- #1

bernd

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- TL;DR Summary
- baccarat odds calculations, weighing results on their likeliness or not?

Hello, this question isnt really much about calculation but rather which view point is more correct.

See, in a gambling game called Baccarat a game is played where a player A ("player") and a player B ("bank") draw cards according to a fixed ruleset from a given card pot.

First A and B both draw 2 card.

depending on A's cards, he might draw a third card or not.

Depending on that, B might also draw a third card or not.

The ruels are complicated.

But in the end, the final game situation is 4-6 cards.

Now I went ahead (in a java Program) and first calculated all possible end situations, by first building all possible sixtuples (where the slot for the respectively third card is set to -1 if no such third card was drawn. )

Then I use the super complicated rule set and eleminate sixtuples that are impossible to achieve.

so I got a list of legit endgame scenarios.

now for each such scenario e, I can first calculate the winner (just add A's cards togehter modulo 10, do same for Bs cards and compare.)

And, more important, I can calculate the odds for that scenario happening and by using all thos odds, calculate who wins more often.

1. How I initially did it:

for each scenario, I calculated the odds of it with happening by simple stochastic rules with putting bakc and such.

Like if you first draw a card from a pool of 52 cards, then draw another card from a pool of 51 cards, etc.

you get the drill. obviously keping in mind that some cards jsut appear more often in the pool and other details.

so I this way get odds for each scenario.

and I go through the list, add up all the odds of scenarios where A wins, all odds of scenarios where B wins.

and all odds for scenarios where its a draw.

this way I get 3 odds for 3 different outcomes.

however this result doesnt fit in what is plastered all over the internet.

internet says, player and bank win in about 45% of cases.

however I get odds of more lik 35%.

so big descrepancy.2. now how some other person I spoke to did it:

list of legit endgames as usual.

he goes also through the list, looks for each one whos winner and jsut counts them up depending on winner.

so, like you would do on votes "1 vote for A, 1 vote for B, another vote for A, etc."

so, basically he weights all outcomes the same, ignoring how likely each one of them is to happen in reality.

so he jsut counts hopw many games end in A winning, how many in B, how many in a draw.

dvidie by total naumber of games.

bam, got the 3 outcomes that are all over the internet.

I tried to simulate this too, by jsut using "odds" of fixed 1 for each scenario and in the end dividing by total number of games.

And yep, I get otucomes of 46% for A, 44,5 for B and 10% for draw.

still off by like .5% each from the ideal result,(which might be due to programming issues, rounding and such)

but basically, confirmed his methods does get the desired result.

now unintendedly long story short:

I base my calculations on how likely each end result is to actually happening, therefor obviously weighing super unlikely events less than others.

friends jsut counts how many games gives each winner, basically weighing all endresults equally likely, in a way.

friends endresults are wha<t the internet says is right.

I think mine is actually more right as it incorporates how less or more likely an event is to happen.

Who is "in the right" here?

I shpould mention that this whole calculation is important to me as I want to do some expectancy value calculations for baccarat

where i then basically want to go

exp value for A winning=odds for A winning * payout for A winning - odds of A not winning * payout in case A doesnt win

same for B and draw.

Then just compare which of the 3 outcomes I would be best of betting on (yeah, internet tells me that already too but I want to derive it on my own!)

So I kind of want my calculations to be realsitic in the way that obviously the unlikeliness of an event should be reflected in the final determiantion on what to bet on! :-)

See, in a gambling game called Baccarat a game is played where a player A ("player") and a player B ("bank") draw cards according to a fixed ruleset from a given card pot.

First A and B both draw 2 card.

depending on A's cards, he might draw a third card or not.

Depending on that, B might also draw a third card or not.

The ruels are complicated.

But in the end, the final game situation is 4-6 cards.

Now I went ahead (in a java Program) and first calculated all possible end situations, by first building all possible sixtuples (where the slot for the respectively third card is set to -1 if no such third card was drawn. )

Then I use the super complicated rule set and eleminate sixtuples that are impossible to achieve.

so I got a list of legit endgame scenarios.

now for each such scenario e, I can first calculate the winner (just add A's cards togehter modulo 10, do same for Bs cards and compare.)

And, more important, I can calculate the odds for that scenario happening and by using all thos odds, calculate who wins more often.

1. How I initially did it:

for each scenario, I calculated the odds of it with happening by simple stochastic rules with putting bakc and such.

Like if you first draw a card from a pool of 52 cards, then draw another card from a pool of 51 cards, etc.

you get the drill. obviously keping in mind that some cards jsut appear more often in the pool and other details.

so I this way get odds for each scenario.

and I go through the list, add up all the odds of scenarios where A wins, all odds of scenarios where B wins.

and all odds for scenarios where its a draw.

this way I get 3 odds for 3 different outcomes.

however this result doesnt fit in what is plastered all over the internet.

internet says, player and bank win in about 45% of cases.

however I get odds of more lik 35%.

so big descrepancy.2. now how some other person I spoke to did it:

list of legit endgames as usual.

he goes also through the list, looks for each one whos winner and jsut counts them up depending on winner.

so, like you would do on votes "1 vote for A, 1 vote for B, another vote for A, etc."

so, basically he weights all outcomes the same, ignoring how likely each one of them is to happen in reality.

so he jsut counts hopw many games end in A winning, how many in B, how many in a draw.

dvidie by total naumber of games.

bam, got the 3 outcomes that are all over the internet.

I tried to simulate this too, by jsut using "odds" of fixed 1 for each scenario and in the end dividing by total number of games.

And yep, I get otucomes of 46% for A, 44,5 for B and 10% for draw.

still off by like .5% each from the ideal result,(which might be due to programming issues, rounding and such)

but basically, confirmed his methods does get the desired result.

now unintendedly long story short:

I base my calculations on how likely each end result is to actually happening, therefor obviously weighing super unlikely events less than others.

friends jsut counts how many games gives each winner, basically weighing all endresults equally likely, in a way.

friends endresults are wha<t the internet says is right.

I think mine is actually more right as it incorporates how less or more likely an event is to happen.

Who is "in the right" here?

I shpould mention that this whole calculation is important to me as I want to do some expectancy value calculations for baccarat

where i then basically want to go

exp value for A winning=odds for A winning * payout for A winning - odds of A not winning * payout in case A doesnt win

same for B and draw.

Then just compare which of the 3 outcomes I would be best of betting on (yeah, internet tells me that already too but I want to derive it on my own!)

So I kind of want my calculations to be realsitic in the way that obviously the unlikeliness of an event should be reflected in the final determiantion on what to bet on! :-)