Gaming coupon question

I have an argument with a friend that I need help settling. Some of our local casinos give away Match Play coupons and Free Play coupons. For clarification, the Match Play requires a matching amount of chips to accompany the coupon, and the Free Play can stand alone with no chips with it. Our disagreement is over how much the casino is giving away in each case.
He says, in terms of value to the player, the Free Play is worth twice as much as the Match Play. I say the difference is nominal, the only difference between the two is the theoretical house advantage on the chips that accompany the Match Play. My case, put

you are correct.

Quote: theodopolis

He says, in terms of value to the player, the Free Play is worth twice as much as the Match Play.

Your friend is correct. Here is an example to help clarify this.

Assume a $10 free play. This must be cycled through a slot machine one time before it is cashed. If the slot has H/A = 7%, then $10 is worth $9.30.

Assume a $10 match play. For ease, let's play it on baccarat. Then the player must wager an additional $10 of his own. For ease, assume the wager is made on the "player" side. Assume that in the case of a tie, the match play coupon remains. Then with probability 0.493176, the player will make win $20. With probability 0.506824 the player will lose $10. So the expected value of the MP is EV = (0.493176)*20 + 0.5068243*(-10) = $4.80.

$10 FP played on a 7% hold slot is worth $9.30.

$10 MP played on "player" in baccarat is worth $4.80.

Now assume you play that same $10 match play on 34-red in roulette. Then with probability 1/38 you will win 35*20 = $700. With probability 37/38 you will lose $10. So the expected value of the MP is (1/38)*700 + (37/38)*(-10) = $8.68. The higher the variance of the wager, the more valuable the MP. This is why MP is usually restricted to even-money bets.

Quote: teliot

Your friend is correct. Here is an example to help clarify this.

Assume a $10 free play. This must be cycled through a slot machine one time before it is cashed. If the slot has H/A = 7%, then $10 is worth $9.30.

Assume a $10 match play. For ease, let's play it on baccarat. Then the player must wager an additional $10 of his own. For ease, assume the wager is made on the "player" side. Assume that in the case of a tie, the match play coupon remains. Then with probability 0.493176, the player will make win $20. With probability 0.506824 the player will lose $10. So the expected value of the MP is EV = (0.493176)*20 + 0.5068243*(-10) = $4.80.

$10 FP played on a 7% hold slot is worth $9.30.

$10 MP played on "player" in baccarat is worth $4.80.

Now assume you play that same $10 match play on 34-red in roulette. Then with probability 1/38 you will win 35*20 = $700. With probability 37/38 you will lose $10. So the expected value of the MP is (1/38)*700 + (37/38)*(-10) = $8.68. The higher the variance of the wager, the more valuable the MP. This is why MP is usually restricted to even-money bets.

i thought he was talking about free slot play at first too but pretty sure he means a free bet coupon.

Quote: rudeboyoi

i thought he was talking about free slot play at first too but pretty sure he means a free bet coupon.

Maybe the OP can clarify. It is often the case that casinos will allow players to redeem their points for free play (slots) or match play (tables) at the same conversion rate. Obviously it's better to take free play.

I am referring to coupons that play on table games, specifically blackjack. Match Play requires chips to go with it, Free Play can be played with no chips to go with it. My argument is that a Free Play is only nominally more valuable to me (about 2% on Blackjack) than the Match Play, while he says the Free Play is worth twice as much (200 %).

Let's make an assumption that you can choose to play the Match Play (MP) or the Free Play (FP) on the same game, with the same bet. For simplicity sake, let's assume you can make a wager with a 50% chance of winning.

With FP, you will either win the amount (+x) or you will lose, but since you put up nothing, you lost nothing. So 50% chance of +x, and 50% chance of -0.

With MP, you have to put up an amount to bet. So, you are risking x to possibly win 2x. You will either win twice the amount (+2x), or you will lose your matched about (-x). So 50% chance of +2x, 50% chance of -x.

FP = 0.5(x) + (0.5)(0) = 0.5(x)

MP = 0.5(2x) + (0.5)(-x) = x - 0.5(x) = 0.5(x)

Thus, FP = MP.

Quote: konceptum

Let's make an assumption that you can choose to play the Match Play (MP) or the Free Play (FP) on the same game, with the same bet. For simplicity sake, let's assume you can make a wager with a 50% chance of winning.

With FP, you will either win the amount (+x) or you will lose, but since you put up nothing, you lost nothing. So 50% chance of +x, and 50% chance of -0.

With MP, you have to put up an amount to bet. So, you are risking x to possibly win 2x. You will either win twice the amount (+2x), or you will lose your matched about (-x). So 50% chance of +2x, 50% chance of -x.

FP = 0.5(x) + (0.5)(0) = 0.5(x)

MP = 0.5(2x) + (0.5)(-x) = x - 0.5(x) = 0.5(x)

Thus, FP = MP.

That's only true with a bet with no house advantage. I'll use a terrible house advantage (20%) to illustrate my point:

FP = 0.4(x) + (0.6)(0) = 0.4(x)
MP = 0.4(2x) + (0.6)(-x) = 0.8(x) - 0.6(x) = 0.2(x)
Thus, FP > MP.

And another (10%)...

FP = 0.45(x) + 0.55(0) = 0.45(x)
MP = 0.45(2x) + 0.55(-x) = 0.9(x) - 0.55(x) = 0.35(x)
Still, FP > MP.

But what this shows is that FP isn't necessarily 2x more valuable than MP. The factor of greater value depends on the House Advantage of the bet.

Hopefully you wouldn't use your play coupons on such a horrible bet. :) But, the assertion is valid. At a fair game, FP and MP are the same, however as house advantage goes up, the FP becomes more valuable. Although, I will contend that at a reasonable bet, such as Baccarat Banker or Blackjack, the house edge is so low as to make them basically identical.

Quote: konceptum

Hopefully you wouldn't use your play coupons on such a horrible bet. :) But, the assertion is valid. At a fair game, FP and MP are the same, however as house advantage goes up, the FP becomes more valuable. Although, I will contend that at a reasonable bet, such as Baccarat Banker or Blackjack, the house edge is so low as to make them basically identical.

I agree. Academically, OP and his friend could each be right under different circumstances. But realistically, OP is correct.

Quote:

He says, in terms of value to the player, the Free Play is worth twice as much as the Match Play. I say the difference is nominal