Casino War Odds

Quote: russ451

Casino War online pays 10 to 1 for a tie and the bet range is $1 to $250.

Are the real casino rules the same?

Also, how often would one hit a streak of 40, 45, 50, 55 or 60 hands without a tie?

I have no idea how to figure this out.

Thanks,

Russ

Quote: russ451

Also, how often would one hit a streak of 40, 45, 50, 55 or 60 hands without a tie?

I have no idea how to figure this out.

Quote: russ451

Thanks for the reply,

I am playing War on an online casino which says it uses six decks and reshuffles after every hand.

So, if I dealt the first card, then dealt every other card one at a time I would match 23 times and not match 288, which would be the same for every hand.

I don't know how to figure a streak.

Quote: russ451

Also, years ago I heard a "Bet you can't lose" that said in a shuffled single deck if you dealt the cards one at a time there would be at least one pair, and usually two or three. They gave the math, but it was beyond me.

Quote: mustangsally

*****
I think just dealing 12 or 13 cards would be more fun
and faster too

the math is still difficult without computer help

I simulated it instead(for now)

shuffle and deal 12 cards
probability of no 2 in a row same rank about
[1] 0.508

Quote: LuckyPhow

The [1] suggests to me you may be doing your simulation(s) in R, as that is often how it reports output. If so, can you please share your code (for the R neophytes, such as myself)?

If not in R, then how simulated? (Curious minds want to know learn.)

Many thanx.

> V = 4 # number of values per rank
> R = 13 # number of ranks in deck
> # V*R = # of total cards in deck
> C = 13 # last card to check for a run of 2
> F = 2 # 1st card to check for a run of 2
> 
> check_deck <-function(deck){
+   for(i in F:C){
+     if(deck == deck[i-1]){
+       return(0)
+     }
+   }
+   return(1)
+ }
> 
> N = 10000000   # number of sims
> count = 0 
> for(i in 1:N){
+   d = sample(rep(1:R,V))  
+   count = count + check_deck(d)
+ }
> 
> p = count/N
> p # probability of NO 2 run
[1] 0.478026
> 1-p # probability of at least one 2 run
[1] 0.521974
> 
> ############################
> V = 4 # number of values per rank
> R = 13 # number of ranks in deck
> # V*R = # of total cards in deck
> C = 12 # last card to check for a run of 2
> F = 2 # 1st card to check for a run of 2
> 
> check_deck <-function(deck){
+   for(i in F:C){
+     if(deck == deck[i-1]){
+       return(0)
+     }
+   }
+   return(1)
+ }
> 
> N = 10000000   # number of sims
> count = 0 
> for(i in 1:N){
+   d = sample(rep(1:R,V))  
+   count = count + check_deck(d)
+ }
> 
> p = count/N
> p # probability of NO 2 run
[1] 0.5081397
> 1-p # probability of at least one 2 run
[1] 0.4918603
>