Parlay’ is when Joe combines the present winnings with the prior bet for the next bet. For example, if a hard 6 rolls and the bet is $5, the payoff is $45; if the player parlays, the hard 6 now has a $50 bet.
  • The probability of the hard ways 6 and 8 hitting is 1 in 11 (9.09%), so let’s assume that with 100 rolls an hour, he will hit 9 each of the hard 6 and hard 8. When he hits, he parlays because he can’t stand to miss the possibility of the parlay hitting.
  • At 91 normal rolls per hard number, Joe’s expected loss per hour is $25.30 for both the hard 6 and hard 8.
  • At 9 tilt/parlay rolls per hard number, Joe’s expected loss per hour is $25.02 for both the hard 6 and hard 8.
  • At 100 rolls an hour with tilt, Joe’s expected loss per hour from betting both the hard ways 6 and 8 is $50.32 ($25.16 per number).
• $5 Any Craps on the come out
  • Most players who bet the Any Craps on the come out do so to ‘protect’ their pass line bet. In this case, since Joe is pass betting $25 when he is on tilt, let’s just assume that Joe does not increase his Any Craps at all. The payoff of 7-1 is enough to protect his $25 pass.
  • At 29 Any Craps bets per hour, Joe’s expected loss per hour from betting the Any Craps is $16.10.
• $12 each on the Place bet of 6 and 8
  • Increases on the Place 6 and 8 are likely candidates for increasing bets due to tilt.
  • Let’s assume that Joe increases his bets on the place 6 and place 8 to $24 when he goes on tilt, hoping to chase his losses. Each place bet has a probability of winning 46% of the time, so on his losses, which happen 54% of the time, Joe will increase his bet to $24. But let’s not assume that Joe tilts after every loss. Instead, let’s say he only tilts 1/3 of the time when his place bets lose. Thus, only tilting on 18 of his 100 place bet rolls.
  • At 82 normal bets per hour, his expected loss per hour is $9.05 for both the place 6 and place 8 bets.
  • At 18 tilted rolls per hour, his expected loss per hour is $3.97 for both the place 6 and place 8 bets.
  • At 100 rolls an hour, Joe’s expected loss per hour from tilt betting both the Place 6 and 8 is $13.02.

Joes expected loss over his vacation, while playing on on tilt roughly 1/3 of the time, is $1,715.

Theoretical Probability Of Winning Craps Against

Even on mild tilt – not steaming raging tilt – Joe has lost almost all of his bankroll.

Press it!

You’ve probably seen the RoadGambler videos, and if you read the comments, one of the most common bits of advice from commenters is to press your bets if they hit.

So let’s see what happens when the bets are pressed.

Note that the reader might think that it’s not proper to account for losses from parlay or presses because that was ‘house’ money. It is not proper to exclude the increases in bets because the money at that point belongs to Joe. Whether the wager comes from the winnings or from the Joe’s own pocket, it makes no difference to the overall calculation.

When making bets, the dice and the laws of probability – and consequently the house edge – do not care if the player used their own money to bet or the casino’s money to make the bet. It’s all the same and does not matter.

Expected losses using the press technique

• $10 pass line + $20 odds
  • Player’s usually do not advocate for pressing the pass line bet, so this will remain the same.
  • At 100 rolls per hour, Joe’s expected loss per hour from pass line betting is $4.20.
• $5 each on the hard ways 6 and 8
  • This is a common candidate for pressing. Let’s say Joe is a jackpot player and likes to parlay. So his first bet is $5, when he hits he will parlay to $50, hoping to win $500 from his original $5 wager.
  • If the player plays 100 rolls an hour, and his hard ways are always on, then he will win a 1 and out of 11 attempts on the hard 6 or hard 8 (ten ways to lose, one way to win). This means that 9 of his 100 rolls will have the pressed amount.
  • At 91 rolls per hard number, not pressed, Joe’s expected loss per hour is $25.30 for both the hard 6 and hard 8.
  • At 9 rolls per hard number that have parlayed bets, Joe’s expected loss per hour is $25.02 for both the hard 6 and hard 8.
  • At 100 rolls an hour with parlayed bets, Joe’s expected loss per hour from betting both the hard ways 6 and 8 is $50.32 ($25.16 per number).
• $5 Any Craps on the come out
  • Most players do not press the Any Craps, so we will not add a press to this bet.
  • At 29 Any Craps bets per hour, Joe’s expected loss per hour from betting the Any Craps is $16.10
• $12 each on the Place bet of 6 and 8
  • This is the bet most likely to be pressed, and players will routinely press this bet three or four times or more. For purposes of this calculation, let’s press the bet three times.
  • 100 total rolls, the player will win 46% of his rolls roughly, and of that 46% will win, and 46% of that.
    • Out of 100 total rolls involving a place bet of 6 and 8, the following is the approximate number of rolls for each press
      • 54 rolls, on average, involve bets that are never pressed and stay at $12
        • expected loss per hour for both numbers is $5.96
      • 25 rolls, on average, involve bets that are pressed only once (lose before the second press occurs) and thus are pressed to $24
        • expected loss per hour for both numbers at this press level is $5.52
      • 11 rolls, on average, involve bets that are pressed twice (lose before the third press) and are thus pressed to $48
        • Expected loss per hour for both numbers at this press level is $4.85
      • 10 rolls, on average, involve bets that are pressed three times (this level is similar to the above level because no bets are pressed if the number hits) and are thus wagered at $96.
        • Expected loss per hour for both numbers at this press level is $9.71
  • At 100 rolls an hour, Joe’s expected loss per hour from place betting both the 6 and 8 and pressing each win 3 times is $26.04.

Thus when we add up all the expected losses and add the advice to press numbers, using the same parameters as Gambler Joe on his vacation, the expected loss over the vacation is now $1,933.

Joe has practically busted his entire bankroll. If anything, Joe has done more damage to his bankroll by pressing his wins than if he had followed his milder tilt desires.

This is why the RoadGambler rarely presses bets, unless it’s done to entertain the viewer, which is an overarching goal of the Real Craps Series.

I’m not saying to never press bets. It’s ok to press bets because, in the end, it’s sometimes fun to press; however, it’s another thing to press thinking that pressing will give the player an advantage because certain numbers appear to be ‘hot’. The dice do not know how many times any number has rolled. The justification that a number is more likely to roll because the table is hot is just pure Gambler’s Fallacy: https://en.wikipedia.org/wiki/Gambler%27s_fallacy

Note that the above play is rather conservative: pass line with odds, one prop bet, a place bet on the 6 and 8, and a pair of hard ways bets on the 6 and 8. If the player adds other bets, such as the ‘Yo’ or covers all the hard ways, it gets way worse.

Add something like the World bet on a regular basis, and you will lose so regularly that you’ll question why you play craps at all.

Beserker’s tilt, aka crazy tilt

Many gambler’s have seen this form of tilt. It’s when the player goes on a rampage and presses or increases his bets significantly beyond what he would normally bet. He’s not just chasing his losses and increases his bets to outsized proportions.

• $10 pass line + $20 odds, increased to $50 pass
  • Tilt causes Joe to increase his pass line bet to $50 and he can’t stop. In addition to increasing his bet he also stays at the table much longer, refusing to leave because he’s down. So his number of hands played at the higher amount balloons. Because all of this additional time at the table is tilted, 75% of his play is tilted.
  • 100 total rolls an hour, of which 66 are normal play, and 34 are on tilt play.
  • At 25 normal rolls, expected loss per hour is $1.15.
  • At 75 tilt rolls, expected loss per hour is $17.25
  • At 100 rolls per hour, Joe’s expected loss per hour from pass line betting with berserker tilt is $18.14.
• $10 each on all the hard ways.
  • Joe starts is super tilted because he has been losing, has been seeing the 4 and 10 hit, and now covers all the hard ways and at $10 each, parlaying each bet.
  • The probability of hitting the hard way 6 and 8 is 1 in 11 (9.09%), so let’s assume that with 100 rolls an hour, he will hit 9 each of the hard 6 and hard 8. When he hits, he parlays.
  • At 91 normal rolls per hard number, Joe’s expected loss per hour is $50.60 for both the hard 6 and hard 8.
  • At 9 tilt/parlay rolls per hard number, Joe’s expected loss per hour is $50.04 for both the hard 6 and hard 8.
  • At 100 rolls an hour with berserker tilt, Joe’s expected loss per hour from betting both the hard ways 6 and 8 is $100.64
  • The probability of the hardways 4 and 10 hitting is 1 in 9 (11.11%), so let’s assume that with 100 rolls an hour, he will hit 9 each of the hard 4 and hard 10. When he hits, he parlays.
  • At 89 normal rolls per hour on hard 4 and 10, Joe’s expected loss per hour is $49.04 for both the hard 4 and 10.
  • At 11 tilt/parlay rolls per hard number, Joe’s expected loss per hour is $61.16 for both the hard 4 and 10.
  • At 100 rolls an hour with berserker tilt, Joe’s expected loss per hour from betting the hard 4 and 10 is $110.20.
  • Joes expected loss from covering all the hardways and parlaying one time is a staggering $210.84 per hour.
• $5 Any Craps on the come out
  • Most of the time, drop any thought of ‘protecting’ their come out roll once they’re on crazy tilt.
• $96 each on the Place bet of 6 and 8
  • Increases on the Place 6 and 8 are likely candidates for increasing bets due to tilt.
  • So Joe increases his place bet to $96 per number for the second half of his vacation because he’s really trying to chase.
  • At 100 rolls an hour, his expected loss per hour from betting both the Place 6 and 8 is $88.32
  • But no one plays on tilt the entire time, as there must be some sort of stimulus that triggers the tilt. So let’s say half the time, Joe is not on tilt, so the expected loss from this tilted bet is $44.32 per hour.

Joes expected loss per hour is a staggering $273.30

Added all up, over five days of vacation, if Joe goes on crazy berserker tilt, his expected loss is $5,466.

Want to know something else that’s scary? If you regularly play at that level and make those bets and parlays, you will have the same expected losses…without tilt!

Even if you remove the $96 place bet on the 6 and 8 and stick to the smaller $10 bets on the hard ways cover all, your expected loss over the same vacation will still be a relatively high $4,579.

Do you still wonder why you go home broke?

Theoretical Probability Of Winning Craps Rules

CONCLUSION

I have many conversations with gamblers. I’ve heard every reason why a player loses, many will admit to tilt; but I do not recall the last time that I heard someone say, ‘I lost because of the house edge’.

In the end, the direct cause of all losses is directly traced back to one culprit: the house edge that is built into the game. Tilt is then the amplifier – the executioner – that comes in and finishes your bankroll.

This is the final take away from Part 2:

The dice and the laws of probability do not know or care that bet was made by a drunk person, an angry person, a happy person, a mad person, a person who had just lost a bet, a person who had just won a bet, an old person, a young person, a virgin shooter, etc.

The laws of probability coldly dictate that on the next roll, a 12 bet has 1 way to win and 35 ways to lose, and the casino knows that to make a profit, the casino must pay less than true odds, so it pays 30-1. That’s how the house edge is applied.

Really, that’s the only reason why any gambler loses. Then, if the gambler becomes tilted, his losses will increase significantly.

But there’s hope…

In Part 3, we will discuss how to control the house edge and control tilt. Doing so will help you deal with your losses and maximize your wins.

The house edge might be an unavoidable statistical reality, but large ruinous losses do not need to be inevitable.

You can win.

You just need to identify the real culprits of this bankroll murder so that you can be on guard against them. Otherwise, you’ve identified the wrong suspects, and the crime will continue.

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