Joined: Nov 2, 2009
• Posts: 52
November 30th, 2010 at 1:25:44 PM permalink
I posted this in the Terrible's thread, but this thread seemed to me geared more toward the information I'm seeking.

http://wizardofvegas.com/forum/las-vegas-casinos/terribles/1624-10-cashback/5/

Terrible's currently has a rebate of 10% on losses, and the rebate may be requested once after 24 hours have passed since your last rebate request. The 10% rebate is for losses exceeding \$1,000.00. (a 5% rebate on losses off \$500 - \$999.00 should be ignored for the sake of this discussion.)

The Terrible’s 10% rebate is still in effect. I telephoned and verified today (11/30/2010) with a pit critter named Tom. They will issue the rebate once every 24 + hours for a player.

On the surface, it originally appears to me to be a profitable and potentially exploitable opportunity. I was ready, willing, and able to make reservations and hop a flight.

But on closer examination, and if my math is “right”, it does not appear to be profitable in the long run. I know my math is not correct for this scenario (written below) but have included my thoughts anyway.

Here is what I originally thought would be the “correct” math, if played on the 0.47% double deck Blackjack table. Table limit is \$500.00 maximum bet. For simplicity, I used \$1,000 bets in my calculations, seeking one decision per 24 hour 01 minute time period to qualify for a rebate if a loss is incurred. After 100 trials, my very rough and most likely inaccurate calculations were:

47 winners @ \$1,000 = \$47,000.00
53 losers @ \$900 = 47,700.00

Net: – \$700 over 100 trials @ \$1,000 per trial.

I don’t think I am correct, but is may be roughly accurate.

Is this offer, long term, really a loser for the player, assuming perfect play?

Since the maximum bet allowed is \$500.00, this bet size should be used to calculate the long term results with the following parameters:

The 100 trials should fall exactly on mathematical expectation. If necessary for computing the results, a larger number of trials could be used. My definition of “trials” in this message is the daily session, whether one hand or many until the daily goal is reached, every 24+ hours to be eligible for the rebate.

I would expect some “daily” trials could involve many individual hands if the results are choppy. Other considerations would include pushes, dealer and player simultaneous naturals, etc.

The player will stop for 24 hours once a \$1,000+ winner goal, or \$1,000+ stop loss is reached. Bankroll is "unlimited".

Considering splits and doubles, a win or loss could be \$2750.00 (\$2,000 on second wager with split and double, following a natural 3-2 payoff win on first trial.) It is probably more, as I did not consider potential results on re-splits and doubles. Again, I am only looking for “expectation”.

What are the anticipated results, deviation, and ROR using \$500 wagers, and 100 trials? Would the expectation be different for 50 trials? 10 trials? I do realize the ROR will change drastically with fewer trials.

Maybe someone with better math abilities and understanding will come along and provide accurate information on the EV of this scenario. How profitable, or how big a loser is it really?

I just do not know, and would truly like to know.

rdw4potus
Joined: Mar 11, 2010
• Posts: 7237
November 30th, 2010 at 1:48:04 PM permalink

Here is what I originally thought would be the “correct” math, if played on the 0.47% double deck Blackjack table. Table limit is \$500.00 maximum bet. For simplicity, I used \$1,000 bets in my calculations, seeking one decision per 24 hour 01 minute time period to qualify for a rebate if a loss is incurred. After 100 trials, my very rough and most likely inaccurate calculations were:

47 winners @ \$1,000 = \$47,000.00
53 losers @ \$900 = 47,700.00

Net: – \$700 over 100 trials @ \$1,000 per trial.

Maybe someone with better math abilities and understanding will come along and provide accurate information on the EV of this scenario. How profitable, or how big a loser is it really?

I just do not know, and would truly like to know.

I think you're off a decimal point. .47% would round to 50 wins and 50 losses in 100 decisions. So you'd come out \$5000 ahead over 100 trials (50000 in wins - 45000 in losses)
"So as the clock ticked and the day passed, opportunity met preparation, and luck happened." - Maurice Clarett
thecesspit
Joined: Apr 19, 2010
• Posts: 5936
November 30th, 2010 at 2:14:36 PM permalink
For Blackjack there's a difference between the EV and the frequency of winners.

You win less than half the hands, and make your money "back" on the splits, doubles and blackjacks.

The exact numbers are published somewhere for some rule sets, but no idea where that is.
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
Joined: Nov 2, 2009
• Posts: 52
November 30th, 2010 at 2:32:15 PM permalink
Quote: rdw4potus

I think you're off a decimal point. .47% would round to 50 wins and 50 losses in 100 decisions. So you'd come out \$5000 ahead over 100 trials (50000 in wins - 45000 in losses)

I purposely did not want to round off the calculations I made, wanting to have an exact EV, whether plus or minus, and figuring the rebate into the losses.

Since the game is known to be 0.47%, in the long term, that equates to 47 wins out of 100, and 53 losses. With \$1,000 per (or \$900 for a loss), rounding the numbers would be a disservice and misleading information.
Joined: Nov 2, 2009
• Posts: 52
November 30th, 2010 at 2:44:32 PM permalink
Quote: thecesspit

For Blackjack there's a difference between the EV and the frequency of winners.

You win less than half the hands, and make your money "back" on the splits, doubles and blackjacks.

The exact numbers are published somewhere for some rule sets, but no idea where that is.

I do realize this, and have "sort of decided" that this offer is only beneficial to the player for a very short trial.

Specifically:

0.47% equates to \$47.00 per \$1,000 wager as the house advantage (theoretical win). That advantage is on every wager made.

Regardless of the results, win, lose, or push, the house theoretical is \$47.00 per \$1,000 bet.

With that thinking, it now seems apparent to me, that this rebate offer is still player friendly, but only until approximately \$2100 total wagers are made. Effectively 4 hands @ \$500 per, if there are no doubles, splits, etc.

After the sum of \$2100 total bets is made, regardless of results, the house would have ground out the player temporary advantage, although the house win would become a lower theoretical, increasing toward the expected norm as more and more trials are made.

I'm hoping the Wizard will come along and comment, as well as those who have played this offer. :)

Am I on the money with my thinking this is not an "Advantage Play" long term, yet short term does have benefits, and once those limits are reached, if truly a high roller, a return to a more prestigious gaming venue for better comps should be made?

Incidentally, I am NOT a high roller. But I am willing to make Advantage Plays when I think I'm getting the best of it.

Thanks!
thecesspit
Joined: Apr 19, 2010
• Posts: 5936
November 30th, 2010 at 2:47:24 PM permalink
A game where you win 47 times and lose 53 is not a 0.47% house advantage.
\$100 per hand :

47 winners : +\$4,700
53 Losers : -\$5,300

Total loss = \$600 on \$10,000 bet = 6% House advantage, or 94% EV.

It's pretty close to betting the odds/evens in Roulette.

Here's the table I was looking for :

http://wizardofodds.com/blackjack/appendix4.html

So for 100 hands you'll get (roughly) :

4.5 Blackjacks
32 Single bet winners
6 2+ bet winners
8.5 Pushes
40 Single bet losses
4.5 2+ bet losers
4.5 Surrenders (half bet losses).

If you assumed no more than one split or double, \$1000 per hand :

Blackjacks : \$6,750
Winners : \$32,000
Multi Winners : \$12,000
Pushes : \$0
Surrenders : -\$2,250
Losers : - \$40,000
Multi Losers : -\$9,000

Total after = -\$500 = 0.5% EV (close as dammit to your 0.47%).
With loss rebate of 10% :

Blackjacks : \$6,750
Winners : \$32,000
Multi Winners : \$12,000
Pushes : \$0
Surrenders : -\$2,025
Losers : - \$36,000
Multi Losers : -\$8,100

Total after = +\$4625

Hope this helps.
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
ahiromu
Joined: Jan 15, 2010
• Posts: 2102
November 30th, 2010 at 4:09:57 PM permalink
I would say you'd need 10000-100000 trials to properly decide, 100 isn't even close. The problem with betting 1k a single time is that although your EV is in the positive range, you are completely getting rid of any variance (standard deviations) - it's either you win it or you lose it. I would recommend that you walk up and buy in for \$1000 and bet in units of \$250. I'm fairly certain you'd still be in +EV territory, have the ability to double up / split / resplit (the EV you lose from flat betting 1k and not being able to double/split is probably more than what you lose by betting \$250 instead of 1k), bow out at \$500-750 up if that's a somewhat life changing amount of money for you. If losing a few grand isn't a problem, I think starting at \$500 and running a martingale would be an awesome few minutes.
Its - Possessive; It's - "It is" / "It has"; There - Location; Their - Possessive; They're - "They are"
Joined: Nov 2, 2009
• Posts: 52
November 30th, 2010 at 5:15:01 PM permalink
Quote: ahiromu

I would say you'd need 10000-100000 trials to properly decide, 100 isn't even close. The problem with betting 1k a single time is that although your EV is in the positive range, you are completely getting rid of any variance (standard deviations) - it's either you win it or you lose it. I would recommend that you walk up and buy in for \$1000 and bet in units of \$250. I'm fairly certain you'd still be in +EV territory, have the ability to double up / split / resplit (the EV you lose from flat betting 1k and not being able to double/split is probably more than what you lose by betting \$250 instead of 1k), bow out at \$500-750 up if that's a somewhat life changing amount of money for you. If losing a few grand isn't a problem, I think starting at \$500 and running a martingale would be an awesome few minutes.

Maximum bet at Terrible's is \$500.00 Multiple hands may be played.

I purposely chose a trial of 100 because that would represent 100 separate and distinct visits to the casino. Each session is a 24 hour period plus a few minutes, to maintain eligibility for rebate on a loss.

Yes, I seek the actual expectation, and realize millions of trials would be appropriate to reach accurate numbers. But on a practical basis, there is basically no way for any player to have more than about 350 "results" in a year. 100 distinct visits for a resident or frequent visitor is doable. More than that is unlikely for most, there are easier ways to make money. But, each distinct visit should take less than 1 hour, including parking the car and going in, etc.

So, if I can "find" the expected normal distribution of results for this offer, using a max bet of \$500.00, with adequate bankroll, the EV of this offer could be determined, whether plus or minus.

And that is what I'm looking for. The actual EV, long term, even though it will only be for 100 trials.

Perfect strategy would be used. Doubles, splits, etc. Losing more than \$1000 because of splits, doubles, etc is not an issue, it is part of the EV, and there will be occasions where more than \$1,000 will be won because of those type of hands.
rdw4potus
Joined: Mar 11, 2010
• Posts: 7237
November 30th, 2010 at 5:47:31 PM permalink

I purposely did not want to round off the calculations I made, wanting to have an exact EV, whether plus or minus, and figuring the rebate into the losses.

Since the game is known to be 0.47%, in the long term, that equates to 47 wins out of 100, and 53 losses. With \$1,000 per (or \$900 for a loss), rounding the numbers would be a disservice and misleading information.

A .47% house advantage means that you should expect to lose \$4.70 for every \$1000 that you wager. The house will win about 50.235% of the decisions, and the player will win about 49.765% of decisions.

*edit* in an even money game. Which others have correctly pointed out is not the case with BJ.
"So as the clock ticked and the day passed, opportunity met preparation, and luck happened." - Maurice Clarett
Joined: Nov 2, 2009
• Posts: 52
December 1st, 2010 at 9:38:46 PM permalink
Quote: thecesspit

A game where you win 47 times and lose 53 is not a 0.47% house advantage.
\$100 per hand :

47 winners : +\$4,700
53 Losers : -\$5,300

Total loss = \$600 on \$10,000 bet = 6% House advantage, or 94% EV.

It's pretty close to betting the odds/evens in Roulette.

Here's the table I was looking for :

http://wizardofodds.com/blackjack/appendix4.html

So for 100 hands you'll get (roughly) :

4.5 Blackjacks
32 Single bet winners
6 2+ bet winners
8.5 Pushes
40 Single bet losses
4.5 2+ bet losers
4.5 Surrenders (half bet losses).

If you assumed no more than one split or double, \$100 per hand :

Blackjacks : \$6,750
Winners : \$32,000
Multi Winners : \$12,000
Pushes : \$0
Surrenders : -\$2,250
Losers : - \$40,000
Multi Losers : -\$9,000

Total after = -\$500 = 0.5% EV (close as dammit to your 0.47%).

With loss rebate of 10% :

Blackjacks : \$6,750
Winners : \$32,000
Multi Winners : \$12,000
Pushes : \$0
Surrenders : -\$2,025
Losers : - \$36,000
Multi Losers : -\$8,100

Total after = +\$4625

Hope this helps.

Thanks. Now I am completely confused. Could you please simplify your last respons ? Are you saying the expectation for this 10% loss rebate is +4625 after 100 hands with perfect distribution of potential results? A profit of \$46.25 per \$500 wager?

Remember, to qualify for the 10% loss rebate, a \$1,000 loss is required. The loss rebate for \$500.00 - \$999.00 is 5%.

I'm primarily interested in knowing the numbers over 100 "sessions" (days) when the strategy being used is:
1: a stop loss of \$1,000+ (or more due to doubles & splits, etc), or a win of \$1,000 or more
2: perfect strategy is used for the rules of the game to double, split, DAS, etc.

It is likely that most sessions will be more than 1 hand played, although due to doubles, splits, etc, there should be sessions where only one hand is played. There could also be sessions where more than 4+ hands are played with pushes, etc.

Thanks