3 card poker FREEPLAY

[Gronbog]

The high value of the single number on roulette is due to its high variance. High variance is a good thing for match play and free play because your winning bets pay more than usual when compared to your losing bets. This is what Grosjean means when he says that the coupons alter the payout structure of the games. Because of this, the high variance occurs disproportionately on the positive side of the payout structure for the bet.

This may become more clear when you look at the match play calculation for the single number, single zero roulette example. He used a $10 match play coupon:

Your cash bet is $10
1 out of 37 times you win 35 x $20 = $700
36 out of 37 times you lose $10

So the ev is (1/37x$700 - 36/37x$10) / $10 or in units (1/37x70 - 36/37x1) = 0.919 = $9.19 which matches Grosjean's result.

From the formula, you can see that winning twice as much when you win in a high variance game dominates the calculation.

[aceside]

The high value of the single number on roulette is due to its high variance. High variance is a good thing for match play and free play because your winning bets pay more than usual when compared to your losing bets. This is what Grosjean means when he says that the coupons alter the payout structure of the games. Because of this, the high variance occurs disproportionately on the positive side of the payout structure for the bet.

This may become more clear when you look at the match play calculation for the single number, single zero roulette example. He used a $10 match play coupon:

Your cash bet is $5
1 out of 37 times you win 35 x $10 = $350
36 out of 37 times you lose $5

So the ev is (1/37x$350 - 36/37x$5) / $5 or in units (1/37x70 - 36/37x1) = 0.919 = $9.19 which matches Grosjean's result.

From the formula, you can see that winning twice as much when you win in a high variance game dominates the calculation.

This is very creative. When I used my match play coupons on Roullette with a 0 and a 00, I always bet on either the red or black box. Now I learned something from you. Thank you.

[aceside]

The high value of the single number on roulette is due to its high variance. High variance is a good thing for match play and free play because your winning bets pay more than usual when compared to your losing bets. This is what Grosjean means when he says that the coupons alter the payout structure of the games. Because of this, the high variance occurs disproportionately on the positive side of the payout structure for the bet.

This may become more clear when you look at the match play calculation for the single number, single zero roulette example. He used a $10 match play coupon:

Your cash bet is $5
1 out of 37 times you win 35 x $10 = $350
36 out of 37 times you lose $5

So the ev is (1/37x$350 - 36/37x$5) / $5 or in units (1/37x70 - 36/37x1) = 0.919 = $9.19 which matches Grosjean's result.

From the formula, you can see that winning twice as much when you win in a high variance game dominates the calculation.

Most casinos probably will not pay 35:1 on a match play coupon though. I am still thinking about this. Can you calculate the variance for getting the 0.919 expected value? As opposed to the real money bet?

[Marvin]

Blackjack is rarely the best play for free-play and promo chips.

Mathematically, a good BJ game is often the best option for non-cashable chips, which is the scenario Blue presented when asking about a situation where you keep the promo chip on wins.

For chips that are relinquished after 1 bet, win or lose, roulette is best if you can make non even money bets, otherwise 3cp is best.

[Gronbog]

Yes. Good point. Non cashable chips are mathematically equivalent to normal chips. Grosjean calls them "funny chips" in his article.

[Gronbog]

Most casinos probably will not pay 35:1 on a match play coupon though. I am still thinking about this. Can you calculate the variance for getting the 0.919 expected value? As opposed to the real money bet?

Most casinos know about the value of coupons for high variance bets and will only allow their use on so-called even money bets. Even then blackjack is not usually the best choice for match play or free bets.

The variance for the match play with 0.919 expected value is: 1/37x((70 - 0.919)^2) + 36/37x((-1 - 0.919)^2) = 132.57

The variance for the real money bet is 1/37((35 - -0.027)^2) + 36/37x((-1 - -0.027)^2) = 34.080 (-0.027 is the ev for the real money bet)

[aceside]

Most casinos know about the value of coupons for high variance bets and will only allow their use on so-called even money bets. Even then blackjack is not usually the best choice for match play or free bets.

The variance for the match play with 0.919 expected value is: 1/37x((70 - 0.919)^2) + 36/37x((-1 - 0.919)^2) = 132.57

The variance for the real money bet is 1/37((35 - -0.027)^2) + 36/37x((-1 - -0.027)^2) = 34.080 (-0.027 is the ev for the real money bet)

I am absolutely confident with your calculation of the variance with the real money bet, but not so confident with your result of the match play.

I am learning the math here, but I feel it should be 132.57*37. Is this correct? When you calculate the variance for the match play with the 0.919 expected value, you automatically assume you have many (>37) match play coupons to bet in a roll on every hands (>37) you are going to play. However, the reality is that you often only have one coupon to use. Does this problem of the limited coupon number make your variance 37 times larger?

[Gronbog]

If you think my variance is 37 times too large, wouldn't you want to divide it by 37?

However, I believe that both variance calculations are correct. If you're ok with the real money calculation, you should be ok with the match play calculation, because they use the same formula.

Finally, the variance calculation above is for a single bet (the frequencies add up to 1). You would multiply it by the number coupons to get the total variance for playing all of them.

[aceside]

If you think my variance is 37 times too large, wouldn't you want to divide it by 37?

However, I believe that both variance calculations are correct. If you're ok with the real money calculation, you should be ok with the match play calculation, because they use the same formula.

Finally, the variance calculation above is for a single bet (the frequencies add up to 1). You would multiply it by the number coupons to get the total variance for playing all of them.

I meant to say your calculation of 132.57 is too small. If we consider the real world situation that we only have one match play coupon to use, the chance of winning this particular coupon is 37 times smaller, therefore, the variance with this particular coupon should be be 37 times larger. Is this correct?

Let us just do these two experiments. #1: I give you only one match play coupon for you to bet 37 times on a Roulette, and your chance of getting an EV of 0.919 is almost zero because this particular coupon will be confiscated after your first use. #2: I give you 37 match play coupons for you to bet each for 37 times on a Roulette, and your chance of getting an EV of 0.919 is likely verified. How do you calculate the EV and variances for these two different cases?

[bjarg]

You read a quote like that from one of the greatest advantage players and researchers of our time and you still think you know better?

Glad to see I wasn't that far off with my Brady prediction.

[aceside]

Glad to see I wasn't that far off with my Brady prediction.

As I mentioned, I used match play coupons on almost every casino games myself. Trust me.

[Gronbog]

I meant to say your calculation of 132.57 is too small. If we consider the real world situation that we only have one match play coupon to use, the chance of winning this particular coupon is 37 times smaller, therefore, the variance with this particular coupon should be be 37 times larger. Is this correct?

No.

Let us just do these two experiments. #1: I give you only one match play coupon for you to bet 37 times on a Roulette, and your chance of getting an EV of 0.919 is almost zero because this particular coupon will be confiscated after your first use. #2: I give you 37 match play coupons for you to bet each for 37 times on a Roulette, and your chance of getting an EV of 0.919 is likely verified. How do you calculate the EV and variances for these two different cases?

EV and variance have nothing to do with actual outcomes of particular sequences of bets. They are mathematical measures of how much you can expect to win/lose on average and of how far from that expectation you might end up. I have already showed you how to calculate both.

As I mentioned, I used match play coupons on almost every casino games myself. Trust me.

Based on your fundamental misunderstanding of the basic concepts of the mathematics of games of chance, no one should trust you about anything.