if casino offer 30% loss rebate ....
- Thread starter beyondbj
- Start date
I assumed that the HE is 0.5% and that we flat bet for 500 hands. Our EV in that situation is -2.5 units. Using Excel and numerical methods, I calculated that with a 30% loss rebate, our -2.5 unit EV turns into approximately +0.97 units, which comes out to about a 0.2% player edge. It isn't much, but even a basic strategy player is playing at an edge. However, as you mentioned before, there are strategies to improve on this.
The key here is the loss rebate does nothing when we win, but gives us 30% back when we lose. This reminds me of the description of match play coupons in the Beyond Coupons article, and the strategy is going to be somewhat similar. Essentially, we want to find a way to increase our standard deviation without dramatically increasing our expected loss (I'm assuming we aren't counting). That means we either win a lot (which is fine) or lose a lot (and get a discount). The way to do this was mentioned earlier in this thread. We want to make lots of minimum bets and a few huge bets. How many huge bets and how huge? I don't know the answer to those questions, but as RJT said, I would be willing to bet that the sticky bonus math could be used here in some form. In a normal sticky bonus, you would make big bets until you hit your target or busted. In your situation, I'm thinking you would have a target win and a stop loss. At the target win, you would simply quit as there is no need to continue playing for the loss rebate. It would only help if you had a significant loss at that point, since you are already ahead by some amount. On the other hand, if you hit your stop loss, you would grind out the remainder of the 500 bets so you could collect the 30% rebate.
Now, how do you calculate the optimal stop win and stop loss for your bankroll? I do not know the answer to that. Intuitively, I suspect that we want to look for some relationship between the stop loss and stop win, then scale both depending on bankroll. But should stop win be greater than stop loss so that losses are more frequent (but smaller than the wins) and we claim the rebate more frequently? Or do we want the stop loss greater so that the times we do lose, we get more benefit from the rebate? I suspect this will be better because we will make the min bets less often. Not sure about this...I'm gonna think on it some more and play around with Excel. I'll update this if I come up with anything interesting... Would be nice if I could remember anything about C++, as it should be easy to code this and test different strategies. No cards needed, just win/loss distributions and random number generators...
The key here is the loss rebate does nothing when we win, but gives us 30% back when we lose. This reminds me of the description of match play coupons in the Beyond Coupons article, and the strategy is going to be somewhat similar. Essentially, we want to find a way to increase our standard deviation without dramatically increasing our expected loss (I'm assuming we aren't counting). That means we either win a lot (which is fine) or lose a lot (and get a discount). The way to do this was mentioned earlier in this thread. We want to make lots of minimum bets and a few huge bets. How many huge bets and how huge? I don't know the answer to those questions, but as RJT said, I would be willing to bet that the sticky bonus math could be used here in some form. In a normal sticky bonus, you would make big bets until you hit your target or busted. In your situation, I'm thinking you would have a target win and a stop loss. At the target win, you would simply quit as there is no need to continue playing for the loss rebate. It would only help if you had a significant loss at that point, since you are already ahead by some amount. On the other hand, if you hit your stop loss, you would grind out the remainder of the 500 bets so you could collect the 30% rebate.
Now, how do you calculate the optimal stop win and stop loss for your bankroll? I do not know the answer to that. Intuitively, I suspect that we want to look for some relationship between the stop loss and stop win, then scale both depending on bankroll. But should stop win be greater than stop loss so that losses are more frequent (but smaller than the wins) and we claim the rebate more frequently? Or do we want the stop loss greater so that the times we do lose, we get more benefit from the rebate? I suspect this will be better because we will make the min bets less often. Not sure about this...I'm gonna think on it some more and play around with Excel. I'll update this if I come up with anything interesting... Would be nice if I could remember anything about C++, as it should be easy to code this and test different strategies. No cards needed, just win/loss distributions and random number generators...
So I didn't really look into this any significant detail after my last post, but I did calculate the EV assuming the following strategy:
Play one hand of 100 units (I'm assuming table max is 100x table min). If you win, you collect your winnings and quit. If you lose, you play your 500 hands and collect your 30% loss rebate. If you push, you play another hand at 100 units until you win or lose. I modeled this last rule by simply ignoring the pushes entirely and recalculating the probabilities, starting with the win/loss combinations given here at the WizardOfOdds website.
I found that playing this strategy will improve our EV from +0.97 units to +15.68 units, although I'm sure we can do better. Note that our improvement with this strategy is roughly 15 units, and we made a 100 unit bet, which loses about half the time, and earns a 30% rebate when it loses. I suspect that if we use a stop win equal to our stop loss for our big bets, we may see that our EV is approximately 15% of our stop. If, for example, we were flipping coins instead of playing blackjack, our EV for the big bets alone would be 0 with an equal chance of hitting either stop. The losses would be discounted 30%, so in this case our EV would be exactly 15%. The effects of our minimum bet grind portion of this play become relatively insignificant compared to the 100 unit bets, so I think we can ignore those when it comes to figuring out the optimal strategy.
As far as bankroll, the results of our big bet will dominate our overall result, and our edge is about 15% of that bet, with very roughly the same variance associated with one hand of 100 units. If your bankroll is such that you are comfortable betting 100 units on a single hand of blackjack with a 15% edge, you should be comfortable with this first draft strategy.
Can anyone point me toward something to tell me how to figure out the odds of reaching +X before -Y when flipping a coin (hitting stop win before stop loss)? I think I'm not looking for anything related to a normal distribution because we will be dealing with a small number of trials. I think binomial distribution might not be it either since the number of trials is not fixed. Any suggestions? Been a while since stats class...
I think we're getting somewhere
Edit:
I probably should explain my methodology thus far. It's nothing too sophisticated, but it does what I want it to do.
First, to calculate the value of the rebate, I calculated the EV and SD for a series of 500 bets of 1 unit. I then created a table. The first column was possible results, from about -7SD to +7SD, broken into very small chunks (0.5 units). The next column is the Z score for that result, or how many standard deviations it would be from the EV. Third, I used the NORMSDIST function. The fourth column multiplies the result (first column) by the probability (calculated from the third column). The fifth column contains an if statement that returns 70% of the fourth column if negative or 100% if positive. I then simply summed the fifth column to get the EV.
To calculate the EV of the strategy I gave above, I started with the same spreadsheet. Using the Wizard's chart for win/loss distribution, I took each of the losses, multiplied by 100 units, and added that to my starting disadvantage of -2.5 units. I then input that (negative) number in my previous spreadsheet and read the EV, given that I started at -100 units, or -200 or -800, etc. I used those conditional EVs along with the Wizard's win/loss distribution to calculate the final EV. See attachment for that final calculation.
Play one hand of 100 units (I'm assuming table max is 100x table min). If you win, you collect your winnings and quit. If you lose, you play your 500 hands and collect your 30% loss rebate. If you push, you play another hand at 100 units until you win or lose. I modeled this last rule by simply ignoring the pushes entirely and recalculating the probabilities, starting with the win/loss combinations given here at the WizardOfOdds website.
I found that playing this strategy will improve our EV from +0.97 units to +15.68 units, although I'm sure we can do better. Note that our improvement with this strategy is roughly 15 units, and we made a 100 unit bet, which loses about half the time, and earns a 30% rebate when it loses. I suspect that if we use a stop win equal to our stop loss for our big bets, we may see that our EV is approximately 15% of our stop. If, for example, we were flipping coins instead of playing blackjack, our EV for the big bets alone would be 0 with an equal chance of hitting either stop. The losses would be discounted 30%, so in this case our EV would be exactly 15%. The effects of our minimum bet grind portion of this play become relatively insignificant compared to the 100 unit bets, so I think we can ignore those when it comes to figuring out the optimal strategy.
As far as bankroll, the results of our big bet will dominate our overall result, and our edge is about 15% of that bet, with very roughly the same variance associated with one hand of 100 units. If your bankroll is such that you are comfortable betting 100 units on a single hand of blackjack with a 15% edge, you should be comfortable with this first draft strategy.
Can anyone point me toward something to tell me how to figure out the odds of reaching +X before -Y when flipping a coin (hitting stop win before stop loss)? I think I'm not looking for anything related to a normal distribution because we will be dealing with a small number of trials. I think binomial distribution might not be it either since the number of trials is not fixed. Any suggestions? Been a while since stats class...
I think we're getting somewhere
Edit:
I probably should explain my methodology thus far. It's nothing too sophisticated, but it does what I want it to do.
First, to calculate the value of the rebate, I calculated the EV and SD for a series of 500 bets of 1 unit. I then created a table. The first column was possible results, from about -7SD to +7SD, broken into very small chunks (0.5 units). The next column is the Z score for that result, or how many standard deviations it would be from the EV. Third, I used the NORMSDIST function. The fourth column multiplies the result (first column) by the probability (calculated from the third column). The fifth column contains an if statement that returns 70% of the fourth column if negative or 100% if positive. I then simply summed the fifth column to get the EV.
To calculate the EV of the strategy I gave above, I started with the same spreadsheet. Using the Wizard's chart for win/loss distribution, I took each of the losses, multiplied by 100 units, and added that to my starting disadvantage of -2.5 units. I then input that (negative) number in my previous spreadsheet and read the EV, given that I started at -100 units, or -200 or -800, etc. I used those conditional EVs along with the Wizard's win/loss distribution to calculate the final EV. See attachment for that final calculation.
Attachments
(Dead link: http://www.bjstrat.net/cgi-bin/ror.exe) _This may help_.
Input EV as a fraction < 1, (no decimal needed), can be + or -
Input bank and goal; Example bank=2 and goal=4 will compute probability of losing 2 units before winning 2 units and quitting given the EV that was input.
When finished with input, click 'Compute' to get probability of failure. Probability of success = (1 - Prob of failure)
.
Input EV as a fraction < 1, (no decimal needed), can be + or -
Input bank and goal; Example bank=2 and goal=4 will compute probability of losing 2 units before winning 2 units and quitting given the EV that was input.
When finished with input, click 'Compute' to get probability of failure. Probability of success = (1 - Prob of failure)
.
I intuit that too lol.
Maybe the OP would be willing to host such a 30% rebate game for us lol.
I actually don't know for sure lol but it seems B-E-A utiful to me.
To NYne fingers - I have a paper by Gabor Megyesi on phantom bonuses and loss rebates. I'd post it here but I don't know if that would be OK as I did not acquire it over the internet.
Not that I'd know a good mathematician from a bad one but this guy is tops imho.
Maybe searching the web for papers by him would yield a result.
Maybe the OP would be willing to host such a 30% rebate game for us lol.
I actually don't know for sure lol but it seems B-E-A utiful to me.
To NYne fingers - I have a paper by Gabor Megyesi on phantom bonuses and loss rebates. I'd post it here but I don't know if that would be OK as I did not acquire it over the internet.
Not that I'd know a good mathematician from a bad one but this guy is tops imho.
Maybe searching the web for papers by him would yield a result.
I'll look for in when I have more time. I did come to the realization a couple of nights ago that this is in fact identical to a sticky bonus once you choose your stop loss. As an example, if you set your stop loss at $1000, you are actually only risking $700, but with $1000 available for betting. That's just the same as a $300 sticky bonus with a $700 deposit. That means that the sticky math should apply directly and will give you the appropriate target and EV for your bankroll and a given stop loss. All you'd have to do then is graph your EV vs. stop loss and find the point where EV is maximized. That will tell you the correct stop loss, and the sticky bonus formulas will tell you the correct target. It should be relatively simple to maximize your EV now by knowing that approach.