gajirikun: thanks david, here comes promotion C

[gajirikun]

dear david,

thank you for you easy to understand but through explanation on this topic.

now,let me add that promotion B chip is not a "match play" chip so you can bet this chip alone.
do you still want to bet promotion B chip on player if you can not combine it with promotion A?

and there is promotion C:

just like promotion B chip, you receive promotion C chip when you buy in $1000. but unlike promotion B, you get to keep promotion C chip if you win. it is taken away only when you lose.
how much is promotion C chip really worth?

thank you again for your expertises.

best regards,

gajirikun

[David Spence]

do you still want to bet promotion B chip on player if you can not combine it with promotion A?

If you cannot combine A and B, bet B on Player.

and there is promotion C:
just like promotion B chip, you receive promotion C chip when you buy in $1000. but unlike promotion B, you get to keep promotion C chip if you win. it is taken away only when you lose.
how much is promotion C chip really worth?

The value of a chip that is kept on wins is the sum of an infinite series (vaguely reminiscent of the money multiplier in economics). For a game in which the chance of winning is close to 50%, the value of your "keep on wins" chip is approximately double that of a standard funny money chip. So Promotion C is worth approximately 2*$48.15 = $96.30 if you bet on Banker.

Why Banker instead of Player in this case? Well, I admit that it's just a guess. But for a chip that's kept on wins, you'd prefer making bets that have a greater chance of winning a lower payoff to ones that have a smaller chances of winning a larger payoff (assuming equal, single bet e.v.s for both bets). In Baccarat, Banker wins more often than Player, but pays less (.95 to 1), so my guess is that Banker is a better bet for Promotion C.

David

[OldCootFromVA]

I get a much lower value. Now, I realize you used the word "approximately," but I think the diff is bigger than that.

I reckon it as 0.4815 + 0.4815^2 + 0.4815^3 + ... + 0.4815^infinity, which yields ~0.928639.

Multiply that by 0.95 and you get 0.88221, which is rather lower that 0.9630.

[David Spence]

> I get a much lower value. Now, I realize you used the
> word "approximately," but I think the diff
> is bigger than that.

> I reckon it as 0.4815 + 0.4815^2 + 0.4815^3 + ... +
> 0.4815^infinity, which yields ~0.928639.

> Multiply that by 0.95 and you get 0.88221, which is
> rather lower that 0.9630.

Why use .4815 as the ratio between terms? The chip is only relinquished on a loss, so the probability of being able to win with it an any particular hand equals the probability of winning or TYING on all previous hands, times the probability of winning the current hand. The total value of the $100 Promotion C chip is thus given by

[prob(win1) + prob((win1 or tie1) and win2) + prob((win1 or tie1) and (win2 or tie2) and win3) + ...] * $95

= .4586 + .5538 * .4586 + .5538^2 * .4586 + ... * $95
= .4586 / (1 - .5538) * .$95
= 1.0278 * $95
= $97.64

This is in fairly close agreement with the initial, rough estimate of $96.30.

[David Spence]

Correction: "But for a chip that's kept on wins, you'd prefer making bets that have a greater chance of winning a lower payoff to ones that have a smaller chances of winning a larger payoff..." is utter nonsense. For a negative expectation game, you generally want to make as few bets as possible (all else being equal), since each bet has an expected loss.

It is still better to bet Promotion C on Banker than on Player, with the value that I reported earlier, but that's simply because the Banker bet has a greater, single-bet e.v. than Player. So, in a nutshell, right answer, wrong reason :-)

David