Craps Bonus

Assumptions:

Game: Craps
Prop: Any 7
Payout: 4 to 1
Base House edge: 1/6
Bonus amount: $300,000
Bonus condition: must win 'Any 7' bet, 7 times in a row
Bonus Additional Wager? there is no additional wager needed to qualify for the bonus (that is the bonus is counted as part of the main bet)

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if a craps game offered an 'Any 7' bonus for 7 consecutive wins (7 wins in a row) of $300,000 for $1 gambled, what would the player or house edge^^^ be?

edge^^^: please work out the edge per wager, keeping in mind that 16.66...% is the base house edge of the wager, not taking into account the value of the bonus.

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Hypothetical Example: (please amend/correct this example, whether I am 'close to correct' or not)

Say that I played 839,808 games in a row on the 'Any 7' prop, I would expect to lose $139,968 on the 'normal' part of the game, and expect to win $300,000 about 95.02% of the time (AT LEAST ONCE) for the bonus part of the game, for a net player edge in dollars of at least $145,095, or a player edge per wager of at least 17.27...%^*^*

^*^*: someone with better maths understanding can work out a more accurate or true player edge, but my current understanding can not improve on this figure of '...at least 17.27%;.

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thanks in advance for your help and or comments

I'm sure an amount could be set that would make it +EV

It sounds like you are dreaming this up though. Is it really available somewhere? I would attempt the math if you said yes.

My math always needs to be checked, but I get the chances of hitting once in any given single trial at 0.0000035722450846 or one in 279,936

Quote:

839,808 games in a row on the 'Any 7' prop, I would expect to lose $139,968 on the 'normal' part of the game, and expect to win $300,000 about 95.02% of the time

do you mean "trials" ?

6/36 ways to make a 7... 1/6... What are the odds of getting "any 7" 7 times in a row? (1/6)^7 = .0000036, or about 1 in 280,000. So if they're going to pay 300,000-1, then technically it's a good bet.

What happens if you win "any 7" 8 times in a row? Do you win $300k twice?

Quote: Romes

6/36 ways to make a 7... 1/6... What are the odds of getting "any 7" 7 times in a row? (1/6)^7 = .0000036, or about 1 in 280,000. So if they're going to pay 300,000-1, then technically it's a good bet.

Thus should be easy peasy for that guy that threw 18 yos in a row...

Thanks for your comments everyone,

just plugged the figures in at the beating bonuses simulator and it said the EV is about 90.5% in the players favour (seems too good to be true),

have to go to work now, but yes this is a real deal that is out there at the moment, though i don't know how long it will last,

Quote: RS

What happens if you win "any 7" 8 times in a row? Do you win $300k twice?

It resets after every '7 times in a row', so you have to win 2 lots of 7 consecutive times to win it twice.

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Update:

Also, the maximum payout of the bonus is capped at $1 million per round, so the maximum you would bet in whole dollars is $4.00***

$4.00***: $4.00 is worth about $2.905 per hand and $3.00 is worth about $2.715 per hand in +EV($).

Update,

What would a good bank-roll be, using the parameters below? ( please show the working so that I can try the formula(s) myself, as I am not very good at Standard deviation calculations)

parameters:

chance of getting 1 hit: 1/6
chance of getting 7 hits in a row: 1/6^7, or 1/279936
standard deviation: about 566.99 per hand (according to the beating bonuses simulator)
player edge: 90.5% (about +1.0716 for the bonus, and -0.1666666e ev for the base game)

Quote: odiousgambit

I'm sure an amount could be set that would make it +EV

It sounds like you are dreaming this up though. Is it really available somewhere? I would attempt the math if you said yes.

My math always needs to be checked, but I get the chances of hitting once in any given single trial at 0.0000035722450846 or one in 279,936



do you mean "trials" ?

I guess it may have been better to say, "839,808 trials", but my understanding of that terminology is not very good.

Even thought this is a fantasy bet with a huge combined player edge, I still calculated it since I'm bored. That edge is more like 87.2% not 90.5%. That's because the 16.7% house edge grinds the basic bet down between 1 and 7 times (not just once) while chasing the bonus payout.

I think the more realistic scenario would be for the casino to offer this as a matched side bet to the any seven bet. That way the house has its 16.7 % edge on the any seven (more like 20% assuming the bettor presses until losing side bet) and the player gets a 7.2 % edge on side bet, but it's still a net 9.5 % edge for the house.